grade 2 mathematics curriculum guide · to navigate the curriculum guide, click on the hyperlink...

GRADE 2 MATHEMATICS

CURRICULUM GUIDE

Loudoun County Public Schools 2014-2015

Overview, Scope and Sequence, Unit Summaries, The First 20 Days Classroom Routines, Curriculum Framework, Learning Progressions

(additional attachments: Intervention Ideas, NCSM Great Tasks SOL alignment, Math Literature Connections)

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes

excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional

consensus of Loudoun’s teachers concerning the implementation of these standards. This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.

NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE

The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources.

To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource.

If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

LCPS Grade 2 Mathematics Curriculum Guide 2014-2015

Dates of LCPS Quarters

2014 – 2015 School Calendar

Starts Ends

First Quarter September 2 October 31

Second Quarter November 5 January 23

Third Quarter January 27 March 27

Fourth Quarter April 7 June 16

Quarter 1 Quarter 2 Quarter 3 Quarter 4

AUGUST

S M T W R F S

1 2

3 4 5 6 7 8 9

10 11 12 TI TI NH 16

17 NH NH SD SD P 23

24 CS CS CS P P 30

31

SEPTEMBER

S M T W R F S

H F 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30

OCTOBER

S M T W R F S

1 2 3 4

5 6 7 8 9 10 11

12 H 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31

NOVEMBER

S M T W R F S

1

2 P P 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 H H H 29

30

DECEMBER

S M T W R F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 H H H H H 27

28 H H H

JANUARY

S M T W R F S

H H 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 H 20 21 22 23 24

25 MP 27 28 29 30 31

JANUARY

S M T W R F S

H H 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 H 20 21 22 23 24

25 MP 27 28 29 30 31

FEBRUARY

S M T W R F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 H 17 18 19 20 21

22 23 24 25 26 27 28

MARCH

S M T W R F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 H H

APRIL

S M T W R F S

H H H 4

5 P 7 8 9 10 11

APRIL

S M T W R F S

H H H 4

5 P 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30

MAY

S M T W R F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 H 26 27 28 29 30

31

JUNE

S M T W R F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 L P P 19 20

21 22 23 24 25 26 27

28 29 30

P = Teacher Workday/Planning Day H = Holiday/ No School F = First Day of School TI = Teacher Institute for new professionals NH = New Hire Workday SD = In School Staff Development days CS = County Wide Staff Development Days


Grade 2 Nine Weeks Overview 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS 2.1a Place Value 2.12 Time 2.13 Calendar 2.14 Temperature 2.17 Data Unit 2-Extending Place Value 2.2 Ordinal Positions & Numbers 2.1 Place Value, Round, Compare 2.4 Counting Forward & Backward, Even & Odd 2.20 Patterns Unit 3-Computational Fluency 2.5 Addition and Subtraction Facts 2.9 Related Addition/Subtraction Facts 2.20 Patterns

Unit 1-Classroom Routines: NUMBER TALKS 2.1abc Place Value, Round, Compare 2.4 Count Forward & Backward, Even & Odd 2.5 Addition and Subtraction Facts 2.12 Time Optional SOL to continue: 2.13 Calendar, 2.14 Temp., 2.17 Data Unit 4-Applying Place Value to Computation/Problem Solving 2.5 Addition and Subtraction Facts 2.6 Estimate & Find Sums 2.7 Estimate & Find Differences 2.21 Complete Number Sentences/Create Story Problems 2.22 Equality Unit 5-Probability & Data 2.17 Construct Graphs 2.18 Probability & Outcomes

Unit 1-Classroom Routines: NUMBER TALKS 2.1abc Place Value, Round, Compare 2.4 Count Forward & Backward, Even & Odd 2.5 Addition and Subtraction Facts 2.6 Estimate & Find Sums 2.7 Estimate & Find Differences Optional SOL to continue: 2.12 Time, 2.13 Calendar, 2.14 Temperature, 2.17 Data Unit 6-Data & Problem Solving 2.8 One- and Two-Step Problems Using Data 2.19 Analyze Data Unit 7-Time & Temperature 2.12 Time 2.13 Calendar 2.14 Temperature 2.20 Patterns Unit 8-Geometry & Fractions 2.15 Symmetry 2.16 Compare Plane & Solid Geometric Figures 2.3 Fractions 2.20 Patterns

Unit 1-Classroom Routines: NUMBER TALKS 2.1abc Place Value, Round, Compare 2.4 Count Forward & Backward, Even & Odd 2.5 Addition and Subtraction Facts 2.6 Estimate & Find Sums 2.7 Estimate & Find Differences Optional SOL to continue: 2.12 Time, 2.13 Calendar, 2.14 Temperature, 2.17 Data Unit 9-Measuring My World 2.11 Estimate & Measure Unit 10-Skip Counting & Money 2.10 Money 2.20 Patterns

43 days 44 days 43 days 50 days


Grade 2 Scope & Sequence

Quarter 1: 43 days

Days UNIT Standard Content Strand Topic All year Unit 1-Classroom

Routines “The First 20 Days Classroom Routines”

and NUMBER TALKS, Place Value, Time, Calendar, Temperature, Data

25 Unit 2-Extending Place Value

2.2 Number and Number Sense

Ordinal Positions and Numbers


Place Value, Round, Compare


Counting Forward and Backward, Even and Odd

2.20 Patterns, Functions, and Algebra

Patterns

15 Unit 3-Computational Fluency

2.5 Computation and Estimation

Addition and Subtraction Facts


Related Addition/Subtraction Facts


Patterns

3 Assessment, Review, and Intervention


Quarter 2: 44 days


Routines NUMBER TALKS, Place Value, Time, Calendar, Temperature, Data

21 Unit 4-Applying Place Value to Computation/

Problem Solving


Addition and Subtraction Facts


Estimate and Find Sums


Estimate and Find Differences


Complete Number Sentences/Create Story Problems


Equality

19 Unit 5-Probability & Data 2.17 Probability and Statistics

Construct Graphs

2.18 Probability and Statistics

Probability and Outcomes



Quarter 3: 43 days



10 Unit 6-Data & Problem Solving


One- and Two-Step Problems Using Data

2.19 Probability and Statistics

Analyze Data

10 Unit 7-Time & Temperature

2.12 Measurement Time

2.13 Measurement Calendar

2.14 Measurement Temperature

20 Unit 8-Geometry & Fractions

2.15 Geometry Symmetry

2.16 Geometry Compare Plane and Solid Geometric Figures


Fractions


Patterns



Quarter 4: 50 days



25 Unit 9-Measuring My World

2.11 Measurement Estimate and Measure

15 Unit 10-Skip Counting & Money

2.10 Measurement Money


Patterns


LCPS MATH Unit Summary Grade 2 2014-15

Unit: 1 Quarters 1-4

Classroom Routines

VDOE Standards of Learning:

1st quarter: The First 20 Days Classroom Routines Quarter 1

2.12 The student will tell and write time to the nearest five minutes, using analog and digital clocks. 2.13 The student will a) determine past and future days of the week; and b) identify specific days and dates on a given calendar 2.14 The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees. 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs. 2.1a The student will a) read, write, and identify the place value of each digit in a three-digit numeral, using numeration models.

Quarter 2 Teachers may use their discretion to continue SOL 2.13, 2.14, 2.17 based on student needs. Please continue SOL 2.12, 2.1a, and add the following to your daily routines: 2.4 The student will a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10 b) count backward by tens from 100 c) recognize odd and even numbers. 2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts. 2.1 The students will b) round two-digit numbers to the nearest ten c) compare two whole numbers between 0 and 999, using symbols (>, <, or =)

Quarter 3 Teachers may use their discretion to continue SOL 2.13, 2.14, 2.17, 2.12 based on student needs. Please continue SOLs 2.1, 2.4, 2.5 and add the following to your daily routines: 2.6 The student, given two whole numbers whose sum is 99 or less, will a) estimate the sum b) find the sum, using various methods of calculation 2.7 The student, given two whole numbers, each of which is 99 or less, will a) estimate the difference b) find the difference, using various methods of calculation

Quarter 4 Teachers may use their discretion to continue SOL 2.13, 2.14, 2.17, 2.12 based on student needs. Please continue SOL 2.1, 2.4, 2.5, 2.6, 2.7.

VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations

Learning Targets:

I can communicate (show, tell, and write) the time to the nearest five minutes, using analog and digital clocks.

I can use a calendar to determine specific days and dates in the past, present, and in the future.

I can use a Celsius and Fahrenheit thermometer to tell temperature to the nearest 10 degrees.


I can collect and organize data to construct picture graphs, pictographs, and bar graphs. I can read the information presented on these data graphs

(representations).

The student will identify the place value and value of each digit in a three digit number, round two-digit numbers to tens, and compare whole numbers (0-999) using symbols.

I can count forward by twos, fives, and tens to 100 starting at various multiples of 2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens. I can count backwards by tens from 100 starting at different numbers, including

I can use objects to determine whether a number is odd or even. I can explain why the number is odd or even.

I can recall and write addition facts, with sums to 20 or less, and the corresponding subtraction facts (written either horizontally or vertically).

I can estimate and find sums of addends (99 or less) using a variety of strategies and tools.

I can estimate and find differences of two numbers (99 or less) using a variety of strategies and tools.

Big Ideas Essential Questions

Classroom routines (about 10 minutes each day)

can be used to introduce, support, and extend

topics throughout the yearly curriculum in order to

provide students with regular practice in important

mathematical ideas.

What strategy would you use to determine time to the nearest five minutes, using analog and digital clocks?

How can you demonstrate an understanding of counting by fives to predict five minute intervals when telling time to the nearest five minutes?

How does a calendar measure time?

How does a calendar represent yesterday, today, and tomorrow?

How can you determine the date of the third Tuesday in any given month?

What is data?

How is data collected?

How is data represented?

What is the relationship of ones, tens, and hundreds?

How are numbers written to show how many hundreds, tens, and ones are in the number?

Why would you round a number? (Rounding gives a close, easy-to-use number to use when an exact number is not needed for the situation at hand.)

What is a pattern?

What are different ways numbers can be grouped for skip counting?

How can the same quantity be represented in words, numerals, and objects?

Why would you use estimation skills in situations? What is the structure of an addition problem? A

subtraction problem?


Prerequisite Skills Vocabulary

VDOE Vertical Alignment document K-3 1.8 The student will tell time to half‐hour 1.11 The student will use calendar language appropriately 1.1 The student will a) count/write numbers to 100; b) group up to 100 objects into tens/ones and write numeral – place value 1.2 The student will count by 1/2/5/10 to 100 and back by 1 from 30 1.14 The student will investigate/ID/describe forms of data collection using tables/picture graphs/object graphs 1.5 The students will recall add/sub facts w/ sums to 18 or less

VDOE Vocabulary Word Wall Cards 2.13--yesterday, today, tomorrow, names of months, names of days 2.14--thermometer, Fahrenheit, Celsius, temperature 2.17--data, picture graph, tally mark, table, picture graph, bar graph, columns, rows 2.1--digit, place value, ones, tens, hundreds, equal, greater than, less than 2.4--digit, sequence, skip count, pair, even, odd 2.5--add, subtract, sum, difference 2.6—addition, add, addend, sum, estimate, plus 2.7--subtraction, difference, subtract, estimate, minus, subtrahend, minuend

Achievement Criteria How to Assess Achievement

“The content of the mathematics standards is intended to support the following five process goals for students:

• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and

interpret practical situations.” -2009 Mathematics Standards of Learning

Click here for a brief audio powerpoint slide with more information about the Process Goals

Sample Math Tasks are available in VISION:

Search: LCPS-Math: K-12 Math Tasks

Enrollment key: mathisfun

http://loudounvision.net/

NCSM Great Tasks (available in all LCPS Elementary Schools—click link)

Classroom Routines

1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Example: http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf Number Talks sample flipcharts available on the Elementary Math Resources VISION site INVESTIGATIONS:

Mathematical Thinking in Grade 2

Investigation 2, Session 1: How Many Days Have We Been in School?

Today’s Number p. 124

How Many Pockets? P. 127

Time and Time Again p. 131

Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2011/opening_session/2009sol_vertical_articulation_by_topic_k-3_9-15-11.pdf

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_2.pdf

https://www.dropbox.com/s/ve7sxlqo2ps6cyj/Process%20Goals%20audio%20slide.pptx



http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf



Unit: 2 Quarter 1

Extending Place Value


2.2 The student will a) identify ordinal positions first through twentieth, using an ordered set of objects; and b) write the ordinal numbers. 2.1 a, b, c The student will a) read, write, and identify the place value of each digit in a 3-digit numeral, using numeration models; b) round two-digit numbers to the nearest ten, and c) compare two whole numbers between 0 and 999, using symbols (<, >, or =) and words (less than, greater than, or equal to). 2.4 The student will a) count forward by 2, 5s, 10s to 100, starting at various multiples of 2, 5, 10. b)count backward by 10s from 100; and c) recognize even and odd numbers. 2.20 The student will identify, create, and extend a wide variety of patterns.


Learning Targets:

I can communicate (verbally and in writing) the ordinal positions for each object in a set of 20 objects that are in order (i.e. left-to-right, right-to-left, top-to-bottom, and bottom-to-top).

I can identify the place value and value of each digit in a three digit number, round two-digit numbers to tens, and compare whole numbers (0-999) using symbols.

I can count forward by twos, fives, and tens to 100 starting at various multiples of 2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens.

I can count backwards by tens from 100 starting at different numbers, including 1.



Understand ordinal position identification.

Place value is constructed around the Base 10 system.

Using a variety of models (base ten, Digiblocks, pictorial representations) helps students understand the magnitude of numbers.

A variety of strategies to compare and round two or three digit numbers should be investigated, including number lines.

Demonstrate understanding of skip counting patterns, forwards and backwards.

Identify and model even and odd numbers (even numbers are modeled by pairs and odd numbers have one left over when grouped by pairs).

What are the ordinal number words for the 20

objects pictured?

What is the value of each digit in a three digit

number?

What strategies can you use to round to the

nearest ten?

Which symbol, (<, >, or =), would you use to

compare two given numbers?

What are the missing numbers in the pattern?

How can you tell the difference between an odd

and even number?

How can you model odd and even numbers?

Are there an odd or even number of objects?

How do you know?



VDOE Vertical Alignment document K-3 1.1 The student will a) count/write numbers to 100; b) group up to 100 objects into tens/ones and write numeral ‐ place value 1.2 The student will count by 1/2/5/10 to 100 and back by 1 from 30

VDOE Vocabulary Word Wall Cards 2.2 2.1 2.4 ordinal number digit sequence horizontal place value skip count vertical ones even ordinal position terms tens odd (first through twentieth) hundreds greater than less than

equal to







Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun http://loudounvision.net/

NCSM Great Tasks

(available in all LCPS Elementary Schools—click link)

Differentiation Resources

• Have students use large grid paper with large squares on which to draw their objects in ordinal positions.

• Allow students who have difficulty with drawing to use stamps or stickers.

• If students are struggling with going all the way to the twentieth position, break the ordinal positions up into smaller groups, like first through tenth and then eleventh through twentieth.

• Tape ordinal position cards to the floor. Assign ordinal positions to the students as their line position for the day, and have them stand on the appropriate cards. • Use grid paper to help students compare place values vertically rather than horizontally.

• Have students use a blank number line and make decisions about where to place numbers on it. By placing the numbers being compared to each other on the number line, students are able to see instantly which number is larger and which is smaller by looking at their position on the line. Students may choose to add as many other numbers to the line as needed to make a good comparison.

• Use green and red highlighters to color the first number

Investigations: Coins, Coupons, and Combinations: Investigation 1: “10’s and Doubles”: Sessions 4, 5, 6, Investigation 2: Grouping by 2’s, 5’s, and 10’s Investigation 4: One Hundred Putting Together and Taking Apart Investigation 2: Working with 100 ESS Lessons: 2.2--Ordinals 2.1--Race to 100 2.1--Rounding On the 100 Chart 2.1--Three-Digit Place Value 2.4--Guess My Pattern 2.4--Even or Odd? Brain Pop Jr: 2.1--One Hundred 2.1--Place Value 2.1--Rounding 2.1--Comparing Numbers >, < 2.4--Even and Odd






http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php

http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-2ab.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-1a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-1b.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-1c.pdf



http://www.brainpopjr.com/math/numbersense/onehundred/

http://www.brainpopjr.com/math/numbersense/placevalue/

http://www.brainpopjr.com/math/numbersense/rounding/

http://www.brainpopjr.com/math/numbersense/comparingnumbers/

http://www.brainpopjr.com/math/numbersense/evenandodd/


in the comparison green and the second number red. This visual suggests to students that green is where you start and red is where you stop or finish.

• Create a card with the expression “is greater than” written on one side and the expression “is less than” on the other. Have students flip the card as needed to complete the comparison. Have them take turns saying the comparison. • Allow students to use calculators to help them confirm their calculations.

• Use a poster-sized hundred chart and larger manipulatives for students with fine motor challenges. • Have students explore adding numbers together to discover the results: odd + odd = even, even + even = even, odd + even = odd, even + odd = odd.

• Have student explore subtracting numbers to discover the results: odd – odd = even, even – even = even, odd – even = odd, even – odd = odd.

Intervention Ideas (available in all LCPS Elementary Schools—click link)

ELL Model Performance Indicators

(click to link)

Safari Montage: 2.2, 2.1, 2.4--Number Sense 2.1--Cyberbase: Number Sense: And They Counted Happily Ever After 2.4--Numbertime Numbers to 100, Patterns of 5 2.4--Numbertime Numbers to 100, Patterns of 10 2.4--Number and Numbers to 100, Counting by 10 2.4--Emily’s First 100 Days of School Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://safari.lcps.org/SAFARI/montage/play.php?keyindex=61010&location=local&filetypeid=54









Unit: 3 Quarter 1

Computational Fluency


2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts. 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction. 2.20 The student will identify, create, and extend a wide variety of patterns. (Geometric and growing patterns are addressed in quarter 2). *2.20 is to be connected to 2.5 and 2.9 (see Big Ideas)


Learning Targets:

I can recall and write addition facts, with sums to 20 or less, and the corresponding subtraction facts (written either horizontally or vertically). (2.5)

I can demonstrate how addition and subtraction facts are related using models/structures and describe their relationship. (2.9)

I can identify, create, and apply a wide variety of patterns. (2.20)


Relating addition to subtraction by exploring patterns in fact families:

5 + 6 = 11, 6 + 5 = 11 11 – 5 = 6, 11 – 6 = 5

Activities such as Today’s Number helps students to explore number patterns in sums and differences For example: If Today’s Number is 12, students may observe patterns in sums:

0 + 12 = 12 1 + 11 = 12 2 + 10 = 12 3 + 9 = 12, etc.

Gaining facility in manipulating whole numbers to add and subtract and in understanding the effects of the operations on whole numbers

Recognizing whether numerical solutions are reasonable

Developing proficiency with basic addition and subtraction and related facts

What are the addition facts of sums up to twenty?

What is the corresponding subtraction fact to each addition fact?

What are the related facts for a given addition or subtraction fact? (e.g., given 3 + 4 = 7, write 7 – 4 = 3 and 7 – 3 = 4).

What is the relationship between an addition and subtraction problem of a related fact?

What patterns can you identify in related facts?


VDOE Vertical Alignment document K-3 1.5 recall add/sub facts w/ sums to 18 or less 1.17 recognize/describe/extend/create growing/repeating patterns

VDOE Vocabulary Word Wall Cards 2.5 2.9 2.20 add related fact patterns addition fact family core/unit plus inverse operation sum subtract subtraction minus difference















• Allow students to use a calculator to check their sums.

• To generate two-digit numbers, have students use 10-sided number cubes instead of digit cards. • For an extra challenge, pose the following problem: You have a bag with five cubes in it. Some of the cubes are red, and some are blue. Show three of the possible combinations of red and blue cubes that could be in the bag, and list all the related facts for each combination. • Have students use linking cubes on an interactive whiteboard to model operations.

• Provide a template for students to use to fill in the related facts (e.g., ___ + ___ = ___ ). Lines of the template may be color-coded like the examples in the activity.



(click to link)

Investigations: Coins, Coupons, and Combinations Investigation 3: Introducing Addition and Subtraction Situations Putting Together and Taking Apart Investigation 1: Combining and Separating ESS Lessons: 2.5 Four In A Row Addition 2.9 Related Facts 2.20 Exercising Patterns BrainPop Jr.: 2.5 Basic Adding 2.5 Counting On 2.5 Basic Subtraction 2.5 Doubles Safari Montage: 2.5 Numbertime Addition and Subtraction: Patterns of Addition 2.5 Numbertime Addition and Subtraction: Plus and Minus 2.5 Numbertime Addition and Subtraction: Difference 2.5 Numbertime Numbers to 100: Counting On and Back 2.5 Subtraction 2.20 Cyberchase: Patterns in Music: Out of Sync Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-5.pdf



http://www.brainpopjr.com/math/additionandsubtraction/basicadding/

http://www.brainpopjr.com/math/additionandsubtraction/countingon/

http://www.brainpopjr.com/math/additionandsubtraction/basicsubtraction/

http://www.brainpopjr.com/math/additionandsubtraction/doubles/











Unit: 4 Quarter 2

Applying Place Value to Computation/Problem Solving


2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts. 2.6 The student given two whole numbers whose sum is 99 or less, will a) estimate the sum; and b) find the sum, using various methods of calculation. 2.7 The student, given two whole numbers, each of which is 99 or less, will a) estimate the difference; and b) find the difference using various methods of calculation. 2.21 The student will solve problems by completing numerical sentences involving the basic facts for addition and subtraction. The student will create story problems, using the numerical sentences. 2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ≠ indicates that quantities are not equivalent.


Learning Targets:



I can use mathematical models to represent basic addition and subtraction number sentences and create story problems for those sentences.

I can demonstrate that some number sentences are balanced (=) and some are not balanced (≠).


A variety of contexts are necessary for children to develop an understanding of the meanings of the operations such as addition and subtraction. These contexts often arise from real-life experiences in which they are simply joining sets, taking away or separating from a set, or comparing sets.

Although young children first compute using objects and manipulatives, they gradually shift to performing computations mentally or using paper and pencil to record their thinking. Therefore, computation and estimation instruction in the early grades revolves around modeling, discussing, and recording a variety of problem situations. This helps students transition from the concrete to the representation to the symbolic in order to develop meaning for the operations.

Developing and using strategies and algorithms to solve problems and choosing an appropriate method for the situation (strategies focusing on the place value of the numbers should be reinforced, for ex: 23 + 38 = 20 + 3 + 30 + 8 = 50 + 11 = 61)

What is the sum of the two whole numbers?

How can estimating the sum be helpful in finding the sum of the problem?

How is regrouping in subtraction similar to regrouping in addition?

Why do you subtract the smaller number from the larger number instead of the other way around?

How can an unknown number be represented in a number sentence?

How are addition and subtraction related?

Can you explain how you know whether two quantities are equal or not equal?

What symbol would you use to represent whether two sides of a number sentence are equivalent or not?

How can you justify that your answer is reasonable?



VDOE Vertical Alignment document K-3

1.4 The students will a) select order of magnitude from three quantities; b) explain reasonableness 1.18 The students will demonstrate equality using equal sign

VDOE Vocabulary Word Wall Cards 2.6 2.7 2.21 2.22 add difference addition equal addend minuend addend equality sum subtract subtraction equation estimate subtrahend subtrahend equivalent pattern inequality function nonequivalent












• Allow students to use calculators to check their solutions for each addition problem created.

• Have students use place value mats to keep tens and ones organized.

• Allow students to use grid paper to help them line up vertical columns. • Have each student write an addition/subtraction word problem and exchange it with a partner. • Allow students to use calculators to check their solutions for each subtraction problem. A large calculator may be displayed for the whole class to see.

• Allow students who have difficulty drawing to use base-10 stamps, stickers, or cutouts when creating pictorial representations. • Provide enlarged copies of the number line to students who have difficulty using a smaller one.

• Have students use a 10-sided number cube instead of digit cards to create two-digit numbers.

• Have students highlight the tens on the number line to draw attention to them.

• Write in the numbers for each tick mark on the number line.

Investigations: Putting Together and Taking Apart: Investigation 3: Finding the Missing Part Investigation 4: Adding up to 100 Investigation 5: Addition and Subtraction Strategies ESS Lessons: 2.6 Target 100: Computation and Estimation 2.7 What’s the Difference? 2.7 Hopping on the Numberline 2.21 The FUNction Machine 2.22 The Balancing Act Brain Pop Jr.: Adding and Subtracting Tens Adding With Regrouping Subtracting Without Regrouping Safari Montage: 2.6 Numbertime: Addition and Subtraction: Addition with Partrition 2.6 Numbertime: Addition and Subtraction: Patterns in Addition








http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-7ab_2.pdf




http://www.brainpopjr.com/math/additionandsubtraction/addingandsubtractingtens/

http://www.brainpopjr.com/math/additionandsubtraction/addingwithregrouping/

http://www.brainpopjr.com/math/additionandsubtraction/subtractingwithoutregrouping/






• Let students discover, record, and explain the patterns, using a hundred chart or a number line to record the IN and OUT numbers.

• Allow students struggling to understand equal or not equal to connect the cubes on each side of the balance and compare them to each other, using one-to-one correspondence.



(click to link)

2.6 Numbertime Addition and Subtraction, Two-Step Addition 2.7 Numbertime: Addition and Subtraction, Subtracting One Number from Another 2.7 Numbertime: Addition and Subtraction, Two-Step Subtraction 2.22 Cyberchase: Equations: The Battle of the Equals Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)










Unit: 5 Quarter 2

Probability & Data


2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs. 2.18 The student will use data from experiments to predict outcomes when the experiment is repeated.


Learning Targets:

I can collect and organize data to construct picture graphs, pictographs, and bar graphs. I can read the information presented on these data graphs (representations).

I can predict the outcome of an experiment and understand the variables that factor into the outcome.


Collect and record data

Display data in a variety of graphic representations.

In an experiment, make predictions of outcomes and explain the reasoning of why the prediction was made.

Students begin to develop an understanding of the concept of chance. They experiment with spinners, two-colored counters, dice, tiles, coins, and other manipulatives to explore the possible outcomes of situations and predict results. They begin to describe the likelihood of events, using the terms impossible, unlikely, equally likely, more likely, and certain.

What is a graph used for?

What is a picture graph, pictograph and bar graph?

Why is a key important to a graph?

How does the number of items in each group effect the outcome?

How can probability help predict an outcome of an event?

How can you display the data that was collected from the experiment?

How can this data help you predict the outcome of future events?



1.14 The student will investigate/ID/describe forms of data collection using tables/picture graphs/object graphs

VDOE Vocabulary Word Wall Cards 2.17 2.18 data outcomes certain picture graph probability likely tally mark impossible pictograph unlikely bar graph equally likely axis





Sample Math Tasks are available in VISION: Search: LCPS-Math: K-12 Math Tasks

Enrollment key: mathisfun http://loudounvision.net/


NCSM Great Tasks

(available in all LCPS Elementary Schools—click link)








• Have students create graphs using a computer program, create questions for the graphs, and then play the game in a learning center. Place each graph and its questions in a baggie to keep them together. • Allow students who find small motor coloring a challenge to glue strips of colored paper cut to size onto the bars of the bar graph.

• Use more challenging increments for the pictograph key. Ask students to explain the increment that they selected. Ask whether it is appropriate to use increments of 10 when the greatest number of data collected is 7.

• Create a huge bar graph by drawing a large bar graph grid on the floor with sidewalk chalk and laying down whole sheets of construction paper to fill each bar. • Have students survey another class, using the question, “What bug are you most scared of?” Then, have them create picture graphs and/or bar graphs of the data. This data can be also be used with SOL 2.19 and analyzed based on gender, homeroom class, age, etc. • Assist students who have difficulty holding a pencil and spinning a paper clip to use real spinners, writing on them with overhead projector markers.

• Ask students to make a fair spinner and an unfair spinner with two dessert selections on each. Have them make generalizations about these spinners, using correct vocabulary.



(click to link)

Investigations: Mathematical Thinking at Grade 2 Investigation 4: Counting Session 3: Collecting Pocket Data How Many Pockets? How Many Teeth? Investigation 1: Exploring Numerical Data Investigation 2: Teeth Data Does It Walk, Crawl, or Swim Investigation 1: Sorting People and Yekttis Investigation 3: Animals in the Neighborhood ESS Lessons: 2.17 The Graphing Game Show 2.17, 2.18 You Are Bugging Me 2.17 What’s the Problem? 2.18 We Are Spinning In Second Grade! Brain Pop Jr.: 2.17 Tally Charts and Bar Graphs 2.17 Picture Graphs 2.18 Basic Probability 2.18 Probability Safari Montage: 2.17 Gathering and Graphing Data 2.17 Cyberchase: Raising the Bar 2.17 Lemonade for Sale 2.18 Cyberchase: Predicting From Data: Past Perfect Prediction 2.17, 2.18 C yberchase: Using Data: Castleblanca Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.brainpopjr.com/math/data/tallychartsandbargraphs/

http://www.brainpopjr.com/math/data/pictographs/

http://www.brainpopjr.com/math/data/basicprobability/

http://www.brainpopjr.com/math/data/probability/









Unit: 6 Quarter 3

Data & Problem Solving


2.8 The student will create and solve one- and two step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs. 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.


Learning Targets:

I can use problem solving strategies to use information from tables and graphs to solve one- and two-step addition and subtraction problems.

I can understand and use the information from a graph.


Locate and use data from a graph to solve addition and subtraction problems.

Use regrouping strategies when adding and subtracting.

Explain how the graph is representing the data and what the data means.

The focus of statistics instruction at this level is to help students develop methods of collecting, organizing, describing, displaying, and interpreting data to answer questions they have posed about themselves and their world.

What are some strategies for solving practical problems using data from simple tables, picture graphs, and bar graphs?

Can you create your own problems to enhance problem solving skills using data from simple tables, picture graphs, and bar graphs?

How do you read the key used in a graph to analyze of the displayed data?

How do you interpret data in order to analyze it?

How do you analyze data in order to answer the questions posed, make predictions, and generalizations?



1.6 The student will create/solve one‐step story/picture problems using add/sub facts w/ sums to 18 or less. 1.15 The student will interpret information displayed in a picture/object graph

VDOE Vocabulary Word Wall Cards

2.8 2.19 addition data add picture graph data pictograph difference chart picture graph table subtraction most sum least table greatest tally mark equal bar graph data pictograph bar graph one-step two-step















Allow students who have difficulty drawing to use stickers or stamps when creating pictographs or picture graphs, rather than drawing symbols.

• Provide students with pre-drawn data tables and grid paper with pre-drawn axes, as needed. • Guide students in creating headings, labels, and scale calibrations, as needed. • Distribute graphs from everyday life (e.g., from a newspaper, a soup can label, a weather report, a news article). Have students write at least one statement that describes the categories of data and the data as a whole and identifies the parts of the data that have special characteristics (greatest, least, same). Have students write questions that incorporate one-step addition or subtraction problems based on the data. Have students exchange papers and complete, explain, and then evaluate each other’s work. • Have students verbalize statements while a selected scribe records them on paper. • To add a kinesthetic element, have students hop or skip to the front to select their questions, or have students hop to the board to write answers to the questions. • Have students create graphs using a computer program, create questions for the graphs, and then play the game in a learning center. Place each graph and its questions in a baggie to keep them together.



(click to link)

IInvestigations: Mathematical Thinking for Grade 2 Investigation 5: Collecting Data About Ourselves How Many Pockets? How Many Teeth? Investigation 3: Data Projects ESS Lessons: 2.8 What’s the Problem? 2.19 The Graphing Game Show Brain Pop Jr.:

2. 8 Adding and Subtracting Tens 2.8 Adding With Regrouping

2.8 Subtracting Without Regrouping 2.19 Tally Charts and Bar Graphs

2.19 Picture Graphs

Safari Montage: 2.8 Numbertime Addition and Subtraction, Two-Step Addition 2.8 Numbertime: Addition and Subtraction, Subtracting One Number from Another 2.8 Numbertime: Addition and Subtraction, Two-Step Subtraction

2.19 Cyberchase: Bar Graphs: Raising the Bar 2.19 Gathering and Graphing Data

Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.brainpopjr.com/math/additionandsubtraction/addingandsubtractingtens/

http://www.brainpopjr.com/math/additionandsubtraction/addingwithregrouping/

http://www.brainpopjr.com/math/additionandsubtraction/subtractingwithoutregrouping/

http://www.brainpopjr.com/math/data/tallychartsandbargraphs/

http://www.brainpopjr.com/math/data/pictographs/







http://safari.lcps.org/SAFARI/montage/play.php?keyindex=80921




Unit: 7 Quarter 3

Time & Temperature


2.12 The student will tell and write time to the nearest five minutes, using analog and digital clocks. 2.13 The student will a) determine past and future days of the week; and b) identify specific days and dates on a given calendar 2.14 The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees. 2.20 The student will identify, create, and extend a wide variety of patterns.


Learning Targets:

I can communicate (show, tell, and write) the time to the nearest five minutes, using analog and digital clocks.




Time can be measured in small chunks of time: seconds, minutes, hours.

Time can be measured in big chunks of time: days, weeks, months, years.

Time of day uses analog and digital clocks.

Calendars can be used to tell bigger chunks of time.

Students should be able to identify the time on analog and digital clocks, as well as a calendar.

Temperature is measured by thermometers.

There are two scales used: Fahrenheit and Celsius. Often thermometers display both scales.

Students should understand how to read a thermometer to identify the temperature.

Numerical patterns can be incorporated into telling time (counting by 5’s), calendar (counting weeks by 7’s), and temperature (increments on the thermometer, often by 2’s and 10’s).

What technique would you use to determine time to the nearest five minutes, using analog and digital clocks?

How can you demonstrate an understanding of counting by fives to predict five minute intervals when telling time to the nearest five minutes?

How does a calendar measure time?

How does a calendar represent yesterday, today, and tomorrow?

How can you determine the date of the third Wednesday in any given month? Teachers may change the variation of ordinal number and day of the week for this question.

How can you read temperature to the nearest 10 degrees from real Celsius and Fahrenheit thermometers and from physical models?

What patterns do you notice in telling time and reading temperatures?


VDOE Vertical Alignment document K-3 1.8 The student will tell time to half‐hour 1.11 The student will use calendar language appropriately

VDOE Vocabulary Word Wall Cards analog yesterday thermometer digital today Fahrenheit hour tomorrow Celsius half hour names of months temperature quarter after names of days degrees quarter before hour hand minute hand half past a.m. p.m.















• Have students label an analog clock face with small dot stickers, counting by fives.

• Put tape along the length of the minute hand of a large wall clock, and write the word minute along it. Do the same for the hour hand.

• As a quick warm up, have students pretend their bodies are clocks and their arms are the hands on the clocks. Review the vocabulary o’clock and thirty. Hold up time cards that show “o’clock times” and “thirty times.” Have students put arms up in the air (as if pointing to the 12) if the card shows an “o’clock time.” Have students put arms down in front of them (as if pointing to the 6) if the card shows a “thirty time.”

• Enlarge a calendar template on large paper for students who need more space to write. Cut apart the months of a calendar so that students may put them in the correct order. • Prior to this activity, use sidewalk chalk to create a large calendar on the blacktop outside. Call out questions about dates, and have student run and stand on the date.

• Create a transparency version of a calendar so that months can be overlaid and students can easily observe that the first day of a month always follows the last day of the previous month.

• Have students draw a line from the top of each thermometer reading to the temperature number.

• Have students use moveable thermometer manipulatives to show various temperatures.

• Have students make their own paper thermometer and fill in the scale marks, using skip counting by 2’s and 10’s.



(click to link)

Investigations: Mathematical Thinking in Grade 2:

Time and Time Again p. 131 Timelines and Rhythm Patterns Investigation 1: Timelines

ESS Lessons: 2.12 Check The Time 2.13 Let Me Check My Calendar 2.14 A Fine Day For? Brain Pop Jr.: Parts of a Clock Time to the Hour Time to the Half and Quarter Hour Time to the Minute Calendar and Dates Temperature Safari Montage: Telling Time Measurement: Chapter 9: Temperature

Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)








http://www.brainpopjr.com/math/time/partsofaclock/

http://www.brainpopjr.com/math/time/timetothehour/

http://www.brainpopjr.com/math/time/timetothequarterandhalfhour/

http://www.brainpopjr.com/math/time/timetotheminute/

http://www.brainpopjr.com/math/time/calendaranddates/

http://www.brainpopjr.com/math/measurement/temperature/


http://safari.lcps.org/SAFARI/montage/play.php?keyindex=60594&location=local&chapterskeyindex=177158&filetypeid=54



Unit: 8 Quarter 3

Geometry & Fractions


2.15 The student will a) draw a line of symmetry in a figure; b) identify and create figures with at least one line of symmetry 2.16 The student will identify describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism). 2.3 The student will a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths ; b) write the fractions; c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths 2.20 The student will identify, create, and extend a wide variety of patterns.


Learning Targets:

I can develop strategies to identify line(s) of symmetry in a figure, create symmetrical figures, and draw line(s) of symmetry using a variety of math tools.

I can describe, identify, compare and contrast related plane and solid figures.

I can label fractions using a picture / model.

I can compare one unit fraction to another unit fraction using a picture / model.

I can identify, create, and apply a wide variety of patterns.


Define what a line of symmetry means.

Recognize if a shape has symmetry.

Identify and explain the differences between plane and solid figures.

Understand and explain the parts of a fraction and what the parts represent.

The whole must be defined. Parts of a whole can be renamed as the definition of the whole changes (ie: using pattern blocks, a trapezoid is ½ of a whole hexagon, but if the whole is defined as two hexagons, then the trapezoid is ¼ of the whole).

Fractions represent parts of wholes and students need to be flexible in how they view these numbers. Area models, set models, and linear models should all be used in addition to symbols and numerals in developing a conceptual understanding of fractions.

What strategies determine whether or not a figure has at least one line of symmetry?

What strategies create figures with at least one line of symmetry?

How can you explain your understanding that some figures may have more than one line of symmetry?

What are the differences between plane and solid figures?

What is a solid figure made up of?

What is a fraction?

How do you demonstrate, explain, and justify the relationship between fractional parts?

How do you create and explain a fraction using a region model?

How do you create and explain a fraction using a set model?

How do you compare and contrast set and region models of fractions?

What do patterns help explain? What is the difference between repeating and growing patterns?




1.13 The student will construct/model/describe objects as geometric shapes 1.12 The student will ID/trace/describe/sort plane figures according to number of sides, vertices, angles 1.16 The student will sort/classify objects by color/size/shape/thickness 1.17 The student will recognize, describe, extend, create growing and repeating patterns

VDOE Vocabulary Word Wall Cards 2.15 2.16 2.3 half vertex unit fraction fourths vertices equivalent fraction whole angle fair shares line of symmetry plane shape fraction symmetrical triangle numerator unsymmetrical rectangle denominator circle part 2.20 square whole pattern face core edge repeating pattern solid figure growing pattern cube arrangement sphere predict rectangular prism outcome triangular pyramid












• Emphasize the “s” sound in symmetry and same to help students connect with the vocabulary.

• Allow students to use moveable adhesive sticks to show many lines of symmetry on an image. • Challenge students to draw their own symmetrical shapes. Have them test the shapes for symmetry by folding. • Challenge students to find an object in the room that has multiple lines of symmetry.

• Find lines of symmetry in pattern block shapes. Then, order the shapes from the least lines of symmetry to the most lines of symmetry.

Investigations: Mathematical Thinking at Grade 2 Does It Walk, Crawl, or Swim? Investigation 2: Sorting People and Yekttis Session 3: Working with Two Attributes (Guess My Rule) Session 4 & 5: Looking at Yekktis Shapes, Halves, and Symmetry Timelines and Rhythm Patterns Investigation 2: Rhythm Patterns







• Give students sheets of one-inch grid paper with a diagonal line drawn on it. Challenge them to create symmetrical designs, using the diagonal line as the line of symmetry. • To help students recognize the faces on a solid figure, allow student to coat the face in washable paint and then print it on paper. Encourage students to investigate whether there is more than one face shape in a given solid figure. • Have the students act out story problems as they are read aloud to the class.

• Create a set of cards showing the solutions to the fraction story problems, and allow students to match solutions to the problems.

• Modify the fraction story problems to include picture cues for struggling readers. • Have students go on a “fraction hunt” for objects in the classroom, school building, or playground that represent or suggest fractions. If a digital camera is available, students can take pictures of the objects found and write the fractions on the pictures. • Have students investigate the relationship between skip counting and possible fair shares for a given number in a set. For example, a set of 10 items can be divided into 1, 2, 5 and 10 fair shares, but not into 3, 4, 6, 7, 8, or 9 fair shares. Give students an opportunity to predict numbers of fair shares for a given number in a set, based on skip counting patterns, and then to use manipulatives to confirm their predictions.

• Read a story about fractional concepts. Have students use manipulatives to model the fractions represented in the story.

• Have students write their own fraction story problems. Then, have them exchange their problems with partners to solve. Collect all story problems, and create a class book.



(click to link)

ESS Lessons: 2.15 Symmetrical Snow Fun 2.15 Symmetrical Cube Designs 2.16 The Shape Show 2.3 Fair Shares 2.20 Exercising Patterns Brain Pop Jr.: 2.16 Geometry: Plane Shapes 2.16 Geometry: Solid Shapes 2.16, 2.20 Geometry: Patterns 2.3 Fractions: Basic Parts of a Whole 2.3 Fractions: Equivalent Fractions Safari Montage: 2.15 Cyberchase: The Secret of Symmetria 2.16 Geometry

2.3 Cyberchase Fractions: Harriet the Hippo & The Mean Green 2.3 Cyberchase Fractions: Zeus on the Loose 2.3 Fractions 2.20 Cyberchase: Patterns: The Poddleville Case Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.brainpopjr.com/math/geometry/planeshapes/

http://www.brainpopjr.com/math/geometry/solidshapes/

http://www.brainpopjr.com/math/geometry/patterns/

http://www.brainpopjr.com/math/fractions/basicpartsofawhole/

http://www.brainpopjr.com/math/fractions/equivalentfractions/










Unit: 9 Quarter 4

Measuring My World


2.11 The student will estimate and measure a) length to the nearest centimeter and inch b) weight/mass of objects in pounds/ounces and kilograms/grams, using a scale c) liquid volume in cups, pints, quarts, gallons, and liters


Learning Targets:

I can use measuring tools (ruler) to find the measurement of length in centimeters in inches.

I can use measuring tools (scale) to find the measurement of an object’s weight and mass in pounds, ounces, kilograms, and grams.

I understand the relation of the volume units used for measuring liquids; cups, pints, quarts, gallons, and liters.


Explore the differences between the customary and metric systems of measurement.

Recognize which units are used to measure length, weight, and capacity (ie: inches and centimeters are used to measure the length of an object).

Learn to use a variety of tools used for measuring.

Understand that an estimate is finding the measurement to the nearest number.

What are two examples of objects measured in length, weight/mass, and capacity in U.S. Customary?

What are two examples of objects measured in length, weight/mass, and capacity in the metric system?

What would be an example of a situation where an estimate is more appropriate than an actual measurement?



1.9 The student will use nonstandard units to measure length, weight, mass, and volume.

1.10 The student will a) compare volumes of two containers; b) weight/mass of two objects

VDOE Vocabulary Word Wall Cards

length estimate width customary ruler metric inch (inl) pound (lb) centimeter (cm) ounce (oz) foot (ft) gram (g) feet kilogram (kg) yard (yd) predict meter (m) cup weight pint mass quart liter volume

Students should begin to become familiar with common abbreviations for measurement units as well.















Allow students to use linking cubes or inch worms instead of rulers.

• To incorporate physical movement, have students participate in a long jump contest and use their measuring skills to measure the distances in inches and centimeters.

• Call attention to the connection between a ruler and a number line. Allow students to use a ruler as a number line as needed during computation. • When listing objects that are of similar weights/masses, use very familiar objects (e.g., a can of beans weighs about 1 pound). • Create a bulletin board divided into four sections with the labels, “Ounce,” “Pound,” “Gram,” and “Kilogram.” Provide students with a basket full of images of familiar objects. Have each student select an image from the basket, decide to which group the depicted object belongs, pin it to the board, and write a sentence explaining his/her reasoning about why the object belongs in that group (e.g., “The paper clip belongs in the gram group because I think it weighs about 1 gram, just like the bean we measured earlier.”).

• Create a sorting activity using interactive technology. • Have students assist you in using tape and markers to label the measuring containers, employing volume vocabulary: cup, pint, quart, gallon, and liter. Encourage the use of volume vocabulary (e.g., “the gallon jug” rather than “the milk jug”).

• Provide students with odd-shaped containers whose volumes are not easily predicted. Encourage them to investigate what effect height and width have on volume.


ELL Model Performance Indicators (click to link)

Investigations: How Long? How Far? Investigation 1: Comparing Lengths Investigation 2: Paths and Geo-Logo ESS Lessons: 2.11a Kite Tail Measurement 2.11b A Weigh We Go 2.11 How Much Will It Hold? Brain Pop: 2.11a Measurement: Inches and Feet 2.11a Measurement: Centimeters, Meters, Kilometers 2.11b Measurement: Ounces, Pounds, Tons 2.11b Measurement: Grams, Kilograms 2.11c Measurement: Cups, Pints, Quarts, Gallons Safari Montage: Measurement Math in Our Lives: Measurement Measure for Treasure Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-11a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/2/mess_2-11b.pdf


http://www.brainpopjr.com/math/measurement/inchesandfeet/

http://www.brainpopjr.com/math/measurement/centimetersmeterskilometers/

http://www.brainpopjr.com/math/measurement/ouncespoundsandtons/

http://www.brainpopjr.com/math/measurement/gramsandkilograms/

http://www.brainpopjr.com/math/measurement/cupspintsquartsgallons/






Unit: 10 Quarter 4

Skip Counting & Money


2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less; b) correctly use the cent symbol (¢), dollar symbol ($), and decimal point (.) 2.20 The student will identify, create, and extend a wide variety of patterns.


Learning Targets:

I can count a collection of coins (pennies, nickels, dimes, and quarters) whose value is $2.00 or less, write the amount using correct symbols, and compare collections from everyday situations.



Identify, sort, and know the value of coins.

Count various coin collection totals up to $2.00.

Demonstrate knowledge by identifying which coin collections are worth more than others (>,<).

Understanding of how to use the decimal point, dollar sign and cent sign in written form.

Create and identify patterns of coins.

Understand how to compare values of coins (ie. 3 dimes and 2 nickels is the same as 1 quarter, 1 dime, and 1 nickel).

Connect skip counting patterns (5’s, 10’s, 25’s) to counting collections of coins.

How do you demonstrate and explain multiple strategies for determining the value of a set of coins?

How do you explain and justify how the value of two sets of coins can be compared (using <, >, =)?

How do you create and explain situations correctly using the cents sign, decimal point, and dollar sign?

What do patterns help explain? (how to recognize order and to predict what comes next in an arrangement).

What is the difference between repeating and growing patterns?


VDOE Vertical Alignment document K-3 1.7 The student will a) ID number of pennies equivalent to nickel, dime, quarter; b) determine value of collection of coins w/ value of 100 cents or less 1.17 The student will recognize/describe/extend/create growing and repeating patterns.

VDOE Vocabulary Word Wall Cards penny greater than pattern nickel less than core/unit dime equal to repeating pattern quarter growing pattern cents arrangement dollars predict decimal point outcome


















• If students are able to count values up to $2.00 with ease, have them count collections of coins whose values are greater than $2.00. • Ask students how much change they would get back if they bought a cool treat, using a given set of coins.

• Allow students to use coin stamps, coin cutouts, or coin rubbings. • Read aloud a story about money. Place coins around the classroom, and allow students to “hunt for money.” Then, ask them to count their coins and compare the value to the value of their neighbors’ coins. Have students share their comparisons.

• Have students select 10 coins from a baggie and “record” them on paper, using coin stamps or photocopies of coin images. Finally, have them write the value of each coin and find and write the total value, using cent, dollar, and decimal point symbols.

• Review counting by ones, fives, and tens to 100, using pennies, nickels, and dimes or pictorial representations of them. You might have students place pennies on a hundred chart while they count by ones, place nickels on the chart while they count by fives, etc.

• Have students develop a rhythm for counting by twenty-fives. Allow them to clap their hands, stomp their feet, or march around to the beat while repeating, “25, 50, 75, a dollar, 25, 50, 75, a dollar, etc.”

• If the lesson requires physical movement that some students may be unable to perform, create other movement cards that they can imitate (e.g., snapping, clapping, smiling, frowning, nodding). • When exploring repeating and growing patterns with numbers, provide students hundred charts and colored chips. Give them directions such as, “Cover the number 2. Add 4 more, and cover the next number (6). Add 4 more, and cover the next number (10). What number will you cover now? Is this pattern growing or repeating?”



(click to link)

Investigations: Coins, Coupons, and Combinations Investigation 2: Grouping2’s, 5’s, and 10’s Session: 6 Ways to Make 15 cents Sessions 7,8,9: Coins and Coupons Putting Together and Taking Apart Investigation 2: Working with 100 Sessions 5 & 6: Collect $1.00 Does It Walk, Crawl, or Swim? Investigation 1: Sorting People and Yekttis Session 3: Working with Two Attributes (Guess My Rule Using Money) ESS Lessons: 2.10 Cool Coin Comparisons 2.20 Exercising Patterns Brain Pop: 2.10 Money: Dollar and Cents 2.10 Money: Counting Coins 2.10 Money : Equivalent Coins Safari Montage: 2.10 Money 2.10 Math in Our Lives 2.10 School House Rock: Money Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)




http://www.brainpopjr.com/math/money/dollarsandcents/

http://www.brainpopjr.com/math/money/countingcoins/

http://www.brainpopjr.com/math/money/equivalentcoins/





The First 20 Days Classroom Routines: Establishing a Mathematics Classroom Community

Overview: The mini lessons included in this guide are intended to be used in conjunction with your first unit of study. The daily 10-15 minute lessons will help

you set routines, develop references for students, establish protocols, and create norms for an engaging math classroom community. The lessons may be

modified or extended based on students’ need or grade level. The routines, protocols, and experiences should be revisited throughout the school year in order

to maintain a productive math community.

Goals:

Build a classroom community of learners

Support students’ understanding of math content by establishing guidelines related to the VA process goals (problem solving, communication,

reasoning, connections, and representation).

Develop routines that will help students become reflective problem solvers and engage in a rigorous study of mathematics.

Background: This guide is based on a document developed by Austin Independent School District. Their document was modeled after the First 20 Days of Independent Reading by Fountas & Pinnell. Many of the suggested routines will also connect to other effective protocols used in Being a Writer and Responsive Classroom. This guide was adapted from a resource created by Arlington Public Schools.

Mini Lesson Key Ideas Essential Understandings

Anchor Charts/Supports Resources Teacher Notes

Day 1 Management: Classroom Procedures/ Community Guidelines

Establish routines, procedures, and student expectations for daily math lessons.

Students develop criteria for a “Being a Mathematician” chart that will be posted in the classroom. Students understand that the information posted in the classroom will be a valuable reference for them.

Develop a “Being a Mathematician” anchor chart to which students can refer. The chart should have less than 6 criteria to be effective and manageable. Example behaviors:

• Remain on task • Participate/stay engaged • Listen actively • Discuss math ideas • Treat materials with respect • Always try your best

*Brainstorm the list with the students

Chart paper, Markers Have a discussion about routines and procedures with the students. This is a good time to have students talk about expectations for engaging in classroom discussions and completing their work.

Day 2 Management: Mathematical Tools VA Process Goals: Problem Solving & Representation

Mathematicians can utilize math tools to help them solve problems.

Tools are a valuable resource for mathematicians. Students are aware of the tools that are available in the classroom.

Brainstorm a list of mathematical tools and discuss how they can be used and stored. Add additional information to the “Being a Mathematician” chart about placing materials in their proper storage containers and location after use. Examples: Base ten blocks Cubes Number cubes Hundreds chart Two-colored counters

Emphasize how and why materials are to be used during math instruction.



Day 3 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Norms for classroom discussions need to be established in order to engage in respectful discourse and have equitable participation.

In order to communicate and learn from each other, mathematicians must listen to, as well as speak, with their classmates. We will function as a respectful classroom community in order to learn.

Create an anchor chart for “Norms for a Math Discussion” or “Rights and Obligations During Discussions” Example norms include: Speak respectfully Take turns (equitable participation) Give others time to think Eyes on the speaker

Norms may be similar to those you establish in other content areas. These established routines should be revisited all year long.

Day 4 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Different talk moves can be used while facilitating classroom discussions. Students learn content through the process goal of communication.

Math can be more rigorous when you communicate with others. There are sentence starters that can be used to help one engage in discussions.

Post and discuss Talk Moves to encourage students to share their thinking. Identify 1 or 2 moves to begin the year with (based on your first units of study).

- Talk bubbles or Talk move sticks

Introduce talk moves

- Turn and Talk (also called partner talk, or think-pair-share)

- Say More: You ask an individual student to expand on what he or she said

- Revoicing (also called verify and clarify)

- Repeat - Agree/Disagree and why?

Encourage students to speak in complete thoughts when communicating orally. The utilization and introduction of talk moves is a continuous process. This day is one way to introduce moves, but it should be ongoing.



Day 5 Collaboration (Game) VA Process Goal: Communication

Mathematicians can work collaboratively while playing a game in order to learn important math concepts.

Students understand that they can work with others to explore math content. Cooperation is a key component of working with a partner.

Establish rules for working with a partner while playing a math game. Try the “Say it to Play it” guideline: When playing a game in partners, the students must state their move and/or provide an explanation for why they are playing that move (Ex: In the game Compare, a student may say “9 is greater than 5, so I win the cards”).

Post rules and directions for engaging in a game with a partner. Consider utilizing a fact fluency game for this mini lesson.

Rules and clear directions will help make group work successful. After the mini lesson, have students practice a game during the math lesson for the day.

Day 6 Collaborative/ Independent Work (Rotations) VA Process Goal: Communication

Mathematicians can explore/ engage in a variety of experiences within a math period. Work may be collaborative or independent.

In order to have a variety of activities during a math block, it is important to be mindful of procedures, noise level, expectations, etc.

Review procedures for moving around the classroom to different centers Consider utilizing visual time reminders Use cues for sound control/reminders

Post clear directions at independent centers. Provide a materials checklist.



Day 7 Real Life Connections to Math VA Process Goal: Connections

Mathematicians make connections between math ideas and the world around them.

Math connects to other content areas/disciplines (i.e. Science). Students relate math to the world around them.

Brainstorm a list of math concepts that relate to the real world. Consider using the following discussion prompts: Where in the world do you see numbers? When do you use math in your everyday life?

Chart paper Calendar / Daily Schedule

Consider connecting this discussion to everyday events in their life.

Day 8 Representing Thinking VA Process Goals: Representation, Communication

Mathematicians can represent ideas in multiple ways. Mathematicians use words to explain their thinking. Mathematicians can explain their thinking verbally or in writing in order to process information.

Students will become more familiar with ways they can represent math ideas. Students can show their math thinking in written words.

In order to fully communicate their understanding, mathematicians may provide written explanations of their reasoning.

Brainstorm ways that students can represent their thinking. Ex: Pictures/drawing Words Numbers Symbols Manipulative models

Utilize sentence frames: “This is a ______________. It is a ______ because it ______________. “ This example shows a picture, numbers, and a written explanation.

Encourage students to show math concepts in a variety of ways. Encourage students to write about their understanding or show their thinking using words, pictures, numbers, etc.



Day 9 Recording & Reflecting in Math

VA Process Goal: Communication

Mathematicians keep a record of their daily experiences (i.e. math game).

Students will understand how to utilize a recording sheet or guide as they play a game or solve a problem. Students will record and reflect upon their work to communicate their understanding in writing.

Example of Game Recording Sheet:

Introduce a Recording Sheet as a student tool.

Day 10 Academic Language of Math VA Process Goal: Communication

Specialized language is used in math. Mathematical language can be modeled and explicitly taught.

Students will develop an understanding of specific math terminology. Conceptual understanding is developed as students use math terminology.

Post examples of key vocabulary terms with visual examples.

Math Word Wall, Word Banks, VDOE Vocabulary Cards http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml The vocabulary terms introduced are then posted for class reference.

New vocabulary should be explicitly introduced and utilized within daily lessons. This is a continuous routine/ element for all units of study.

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml





Day 11 Vocabulary Development VA Process Goals: Representation, Communication, Connections

Mathematicians use a variety of strategies to build vocabulary.

Students will utilize a tool to reinforce their math vocabulary.

Select model to implement with students (i.e. Frayer).

Student math journal VDOE Math Vocabulary Cards Frayer Model

Students can utilize math journals to keep a record of math vocabulary. Their journals can also serve as a valuable resource in addition to the Word Wall or class references (see Day 10).

Day 12 Math Strategies VA Process Goals: Problem Solving, Representation, Connections

A variety of strategies can be used to solve problems and explore mathematical concepts.

Students develop a repertoire of strategies. Students see connections between different strategies used to solve problems.

Build or add to a strategy wall showing models of strategies for various skills or concepts.

Anchor charts can be developed for a wide variety of strategies depending on the grade level. Examples are shown to the left.



Day 13 Connections VA Process Goals: Connections, Communication

Mathematicians make and recognize connections among mathematical ideas.

Students understand that they can make connections among math ideas. Math can be related to the world outside the classroom.

Discussion questions: How is that answer like the one you modeled yesterday? Where have you seen that before?

Consider having students glue question/ comment starters in the back of their math journal. They can refer to it during class discussions.

Day 14 Justification VA Process Goals: Reasoning, Representation

Mathematicians verify their thinking by showing it multiple ways.

Students will develop a deeper understanding of content when asked to justify their thinking.

Create an anchor chart that depicts ways that students can justify their thinking.

Justify means: explain, defend,

describe, prove, give reasons, show

you understand, validate…

Using verbal explanation first can help facilitate written justification.



Day 15 Problem Solving Strategies VA Process Goals: Problem Solving, Communication

Mathematicians choose from a variety of strategies to solve problems.

Students have a resource of strategies to help them solve problems . Sample strategies: -find a pattern - estimate and check -make an organized list -draw a diagram -write an equation -work backward -solve a simpler problem -read a table/chart

Introduce problem solving strategies (a variety of strategies can be used). Explain that the different strategies can be used to help students with problem solving. Choose 1 strategy to explain/highlight for the mini lesson. You will continue to model/introduce/use the strategies throughout the year.

Students can create their own problem solving strategy icons or bookmarks as well as refer to a class anchor chart of strategies.

During classroom instruction, teachers can engage students in discourse about their problem solving strategy.

Day 16 Problem Solving Protocol VA Process Goals: Problem Solving, Communication

There are processes that can be used to help solve problems.

Students will be introduced to a problem solving protocol. Students will become familiar with the protocol steps.

Develop and post a problem solving protocol.

Post the protocol in the classroom for student reference.

Consider trying a problem as a class to model how the protocol is used. The emphasis should be on the steps, so it may be easiest to select content that is readily accessible to all learners.

Step 1: Read and quietly think on your own – release your pencils. Step 2: Talk about the problem. What is your plan to solve? Pick your strategy. Step 3: Share your strategy. Step 4: Solve the problem and communicate your thinking.



Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections

There are tools mathematicians use to monitor and assess their work or behavior.

Students understand how to use a rubric to assess themselves/ their work.

Create a class rubric that is not math related. The topic should be something relevant to an everyday student activity in the classroom or school. Examples include: Lunchroom behavior Morning routine Dismissal Cubbie/desk organization

Day 18 Reflection/ Self-Monitoring VA Process Goal: Reasoning

Mathematicians modify their work as needed.

Students reflect upon and revise their work to demonstrate their full understanding.

Introduce a criteria chart and rubric for self- monitoring of work.

Sample Rubric:

Rubric & Problem Solving Protocol Create an anchor chart with “How to Self-Correct or Modify Your Work”

Help students develop a clear understanding of the criteria and how upcoming math tasks will be scored. Emphasize how this is similar to the revisions they do during the writing process.



Day 19 Collaboration (Task) VA Process Goal: Communication

Mathematicians can work collaboratively on a problem solving task to learn important math concepts.

Students understand that they can work with others to solve problems and learn new information.

Review roles that pairs or small groups should follow/hold when working together on a task. Examples: Materials manager Recorder Reporter Time keeper

Develop an anchor chart with roles/procedures for group work on a task/problem. Self-assess/reflect upon collaborative work experiences. Students can use the problem solving protocol together (See Day 16).

Save time at the end of the lesson to debrief the experience. What went well? What could be improved next time they are working in a group?

Day 20

Process Goals

VA Process Goals: Problem Solving, Reasoning, Communication, Connections, & Representation

“The content of the mathematics standards is intended to support the following five process goals for students: *becoming mathematical problem solvers *communicating mathematically *reasoning mathematically *making mathematical connections and *using mathematical representations to model and interpret practical situations.”

-2009 Mathematics Standards of Learning

Student-friendly process goals poster (can be a poster for the classroom and/or a small version can be taped to desks or in math journals) Process Goals bookmark (click on picture to the left to access the file for the poster and bookmark)

Students should be engaged in process goals throughout every mathematical task and lesson throughout the year.

https://www.dropbox.com/s/t2pvle6rn86heu2/Process Goals student-friendly.docx

VDOE Technical Assistance Document

to be used in conjunction with the VDOE Curriculum Framework (click title above to link to document)

Virginia Mathematics Standards of Learning

Curriculum Framework 2009

Introduction

The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and

amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards

of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an

instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining

essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity

the content that all teachers should teach and all students should learn.

Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the

Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for

each standard. The Curriculum Framework is divided into three columns: Understanding the Standard; Essential Understandings; and Essential

Knowledge and Skills. The purpose of each column is explained below.

Understanding the Standard

This section includes background information for the teacher (K-8). It contains content that may extend the teachers’ knowledge of the standard

beyond the current grade level. This section may also contain suggestions and resources that will help teachers plan lessons focusing on the standard.

Essential Understandings

This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the

Standards of Learning. In Grades 6-8, these essential understandings are presented as questions to facilitate teacher planning.

Essential Knowledge and Skills

Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is

outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills

that define the standard.

The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a

verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills

from Standards of Learning presented in previous grades as they build mathematical expertise.

http://www.doe.virginia.gov/instruction/mathematics/resources/mathematics_sol_technical_assistance.pdf

FOCUS K–3 STRAND: NUMBER AND NUMBER SENSE GRADE LEVEL 2

Mathematics Standards of Learning Curriculum Framework 2009: Grade 2

Students in grades K–3 have a natural curiosity about their world, which leads them to develop a sense of number. Young children are motivated to

count everything around them and begin to develop an understanding of the size of numbers (magnitude), multiple ways of thinking about and

representing numbers, strategies and words to compare numbers, and an understanding of the effects of simple operations on numbers. Building on

their own intuitive mathematical knowledge, they also display a natural need to organize things by sorting, comparing, ordering, and labeling objects

in a variety of collections.

Consequently, the focus of instruction in the number and number sense strand is to promote an understanding of counting, classification, whole

numbers, place value, fractions, number relationships (“more than,” “less than,” and “equal to”), and the effects of single-step and multistep

computations. These learning experiences should allow students to engage actively in a variety of problem solving situations and to model numbers

(compose and decompose), using a variety of manipulatives. Additionally, students at this level should have opportunities to observe, to develop an

understanding of the relationship they see between numbers, and to develop the skills to communicate these relationships in precise, unambiguous

terms.

STANDARD 2.1 STRAND: NUMBER AND NUMBER SENSE GRADE LEVEL 2


2.1 The student will

a) read, write, and identify the place value of each digit in a three-digit numeral, using numeration models;

b) round two-digit numbers to the nearest ten; and

c) compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words (greater than, less than, or equal to).

UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)

ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

The number system is based on a simple pattern of tens

where each place has ten times the value of the

place to its right.

Opportunities to experience the relationships among

hundreds, tens, and ones through hands-on

experiences with manipulatives are essential to

developing the ten-to-one place value concept of our

number system and to understanding the value of

each digit in a three-digit number. Ten-to-one

trading activities with manipulatives on place value

mats provide excellent experiences for developing

the understanding of the places in the Base-10

system.

Models that clearly illustrate the relationships among

hundreds, tens, and ones are physically proportional

(e.g., the tens piece is ten times larger than the ones

piece).

Students need to understand that 10 and 100 are special

units of numbers (e.g., 10 is 10 ones, but it is also 1

ten).

Flexibility in thinking about numbers is critical. For

example, 123 is 123 ones; or 1 hundred, 2 tens, and

3 ones; or 12 tens and 3 ones.

Rounding is finding the nearest easy-to-use number

(e.g., the nearest 10) for the situation at hand.

All students should

Understand the ten-to-one relationship of ones, tens, and

hundreds (10 ones equals 1 ten; 10 tens equals 1

hundred).

Understand that numbers are written to show how many

hundreds, tens, and ones are in the number.

Understand that rounding gives a close, easy-to-use

number to use when an exact number is not needed

for the situation at hand.

Understand that a knowledge of place value is essential

when comparing numbers.

Understand the relative magnitude of numbers by

comparing numbers.

The student will use problem solving, mathematical

communication, mathematical reasoning,

connections, and representations to

Demonstrate the understanding of the ten-to-one

relationships among ones, tens, and hundreds, using

manipulatives (e.g., beans and cups, Base-10

blocks, bundles of 10 sticks).

Determine the place value of each digit in a three-digit

numeral presented as a pictorial representation (e.g.,

a picture of Base-10 blocks) or as a physical

representation (e.g., actual Base-10 blocks).

Write numerals, using a Base-10 model or picture.

Read three-digit numbers when shown a numeral, a

Base-10 model of the number, or a pictorial

representation of the number.

Identify the place value (ones, tens, hundreds) of each

digit in a three-digit numeral.

Determine the value of each digit in a three-digit

numeral (e.g., in 352, the 5 represents 5 tens and its

value is 50).

Round two-digit numbers to the nearest ten.

Compare two numbers between 0 and 999 represented

pictorially or with concrete objects (e.g., Base-10

blocks), using the words greater than, less than or

equal to.









Number lines are useful tools for developing the concept

of rounding to the nearest ten. Rounding to the

nearest ten using a number line is done as follows:

– Locate the number on the number line.

– Identify the two tens the number comes between.

– Determine the closest ten.

– If the number in the ones place is 5 (halfway

between the two tens), round the number to the

higher ten.

Once the concept for rounding numbers using a

number line is developed, the procedure for

rounding numbers to the nearest ten is as follows:

Look one place to the right of the digit in the

place you wish to round to.

If the digit is less than 5, leave the digit in the

rounding place as it is, and change the digit

to the right of the rounding place to zero.

If the digit is 5 or greater, add 1 to the digit in the

rounding place, and change the digit to the

right of the rounding place to zero.









A procedure for comparing two numbers by examining

place value may include the following:

Line up the numbers by place value lining up the

ones.

Beginning at the left, find the first place value

where the digits are different.

Compare the digits in this place value to

determine which number is greater (or which

is less).

Use the appropriate symbol > or < or words

greater than or less than to compare the

numbers in the order in which they are

presented.

If both numbers are the same, use the symbol = or

the words equal to.

Mathematical symbols (>, <) used to compare two

unequal numbers are called inequality symbols.




a) identify the ordinal positions first through twentieth, using an ordered set of objects; and

b) write the ordinal numbers.



Understanding the cardinal and ordinal meanings of

numbers are necessary to quantify, measure, and

identify the order of objects.

An ordinal number is a number that names the place or

position of an object in a sequence or set (e.g., first,

third). Ordered position, ordinal position, and

ordinality are terms that refer to the place or

position of an object in a sequence or set.

The ordinal position is determined by where one starts in

an ordered set of objects or sequence of objects

(e.g., left, right, top, bottom).

The ordinal meaning of numbers is developed by

identifying and verbalizing the place or position of

objects in a set or sequence (e.g., a student’s

position in line when students are lined up

alphabetically by first name).

Ordinal position can also be emphasized through

sequencing events (e.g., months in a year or

sequencing in a story).

Cardinality can be compared with ordinality when

comparing the results of counting. There is obvious

similarity between the ordinal number words third

through twentieth and the cardinal number words

three through twenty.

All students should

Use ordinal numbers to describe the position of an object

in a sequence or set.




Count an ordered set of objects, using the ordinal

number words first through twentieth.

Identify the ordinal positions first through twentieth,

using an ordered set of objects.

Identify the ordinal positions first through twentieth,

using an ordered set of objects presented in lines or

rows from

left to right;

right to left;

top to bottom; and

bottom to top.

Write 1st, 2nd, 3rd, through 20th in numerals.




a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths;

b) write the fractions; and

c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.



The whole should be defined.

A fraction is a way of representing part of a whole (as in

a region/area model) or part of a group (as in a set

model).

In each fraction model, the parts must be equal (i.e., each

pie piece must have the same area; the size of each

chip in a set must be equal). In problems with

fractions, a whole is broken into equal-size parts and

reassembled into one whole.

Students should have experiences dividing a whole into

additional parts. As the whole is divided into more

parts, students understand that each part becomes

smaller.

The denominator tells how many equal parts are in the

whole or set. The numerator tells how many of those

parts are being described.

Students should have opportunities to make connections

among fraction representations by connecting

concrete or pictorial representations with spoken or

symbolic representations.

All students should

Understand that fractional parts are equal shares of a

whole or a whole set.

Understand that the fraction name (half, fourth) tells the

number of equal parts in the whole.

Understand that when working with unit fractions, the

larger the denominator, the smaller the part and

therefore the smaller the fraction.


communication, mathematical reasoning, connections,

and representations to

Recognize fractions as representing equal-size parts of a

whole.

Identify the fractional parts of a whole or a set for2

2,

2

3,

3

4,

2

6,

7

8,

7

10, etc.

Identify the fraction names (halves, thirds, fourths, sixths,

eighths, tenths) for the fraction notations2

2,

2

3,

3

4,

2

6,

7

8,

7

10, etc.

Represent fractional parts of a whole for halves, thirds,

fourths, sixths, eighths, tenths using

region/area models (e.g., pie pieces, pattern

blocks, geoboards);

sets (e.g., chips, counters, cubes); and

measurement models (e.g., fraction strips, rods,

connecting cubes).

Compare unit fractions (1

2 ,

1

3 ,

1

4 ,

1

6 ,

1

8 , and

1

10 ) using

the words greater than, less than or equal to and the

symbols ( >, <, =).




a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths;

b) write the fractions; and

c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.



Informal, integrated experiences with fractions at this

level will help students develop a foundation for

deeper learning at later grades. Understanding the

language of fractions (e.g., thirds means “three

equal parts of a whole” or 1

3 represents one of three

equal-size parts when a pizza is shared among three

students) will further this development.

A unit fraction is one in which the numerator is one.

Using models when comparing unit fractions will

assist in developing the concept that the larger the

denominator the smaller the piece; therefore, 1

3 >

1

4 .




a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10;

b) count backward by tens from 100; and

c) recognize even and odd numbers.



The patterns developed as a result of grouping and/or

skip counting are precursors for recognizing

numeric patterns, functional relationships, and

concepts underlying money, time telling,

multiplication, and division. Powerful models for

developing these concepts include counters, hundred

chart, and calculators.

Skip counting by twos supports the development of the

concept of even numbers.

Skip counting by fives lays the foundation for reading a

clock effectively and telling time to the nearest five

minutes, counting money, and developing the

multiplication facts for five.

Skip counting by tens is a precursor for use of place

value, addition, counting money, and multiplying by

multiples of 10.

Calculators can be used to display the numeric patterns

resulting from skip counting. Use the constant

feature of the four-function calculator to display the

numbers in the sequence when skip counting by that

constant.

Odd and even numbers can be explored in different ways

(e.g., dividing collections of objects into two equal

groups or pairing objects).

All students should

Understand that collections of objects can be grouped

and skip counting can be used to count the

collection.

Describe patterns in skip counting and use those patterns

to predict the next number in the counting sequence.

Understand that the starting point for skip counting by 2

does not always begin at 2.

Understand that the starting point for skip counting by 5

does not always begin at 5.

Understand that the starting point for skip counting by

10 does not always begin at 10.

Understand that every counting number is either even or

odd.




Determine patterns created by counting by twos, fives,

and tens on a hundred chart.

Skip count by twos, fives, and tens to 100, using

manipulatives, a hundred chart, mental mathematics,

a calculator, and/or paper and pencil.

Skip count by twos, fives, and tens to 100.

Count backward by tens from 100.

Use objects to determine whether a number is odd or

even.

FOCUS K–3 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL 2


A variety of contexts are necessary for children to develop an understanding of the meanings of the operations such as addition and subtraction.

These contexts often arise from real-life experiences in which they are simply joining sets, taking away or separating from a set, or comparing sets.

These contexts might include conversations, such as “How many books do we have altogether?” or “How many cookies are left if I eat two?” or “I

have three more candies than you do.” Although young children first compute using objects and manipulatives, they gradually shift to performing

computations mentally or using paper and pencil to record their thinking. Therefore, computation and estimation instruction in the early grades

revolves around modeling, discussing, and recording a variety of problem situations. This approach helps students transition from the concrete to the

representation to the symbolic in order to develop meaning for the operations and how they relate to each other.

In grades K–3, computation and estimation instruction focuses on

relating the mathematical language and symbolism of operations to problem situations;

understanding different meanings of addition and subtraction of whole numbers and the relation between the two operations;

developing proficiency with basic addition, subtraction, multiplication, division and related facts;

gaining facility in manipulating whole numbers to add and subtract and in understanding the effects of the operations on whole numbers;

developing and using strategies and algorithms to solve problems and choosing an appropriate method for the situation;

choosing, from mental computation, estimation, paper and pencil, and calculators, an appropriate way to compute;

recognizing whether numerical solutions are reasonable;

experiencing situations that lead to multiplication and division, such as equal groupings of objects and sharing equally; and

performing initial operations with fractions.

STANDARD 2.5 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL 2


2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.



Associate the terms addition, adding, and sum with the

concept of joining or combining.

Associate the terms subtraction, subtracting, minus, and

difference with the process of “taking away” or

separating (i.e., removing a set of objects from the

given set of objects, finding the difference between

two numbers, or comparing two numbers).

Provide practice in the use and selection of strategies.

Encourage students to develop efficient strategies.

Examples of strategies for developing the basic

addition and subtraction facts include

counting on;

counting back;

“one-more-than,” “two-more-than” facts;

“one-less-than,” “two-less-than” facts;

“doubles” to recall addition facts (e.g., 2 + 2 =__;

3 + 3 =__);

“near doubles” [e.g., 3 + 4 = (3 + 3) + 1 = __];

“make-ten” facts (e.g., at least one addend of 8 or

9);

“think addition for subtraction,” (e.g., for 9 – 5 =

__, think “5 and what number makes 9?”);

use of the commutative property, without naming

the property (e.g., 4 +3 is the same as 3 + 4);

use of related facts (e.g., 4 + 3 = 7 , 3 + 4 = 7, 7 –

4 = 3, and 7 – 3 = 4); and

use of the additive identity property (e.g., 4 + 0 =

4), without naming the property but saying,

“When you add zero to a number, you

always get the original number.”

All students should

Understand that addition involves combining and

subtraction involves separating.

Develop fluency in recalling facts for addition and

subtraction.




Recall and write the basic addition facts for sums to 20

or less and the corresponding subtraction facts,

when addition or subtraction problems are presented

in either horizontal or vertical written format.



2.5 The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.



Manipulatives should be used initially to develop an

understanding of addition and subtraction facts and

to engage students in meaningful memorization.

Rote recall of the facts is often achieved through

constant practice and may come from a variety of

formats, including presentation through counting on,

related facts, flash cards, practice sheets, and/or

games.



2.6 The student, given two whole numbers whose sum is 99 or less, will

a) estimate the sum; and

b) find the sum, using various methods of calculation.



Estimation is a number sense skill used instead of

finding an exact answer. When an actual

computation is not necessary, an estimate will

suffice.

Rounding is one strategy used to estimate.

Estimation is also used before solving a problem to

check the reasonableness of the sum when an exact

answer is required.

By estimating the result of an addition problem, a place

value orientation for the answer is established.

Strategies for mentally adding two-digit numbers include

student-invented strategies, making-ten, partial

sums, and counting on, among others.

– partial sums: 56 + 41 = __

50 + 40 = 90

6 + 1 = 7

90 + 7 = 97

– counting on: 36 + 62 = __

36 + 60 = 96

96 + 2 = 98

Addition means to combine or join quantities.

The terms used in addition are

23 addend

+ 46 addend

69 sum

Strategies for adding two-digit numbers can include, but

are not limited to, using a hundreds chart, number

line, and invented strategies.

All students should All students should

Understand that estimation skills are valuable, time-

saving tools particularly in practical situations when

exact answers are not required or needed.

Understand that estimation skills are also valuable in

determining the reasonableness of the sum when

solving for the exact answer is needed.

Understand that addition is used to join groups in

practical situations when exact answers are needed.

Develop flexible methods of adding whole numbers by

combining numbers in a variety of ways to find the

sum, most depending on place values.




Regroup 10 ones for 1 ten, using Base-10 models, when

finding the sum of two whole numbers whose sum

is 99 or less.

Estimate the sum of two whole numbers whose sum is

99 or less and recognize whether the estimation is

reasonable.

Find the sum of two whole numbers whose sum is 99 or

less, using Base-10 models, such as Base-10 blocks

and bundles of tens.

Solve problems presented vertically or horizontally that

require finding the sum of two whole numbers

whose sum is 99 or less, using paper and pencil.

Solve problems, using mental computation strategies,

involving addition of two whole numbers whose

sum is 99 or less.



2.6 The student, given two whole numbers whose sum is 99 or less, will

a) estimate the sum; and

b) find the sum, using various methods of calculation.



Building an understanding of the algorithm by first using

concrete materials and then a do-and-write approach

connects it to the written form of the algorithm.

The traditional algorithm for two-digit numbers is

contrary to the natural inclination to begin with the

left-hand number.

Regrouping is used in addition when a sum in a

particular place value is 10 or greater.



2.7 The student, given two whole numbers, each of which is 99 or less, will

a) estimate the difference; and

b) find the difference, using various methods of calculation.



Estimation is a number sense skill used instead of

finding an exact answer. When an estimate is

needed, the actual computation is not necessary.

Rounding is one strategy used to estimate.

Estimation is also used before solving a problem to

check the reasonableness of the sum when an exact

answer is required.

By estimating the result of a subtraction problem, a place

value orientation for the answer is established.

Subtraction is the inverse operation of addition and is

used for different reasons:

to remove one amount from another;

to compare one amount to another; and

to find the missing quantity when the whole

quantity and part of the quantity are known.

Three terms often used in subtraction are

minuend 98

subtrahend – 41

difference 57

Regrouping is a process of renaming a number to make

subtraction easier.

An understanding of the subtraction algorithm should be

built by first using concrete materials and then

employing a do-and-write approach (i.e., use the

manipulatives, then record what you have done).

This connects the activity to the written form of the

algorithm.

All students should

Understand that estimation skills are valuable, time-

saving tools particularly in practical situations when

exact answers are not required or needed.

Understand that estimation skills are also valuable in

determining the reasonableness of the difference

when solving for the exact answer is needed.

Understand that subtraction is used in practical situations

when exact answers are needed.

Develop flexible methods of subtracting whole numbers

to find the difference, by combining numbers in a

variety of ways, most depending on place values.




Regroup 1 ten for 10 ones, using Base-10 models, such

as Base-10 blocks and bundles of tens.

Estimate the difference of two whole numbers each 99 or

less and recognize whether the estimation is

reasonable.

Find the difference of two whole numbers each 99 or

less, using Base-10 models, such as Base-10 blocks

and bundles of tens.

Solve problems presented vertically or horizontally that

require finding the difference between two whole

numbers each 99 or less, using paper and pencil.

Solve problems, using mental computation strategies,

involving subtraction of two whole numbers each 99

or less.



2.7 The student, given two whole numbers, each of which is 99 or less, will

a) estimate the difference; and

b) find the difference, using various methods of calculation.



Mental computational strategies for subtracting two-digit

numbers might include

lead-digit or front-end strategy:

56 – 21 = __

50 – 20 = 30

6 – 1 = 5

30 + 5 = 35

counting up:

87 – 25 = __

20 + 60 = 80

5 + 2 = 7

60 + 2 = 62

or

87 – 25 = __

25 + 60 = 85

85 + 2 = 87

60 + 2 = 62

or

87 – 25 = __

25 + 2 = 27

27 + 60 = 87

2 + 60 = 62

partial differences:

98 – 41 = __

90 – 40 = 50

8 – 1 = 7

50 + 7 = 57.

Strategies for subtracting two-digit numbers may include

using a hundreds chart, number line, and invented

strategies.



2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture

graphs, and bar graphs.



Problem solving means engaging in a task for which a

solution or a method of solution is not known in

advance. Solving problems using data and graphs

offers a natural way to connect mathematics to

practical situations.

The ability to retrieve information from simple charts

and picture graphs is a necessary prerequisite to

solving problems.

An example of an approach to solving problems is

Polya’s four-step plan:

Understand: Retell the problem.

Plan: Decide what the operation is.

Solve: Write a number sentence.

Look back: Does the answer make sense?

The problem solving process is enhanced when students

create their own story problems; and

model word problems, using manipulatives or

drawings.

All students should

Develop strategies for solving practical problems.

Enhance problem solving skills by creating their own

problems.




Identify the appropriate data and the operation needed to

solve an addition or subtraction problem where the

data are presented in a simple table, picture graph,

or bar graph.

Solve addition and subtraction problems requiring a one-

or two-step solution, using data from simple tables,

picture graphs, bar graphs, and everyday life

situations.

Create a one- or two-step addition or subtraction

problem using data from simple tables, picture

graphs, and bar graphs whose sum is 99 or less.



2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition

and subtraction.



Addition and subtraction are inverse operations, that is,

one undoes the other:

3 + 4 = 7 7 – 3 = 4

7 – 4 = 3 4 + 3 = 7

For each addition fact, there is a related subtraction fact.

Developing strategies for solving missing addends

problems and the missing part of subtraction facts

builds an understanding of the link between addition

and subtraction. To solve

9 – 5 = __, think 5 + __ = 9.

Demonstrate joining and separating sets to investigate

the relationship between addition and subtraction.

All students should

Understand how addition and subtraction relate to one

another.




Determine the missing number in a number sentence

(e.g., 3 + __ = 5 or __+ 2 = 5; 5 – __ = 3 or

5 – 2 = __).

Write the related facts for a given addition or subtraction

fact (e.g., given 3 + 4 = 7, write 7 – 4 = 3 and 7 – 3

= 4).

FOCUS K–3 STRAND: MEASUREMENT GRADE LEVEL 2


Measurement is important because it helps to quantify the world around us and is useful in so many aspects of everyday life. Students in grades K–3

should encounter measurement in many normal situations, from their daily use of the calendar and from science activities that often require students

to measure objects or compare them directly, to situations in stories they are reading and to descriptions of how quickly they are growing.

Measurement instruction at the primary level focuses on developing the skills and tools needed to measure length, weight/mass, capacity, time,

temperature, area, perimeter, volume, and money. Measurement at this level lends itself especially well to the use of concrete materials. Children can

see the usefulness of measurement if classroom experiences focus on estimating and measuring real objects. They gain deep understanding of the

concepts of measurement when handling the materials, making physical comparisons, and measuring with tools.

As students develop a sense of the attributes of measurement and the concept of a measurement unit, they also begin to recognize the differences

between using nonstandard and standard units of measure. Learning should give them opportunities to apply both techniques and nonstandard and

standard tools to find measurements and to develop an understanding of the use of simple U.S. Customary and metric units.

Teaching measurement offers the challenge to involve students actively and physically in learning and is an opportunity to tie together other aspects

of the mathematical curriculum, such as fractions and geometry. It is also one of the major vehicles by which mathematics can make connections

with other content areas, such as science, health, and physical education.

STANDARD 2.10 STRAND: MEASUREMENT GRADE LEVEL 2



a) count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less; and

b) correctly use the cent symbol (¢), dollar symbol ($), and decimal point (.).



The money system used in the United States consists of

coins and bills based on ones, fives, and tens,

making it easy to count money.

The dollar is the basic unit.

Emphasis is placed on the verbal expression of the

symbols for cents and dollars (e.g., $0.35 and 35¢

are both read as “thirty-five cents”; $3.00 is read as

“three dollars”).

Money can be counted by grouping coins and bills to

determine the value of each group and then adding

to determine the total value.

The most common way to add amounts of money is to

“count on” the amount to be added.

All students should

Understand how to count and compare a collection of

coins and one-dollar bills whose total value is $2.00

or less.

Understand the proper use of the cent symbol (¢), dollar

sign ($), and decimal point (.).




Determine the value of a collection of coins and one-

dollar bills whose total value is $2.00 or less.

Compare the values of two sets of coins and one-dollar

bills (each set having a total value of $2.00 or less),

using the terms greater than, less than, or equal to.

Simulate everyday opportunities to count and compare a

collection of coins and one-dollar bills whose total

value is $2.00 or less.

Use the cent (¢) and dollar ($) symbols and decimal

point (.) to write a value of money which is $2.00 or

less.



2.11 The student will estimate and measure

a) length to the nearest centimeter and inch;

b) weight/mass of objects in pounds/ounces and kilograms/grams, using a scale; and

c) liquid volume in cups, pints, quarts, gallons, and liters.



A clear concept of the size of one unit is necessary

before one can measure to the nearest unit.

Knowledge of the exact relationships within the metric

or U.S. Customary system of measurement for

measuring liquid volume, such as 4 cups to a quart,

is not required at this grade level.

Practical experiences measuring liquid volume, using a

variety of actual measuring devices (e.g., containers

for a cup, pint, quart, gallon, and liter), will help

students build a foundation for estimating liquid

volume with these measures.

The experience of making a ruler can lead to greater

understanding of using one.

Proper placement of a ruler when measuring length (i.e.,

placing the end of the ruler at one end of the item to

be measured) should be demonstrated.

Weight and mass are different. Mass is the amount of

matter in an object. Weight is determined by the pull

of gravity on the mass of an object. The mass of an

object remains the same regardless of its location.

The weight of an object changes dependent on the

gravitational pull at its location. In everyday life,

most people are actually interested in determining

an object’s mass, although they use the term weight

(e.g., “How much does it weigh?” versus “What is

its mass?”).

All students should

Understand that centimeters/inches are units used to

measure length.

Understand how to estimate and measure to determine a

linear measure to the nearest centimeter and inch.

Understand that pounds/ounces and kilograms/grams are

units used to measure weight/mass.

Understand how to use a scale to determine the

weight/mass of an object and use the appropriate

unit for measuring weight/mass.

Understand that cups, pints, quarts, gallons, and liters are

units used to measure liquid volume.

Understand how to use measuring devices to determine

liquid volume in both metric and customary units.




Estimate and measure the length of various line

segments and objects to the nearest inch and

centimeter.

Estimate and then measure the weight/mass of objects to

the nearest pounds/ounces and kilograms/grams,

using a scale.

Estimate and measure liquid volume in cups, pints,

quarts, gallons, and liters.



2.11 The student will estimate and measure


b) weight/mass of objects in pounds/ounces and kilograms/grams, using a scale; and




A balance is a scale for measuring mass. To determine

the mass of an object by using a two-pan balance,

first level both sides of the balance by putting

standard units of mass on one side to counterbalance

the object on the other; then find the sum of the

standard units of mass required to level the balance.

Benchmarks of common objects need to be established

for one pound and one kilogram. Practical

experience measuring the mass of familiar objects

helps to establish benchmarks.

Pounds and kilograms are not compared at this level.

The terms cups, pints, quarts, gallons, and liters are

introduced as terms used to describe the liquid

volume of everyday containers.

The exact relationship between a quart and a liter is not

expected at this level.



2.12 The student will tell and write time to the nearest five minutes, using analog and digital clocks.



Telling time requires reading a clock. The position of the

two hands on an analog clock is read to tell the time.

A digital clock shows the time by displaying the

time in numbers which are read as the hour and

minutes.

The use of a demonstration clock with gears ensures that

the positions of the hour hand and the minute hand

are precise at all times.

The face of an analog clock can be divided into

4 equal parts, called quarter hours, of 15

minutes each.

All students should

Apply an appropriate technique to determine time to the

nearest five minutes, using analog and digital

clocks.

Demonstrate an understanding of counting by fives to

predict five minute intervals when telling time to the

nearest five minutes.




Show, tell, and write time to the nearest five minutes,

using an analog and digital clock.

Match a written time to a time shown on a clock face to

the nearest five minutes.




a) determine past and future days of the week; and

b) identify specific days and dates on a given calendar.



The calendar is a way to represent units of time

(e.g., days, weeks, and months).

Using a calendar develops the concept of day as a 24-

hour period rather than a period of time from sunrise

to sunset.

Practical situations are appropriate to develop a sense of

the interval of time between events (e.g., Boy Scout

meetings occur every week on Monday: there is a

week between meetings).

All students should

Understand how to use a calendar as a way to

measure time.




Determine the days/dates before and after a given

day/date.

Determine the day that is a specific number of days or

weeks in the past or in the future from a given date,

using a calendar.

Identify specific days and dates (e.g., the third Monday

in a given month or what day of the week does May

11 fall on).



2.14 The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees.



The symbols for degrees in Celsius (C) and degrees

in Fahrenheit (F) should be used to write

temperatures.

Celsius and Fahrenheit temperatures should be

related to everyday occurrences by measuring the

temperature of the classroom, the outside, liquids,

body temperature, and other things found in the

environment.

Estimating and measuring temperatures in the

environment in Fahrenheit and Celsius require the

use of real thermometers.

A physical model can be used to represent the

temperature determined by a real thermometer.

All students should

Understand how to measure temperature in Celsius and

Fahrenheit with a thermometer.




Read temperature to the nearest 10 degrees from

real Celsius and Fahrenheit thermometers and from

physical models (including pictorial representations)

of such thermometers.

FOCUS K-3 STRAND: GEOMETRY GRADE LEVEL 2


Children begin to develop geometric and spatial knowledge before beginning school, stimulated by the exploration of figures and structures in their

environment. Geometric ideas help children systematically represent and describe their world as they learn to represent plane and solid figures

through drawing, block constructions, dramatization, and verbal language.

The focus of instruction at this level is on

observing, identifying, describing, comparing, contrasting, and investigating solid objects and their faces;

sorting objects and ordering them directly by comparing them one to the other;

describing, comparing, contrasting, sorting, and classifying figures; and

exploring symmetry, congruence, and transformation.

In the primary grades, children begin to develop basic vocabulary related to these figures but do not develop precise meanings for many of the terms

they use until they are thinking beyond Level 2 of the van Hiele theory (see below).

The van Hiele theory of geometric understanding describes how students learn geometry and provides a framework for structuring student

experiences that should lead to conceptual growth and understanding.

Level 0: Pre-recognition. Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided

polygons.

Level 1: Visualization. Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between components

of a figure. Students should recognize and name figures and distinguish a given figure from others that look somewhat the same. (This is the

expected level of student performance during grades K and 1.)

Level 2: Analysis. Properties are perceived but are isolated and unrelated. Students should recognize and name properties of geometric figures.

(Students are expected to transition to this level during grades 2 and 3.)

STANDARD 2.15 STRAND: GEOMETRY GRADE LEVEL 2



a) draw a line of symmetry in a figure; and

b) identify and create figures with at least one line of symmetry.



A figure is symmetric along a line when one-half of the

figure is the mirror image of the other half.

A line of symmetry divides a symmetrical figure, object,

or arrangement of objects into two parts that are

congruent if one part is reflected over the line of

symmetry.

Children learn about symmetry through hands-on

experiences with geometric figures and the creation

of geometric pictures and patterns.

Guided explorations of the study of symmetry by using

mirrors, miras, paper folding, and pattern blocks

will enhance students’ understanding of the

attributes of symmetrical figures.

While investigating symmetry, children move figures,

such as pattern blocks, intuitively, thereby exploring

transformations of those figures. A transformation is

the movement of a figure — either a translation,

rotation, or reflection. A translation is the result of

sliding a figure in any direction; rotation is the result

of turning a figure around a point or a vertex; and

reflection is the result of flipping a figure over a

line.

All students should

Develop strategies to determine whether or not a figure

has at least one line of symmetry.

Develop strategies to create figures with at least one

line of symmetry.

Understand that some figures may have more than one

line of symmetry.




Identify figures with at least one line of symmetry, using

various concrete materials.

Draw a line of symmetry — horizontal, vertical, and

diagonal — in a figure.

Create figures with at least one line of symmetry using

various concrete materials.



2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and

rectangle/rectangular prism).



The van Hiele theory of geometric understanding

describes how students learn geometry and provides a

framework for structuring student experiences that

should lead to conceptual growth and understanding.

Level 0: Pre-recognition. Geometric figures are

not recognized. For example, students cannot

differentiate between three-sided and four-

sided polygons.

Level 1: Visualization. Geometric figures are

recognized as entities, without any awareness

of parts of figures or relationships between

components of a figure. Students should

recognize and name figures and distinguish a

given figure from others that look somewhat

the same (e.g., “I know it’s a rectangle

because it looks like a door, and I know that a

door is a rectangle.”).

Level 2: Analysis. Properties are perceived but are

isolated and unrelated. Students should

recognize and name properties of geometric

figures (e.g., “I know it’s a rectangle because

it is closed; it has four sides and four right

angles, and opposite sides are parallel.”).

An important part of geometry is naming and describing

figures in two-dimensions (plane figures) and three-

dimensions (solid figures).

A vertex is a point where two or more line segments,

lines, or rays meet to form an angle.

An angle is two rays that share an endpoint.

Plane figures are two-dimensional figures formed by

lines that are curved, straight, or a combination of

both. They have angles and sides.

All students should

Understand the differences between plane and solid

figures while recognizing the inter-relatedness of

the two.

Understand that a solid figure is made up of a set of

plane figures.




Determine similarities and differences between related

plane and solid figures (e.g., circle/sphere,

square/cube, rectangle/rectangular prism), using

models and cutouts.

Trace faces of solid figures (e.g., cube and rectangular

solid) to create the set of plane figures related to the

solid figure.

Identify and describe plane and solid figures (e.g.,

circle/sphere, square/cube, and rectangle/rectangular

prism), according to the number and shape of their

faces, edges, and vertices using models.

Compare and contrast plane and solid geometric figures

(e.g., circle/sphere, square/cube, and

rectangle/rectangular prism) according to the

number and shape of their faces (sides, bases),

edges, vertices, and angles.



2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and

rectangle/rectangular prism).



The identification of plane and solid figures is

accomplished by working with and handling objects.

Tracing faces of solid figures is valuable to

understanding the set of plane figures related to the

solid figure (e.g., cube and rectangular prism).

A circle is a closed curve in a plane with all its points the

same distance from the center.

A sphere is a solid figure with all of its points the same

distance from its center.

A square is a rectangle with four sides of equal length.

A rectangular prism is a solid in which all six faces are

rectangles. A rectangular prism has 8 vertices and 12

edges.

A cube is a solid figure with six congruent, square faces.

All edges are the same length. A cube has 8 vertices

and 12 edges. It is a rectangular prism.

A rectangle is a plane figure with four right angles. A

square is a rectangle.

The edge is the line segment where two faces of a solid

figure intersect.

A face is a polygon that serves as one side of a solid

figure (e.g., a square is a face of a cube).

A base is a special face of a solid figure.

The relationship between plane and solid geometric

figures, such as the square and the cube or the

rectangle and the rectangular prism helps build the

foundation for future geometric study of faces, edges,

angles, and vertices.

FOCUS K–3 STRAND: PROBABILITY AND STATISTICS GRADE LEVEL 2


Students in the primary grades have a natural curiosity about their world, which leads to questions about how things fit together or connect. They

display their natural need to organize things by sorting and counting objects in a collection according to similarities and differences with respect to

given criteria.

The focus of probability instruction at this level is to help students begin to develop an understanding of the concept of chance. They experiment with

spinners, two-colored counters, dice, tiles, coins, and other manipulatives to explore the possible outcomes of situations and predict results. They

begin to describe the likelihood of events, using the terms impossible, unlikely, equally likely, more likely, and certain.

The focus of statistics instruction at this level is to help students develop methods of collecting, organizing, describing, displaying, and interpreting

data to answer questions they have posed about themselves and their world.

STANDARD 2.17 STRAND: PROBABILITY AND STATISTICS GRADE LEVEL 2


2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.



The purpose of a graph is to represent data gathered to

answer a question.

Picture graphs are graphs that use pictures to show and

compare information. An example of a picture

graph is:

Our Favorite Pets

Cat Dog Horse Fish

All students should

Understand that data may be generated from

experiments.

Understand how data can be collected and organized in

picture graphs, pictographs, and bar graphs.

Understand that picture graphs use pictures to show and

compare data.

Understand that pictographs use a symbol of an object,

person, etc.

Understand that bar graphs can be used to compare

categorical data.




Organize data from experiments, using lists, tables,

objects, pictures, symbols, tally marks, and charts,

in order to construct a graph.

Read the information presented horizontally and

vertically on picture graphs, pictographs, and bar

graphs.

Collect no more than 16 pieces of data to answer a

given question.

Represent data from experiments by constructing

picture graphs, pictographs, and bar graphs.

Label the axes on a bar graph, limiting the number of

categories (categorical data) to four and the

increments to multiples of whole numbers (e.g.,

multiples of 1, 2, or 5).

On a pictograph, limit the number of categories to four

and include a key where appropriate.






Pictographs are graphs that use symbols to show and

compare information. A student can be represented

as a stick figure in a pictograph. A key should be

used to indicate what the symbol represents (e.g.,

one picture of a sneaker represents five sneakers in a

graph of shoe types). An example of a pictograph

is:

Our Favorite Pets

Cat Dog Horse Fish

= 1 student






Bar graphs are used to compare counts of different

categories (categorical data). Using grid paper may

ensure more accurate graphs.

A bar graph uses parallel, horizontal or vertical

bars to represent counts for several

categories. One bar is used for each category,

with the length of the bar representing the

count for that category.

There is space before, between, and after the bars.

The axis displaying the scale that represents the

count for the categories should extend one

increment above the greatest recorded piece

of data. Second grade students should be

collecting data that are recorded in

increments of whole numbers, usually

multiples of 1, 2, or 5.

Each axis should be labeled, and the graph should

be given a title.



2.18 The student will use data from experiments to predict outcomes when the experiment is repeated.



A spirit of investigation and experimentation should

permeate probability instruction, where students are

actively engaged in investigations and have

opportunities to use manipulatives.

Investigation of experimental probability is continued

through informal activities, such as dropping a two-

colored counter (usually a chip that has a different

color on each side), using a multicolored spinner (a

circular spinner that is divided equally into two,

three, four or more equal “pie” parts where each part

is filled with a different color), using spinners with

numbers, or rolling random number generators

(dice).

Probability is the chance of an event occurring (e.g., the

probability of landing on a particular color when

flipping a two-colored chip is 1

2 , representing one of

two possible outcomes).

An event is a possible outcome in probability. Simple

events include the possible outcomes when tossing a

coin (heads or tails), when rolling a random number

generator (a number cube or a die where there are

six equally likely outcomes and the probability of

one outcome is 1

6 ), or when spinning a spinner.

If all the outcomes of an event are equally likely to

occur, the probability of an event is equal to the

number of favorable outcomes divided by the total

number of possible outcomes: the probability of the

event =

number of favorable outcomes

total number of possible outcomes.

All students should

Understand that data may be generated from

experiments.

Understand that the likelihood of an event occurring is to

predict the probability of it happening.




Conduct probability experiments, using multicolored

spinners, colored tiles, or number cubes and use the

data from the experiments to predict outcomes if the

experiment is repeated.

Record the results of probability experiments, using

tables, charts, and tally marks.

Interpret the results of probability experiments (e.g., the

two-colored spinner landed on red 5 out of 10

times).

Predict which of two events is more likely to occur if an

experiment is repeated.



2.18 The student will use data from experiments to predict outcomes when the experiment is repeated.



At this level, students need to understand only this

fractional representation of probability (e.g., the

probability of getting heads when flipping a coin is 1

2 ).

Students should have opportunities to describe in

informal terms (i.e., impossible, unlikely, as likely

as, equally likely, likely, and certain) the degree of

likelihood of an event occurring. Activities should

include practical examples.



2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.



Statements that represent an analysis and interpretation

of the characteristics of the data in the graph (e.g.,

similarities and differences, least and greatest, the

categories, and total number of responses) should

be discussed with students and written.

When data are displayed in an organized manner, the

results of investigations can be described, and the

questions posed can be answered.

All students should

Understand how to read the key used in a graph to assist

in the analysis of the displayed data.

Understand how to interpret data in order to analyze it.

Understand how to analyze data in order to answer the

questions posed, make predictions, and

generalizations.




Analyze information from simple picture graphs,

pictographs, and bar graphs by writing at least one

statement that covers one or both of the following:

Describe the categories of data and the data as a

whole (e.g., the total number of responses).

Identify parts of the data that have special

characteristics, including categories with the

greatest, the least, or the same.

Select the best analysis of a graph from a set of

possible analyses of the graph.

FOCUS K–3 STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA GRADE LEVEL 2


Stimulated by the exploration of their environment, children begin to develop concepts related to patterns, functions, and algebra before beginning

school. Recognition of patterns and comparisons are important components of children’s mathematical development.

Students in kindergarten through third grade develop the foundation for understanding various types of patterns and functional relationships through

the following experiences:

sorting, comparing, and classifying objects in a collection according to a variety of attributes and properties;

identifying, analyzing, and extending patterns;

creating repetitive patterns and communicating about these patterns in their own language;

analyzing simple patterns and making predictions about them;

recognizing the same pattern in different representations;

describing how both repeating and growing patterns are generated; and

repeating predictable sequences in rhymes and extending simple rhythmic patterns.

The focus of instruction at the primary level is to observe, recognize, create, extend, and describe a variety of patterns. These students will experience

and recognize visual, kinesthetic, and auditory patterns and develop the language to describe them orally and in writing as a foundation to using

symbols. They will use patterns to explore mathematical and geometric relationships and to solve problems, and their observations and discussions of

how things change will eventually lead to the notion of functions and ultimately to algebra.

STANDARD 2.20 STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA GRADE LEVEL 2


2.20 The student will identify, create, and extend a wide variety of patterns.



Identifying and extending patterns is an important

process in mathematical thinking.

Analysis of patterns in the real world (e.g., patterns on a

butterfly’s wings, patterns on a ladybug’s shell)

leads to the analysis of mathematical patterns such

as number patterns and geometric patterns.

Reproduction of a given pattern in a different

manifestation, using symbols and objects, lays the

foundation for writing numbers symbolically or

algebraically.

The simplest types of patterns are repeating patterns.

Opportunities to create, recognize, describe, and

extend repeating patterns are essential to the

primary school experience.

Growing patterns are more difficult for students to

understand than repeating patterns because not only

must they determine what comes next, they must

also begin the process of generalization. Students

need experiences with growing patterns in both

arithmetic and geometric formats.

In numeric patterns, students must determine the

difference, called the common difference, between

each succeeding number in order to determine what

is added to each previous number to obtain the next

number. Create an arithmetic number pattern.

Sample numeric patterns include

6, 9, 12, 15, 18, (growing pattern);

20, 18, 16, 14, (growing pattern);

1, 2, 4, 7, 11, 16, (growing pattern).; and

– 1, 3, 5, 1, 3, 5, 1, 3, 5… (repeating pattern).

All students should

Understand patterns are a way to recognize order and to

predict what comes next in an arrangement.

Analyze how both repeating and growing patterns are

generated.




Identify a growing and/or repeating pattern from a given

geometric or numeric sequence.

Predict the next number, geometric figure, symbol,

picture, or object in a given pattern.

Extend a given pattern, using numbers, geometric

figures, symbols, pictures, or objects.

Create a new pattern, using numbers, geometric figures,

pictures, symbols, or objects.

Recognize the same pattern in different manifestations.



2.20 The student will identify, create, and extend a wide variety of patterns.



In geometric patterns, students must often recognize

transformations of a figure, particularly rotation or

reflection. Rotation is the result of turning a figure

around a point or a vertex, and reflection is the

result of flipping a figure over a line.



2.21 The student will solve problems by completing numerical sentences involving the basic facts for addition and subtraction. The

student will create story problems, using the numerical sentences.



Recognizing and using patterns and learning to represent

situations mathematically are important aspects of

primary mathematics.

Discussing what a word problem is saying and writing a

number sentence are precursors to solving word

problems.

The patterns formed by related basic facts facilitate the

solution of problems involving a missing addend in

an addition sentence or a missing part (subtrahend)

in a subtraction sentence.

Making mathematical models to represent simple

addition and subtraction problems facilitates their

solution.

By using story problems and numerical sentences,

students begin to explore forming equations and

representing quantities using variables.

Students can begin to understand the use of a symbol

(e.g., __, ?, or ) to represent an unknown quantity.

All students should

Use mathematical models to represent and understand

quantitative relationships.

Understand various meanings of addition and subtraction

and the relationship between the two operations.

Understand how to write missing addend and missing

subtrahend sentences.




Solve problems by completing a numerical sentence

involving the basic facts for addition and subtraction

(e.g., 3 + __ = 7, or 9 – __ = 2).

Create a story problem for a given numerical sentence.



2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent

quantities and the symbol ≠ indicates that quantities are not equivalent.



The = symbol means that the values on either side are

the same (balanced).

The ≠ symbol means that the values on either side are

not the same (not balanced).

In order for students to develop the concept of equality,

students need to see the = symbol used in various

locations (e.g., 3 + 4 = 7 and 5 = 2 + 3).

A number sentence is an equation with numbers (e.g., 6

+ 3 = 9; or 6 + 3 = 4 + 5).

All students should

Understand that the equal symbol means equivalent

(same as) quantities.

The inequality symbol (≠) means not equivalent.




Identify the equality (=) and inequality (≠) symbols.

Identify equivalent values and equations. (e.g., 8 = 8 and

8 = 4 + 4)

Identify nonequivalent values and equations. (e.g., 8 ≠ 9

and 4 + 3 ≠ 8)

Identify and use the appropriate symbol to distinguish

between equal and not equal quantities. (e.g., 8 + 2

= 7 + 3 and 1 + 4 6 + 2)

Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 2

Learning Progressions The following pages are the Learning Progressions for the curriculum. More information about the Learning Progressions can be found on VISION. The Grading and Assessment, Module 3: Learning Progressions is about what Learning Progressions are, how they were developed, and how they are used to support instruction and build student learning.


LP 2.1 SOL 2.1: The student will:

a) read, write, and identify the place value of each digit in a 3-digit numeral, using numeration models; b) round two-digit numbers to the nearest ten. c) compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words

(greater than, less than, or equal to). Learning Target: The student will identify the place value and value of each digit in a three-digit number, round two-digit numbers to tens, and

compare whole numbers (0-999) using symbols.

Learning Progression The student will use problem solving, mathematical communication,

mathematical reasoning, connections, and representations at each level of the learning progression.

Advanced Proficient

I can use the relative magnitude of digits in adjoining places to explain rounding and comparing numbers.

Proficient

I can identify the place value and value of each digit in a three digit number, round two-digit numbers to tens, and compare whole numbers (0-999) using symbols.

Intermediate I can round two-digit numbers to tens.

Beginning I can identify the place value and value of each digit in a three digit number presented pictorially, concretely, and numerically.



a) identify the ordinal positions first through twentieth, using an ordered set of objects; and b) write the ordinal numbers.

Learning Target: I can communicate (verbally and in writing) the ordinal positions for each object in a set of 20 objects that are in order (i.e. left-to-right, right-to-left, top-to-bottom, and bottom-to-top).



Advanced Proficient

I can identify the ordinal positions for each object in a set of objects that are placed in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top), and at any starting point in the set. For example:

Proficient

I can communicate (verbally and in writing) the ordinal positions for each object in a set of 20 objects that are in order (i.e. left-to-right, right-to-left, top-to-bottom, and bottom-to-top).

Intermediate

I can count* the twenty objects that are placed in an order (i.e. from left-to-right, right-to-left, top-to-bottom, and bottom-to-top). *This is about cardinal numbers or counting numbers. Cardinal numbers relates to the quantity or count of the objects in the set or sequence.

Beginner

I can organize a set of twenty objects in order (i.e. from left-to-right, right-to-left, top-to-bottom, and bottom-to-top).



a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths; b) write the fractions

Learning Target: I can label fractions using a picture / model. * Parameters: 1. Only Proper Fractions 2. Halves, Thirds, Fourths, Sixths, Eighths, and Tenths 3. Pictures / Models - Set, Area, Linear



Advanced Proficient

I can create multiple pictures / models of a given fraction and identify the numerator and denominator in my models.

Proficient

I can label fractions using a picture / model.

Intermediate

I can identify the part (numerator) and whole (denominator) in a picture / model.


Beginner

I understand that fractions represent dividing things into fair, equal groups.

LP 2.4a SOL 2.4: The student will:

a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10; Learning Target: I can count forward by twos, fives, and tens to 100 starting at various multiples of 2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens.



Advanced Proficient

I can determine a pattern on a hundreds chart for skip counting by twos, fives, and tens when I start with a different number (not a multiple of 2, 5, or 10). I can make connections between this pattern and the pattern when I start with the number 1.

Proficient

I can count forward by twos, fives, and tens to 100 starting at various multiples of 2, 5, or 10. I can determine a pattern for counting by twos, fives, and tens.

Intermediate

I can count forward by twos, fives, and tens to 100 starting with one. I can use a hundred chart to skip count.


Beginner

I understand that the number of objects in a set is the same if I group the set of objects by ones, twos, fives, or tens. * *This is about conservation of numbers. Students understand that the number of objects remain the same even if you group the objects differently.

LP 2.4b SOL 2.4: The student will: b) count backward by tens from 100; Learning Target: I can count backwards by tens from 100 starting at different numbers, including 1.



Advanced Proficient

I can identify the pattern when counting backwards by tens from 100. I can use this pattern to predict the pattern when counting backwards by twenties or thirties from 100.

Proficient

I can count backwards by tens from 100 starting at different numbers, including 1.

Intermediate

I can count forwards by tens to 100 starting at different numbers, including 1.


Beginner

I can count backwards by ones from 30.

LP 2.4c SOL 2.4: The student will: c) recognize even and odd numbers. Learning Target: I can use objects to determine whether a number is odd or even. I can explain why the number is odd or even.



Advanced Proficient

I can identify the pattern of odd and even numbers on a hundred chart. I can use this pattern to predict the pattern of odd and even numbers on a number line.

Proficient



Intermediate

I can use concrete objects to represent sets of up to 100 objects.

Beginner

I can count by ones up to 100.

LP 2.5 SOL 2.5: The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts. Learning Target: I can recall and write addition facts, with sums to 20 or less, and the corresponding subtraction facts (written either horizontally or vertically).



Advanced Proficient

When given a number, I can create several different facts for that sum or difference that matches the number. (i.e. Given the sum of 12, I can create the facts, 10 + 2 = 12, 6 + 6 = 12, 4 + 8 = 12, etc…)

Proficient

I can recall and write addition facts, with sums to 20 or less, and the corresponding subtraction facts (written either horizontally or vertically).


Intermediate

I can model addition and subtraction using concrete objects for sums up to 20 or less and their corresponding subtraction facts.

Beginner

I can add quantities with sums to 20 or less using concrete objects.

LP 2.6 SOL 2.6: The student, given two whole numbers whose sum is 99 or less, will:

a) estimate the sum; and b) find the sum, using various methods of calculation.

Learning Target: I can estimate and find sums of addends (99 or less) using a variety of strategies and tools.



Advanced Proficient

I can use a variety of strategies to estimate and calculate sums and compare and contrast those strategies based on real-life contexts.


Proficient


Intermediate

I can estimate sums to get a reasonable answer.

Beginner

I can understand the structure of an addition problem (a part plus a part equals a sum).

LP 2.7 SOL 2.7: The student, given two whole numbers, each of which is 99 or less, will:

a) estimate the difference; and b) find the difference, using various methods of calculation.

Learning Target: I can estimate and find differences of two numbers (99 or less) using a variety of strategies and tools.




Advanced Proficient

I can use a variety of strategies to estimate and calculate differences and compare and contrast those strategies based on real-life contexts.

Proficient


Intermediate

I can estimate differences to get a reasonable answer.

Beginner

I can understand the structure of a subtraction problem (whole minus a part equals a part).

LP 2.8 SOL 2.8: The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs. Learning Target: I can use problem solving strategies to use information from tables and graphs to solve one- and two-step addition and subtraction problems.




Advanced Proficient

I can create a real-life problem solving situation involving addition and/or subtraction and a table/graph to represent the problem.

Proficient

I can use problem solving strategies to use information from tables and graphs to solve one- and two-step addition and

subtraction problems.

Intermediate

I can find relevant information in a simple table, picture graph, and/or bar graph and determine whether to add and/or subtract in a problem.

Beginner

I can solve one- and two-step addition and subtraction problems.

LP 2.9 SOL 2.9: The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction. Learning Target: I can demonstrate how addition and subtraction facts are related using models/structures and describe their relationship.

Learning Progression

The student will use problem solving, mathematical communication,



Advanced Proficient

I can use multiple strategies to solve related addition and subtraction facts and compare and contrast those strategies.

Proficient

I can demonstrate how addition and subtraction facts are related using models/structures and describe their

relationship.

Intermediate

I understand that addition and subtraction are inverse relationships.

Beginner

I can model addition facts (combining) and subtraction facts (separating).


a) count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and decimal point (.).


Learning Target: I can count a collection of coins (pennies, nickels, dimes, and quarters) whose value is $2.00 or less, write the amount using correct symbols, and compare collections from everyday situations.



Advanced Proficient

I can create situations in which counting and comparing collections of coins would be relevant and compare and contrast strategies for counting a collection of coins.

Proficient

I can count a collection of coins (pennies, nickels, dimes, and quarters) whose value is $2.00 or less, write the amount using correct symbols, and compare collections from everyday situations.

Intermediate I can count a collection of coins (pennies, nickels, dimes, and quarters) whose value is $1.00 or less and write the amount using correct symbols,

Beginning I can name the value of a penny, nickel, dime, and quarter and recognize the symbols for writing money values.

LP 2.11 SOL 2.11: The student will estimate and measure:


b) weight/mass of objects in pounds/ounces and kilograms, grams, using a scale; and



Learning Target: I can estimate and measure length (nearest inch and centimeter), weight/mass (nearest pounds/ ounces and kilograms/grams) and liquid volume (nearest cups, pints, quarts, gallons, and liters).



Advanced Proficient

Proficient

I can estimate and measure length (nearest inch and centimeter), weight/mass (nearest pounds/ ounces and kilograms/grams) and liquid volume (nearest cups, pints, quarts, gallons, and liters).

Intermediate I can estimate length, weight/mass, and liquid volume of many objects.

Beginning I know what units measure which attributes and have a clear idea of the size of one unit.

LP 2.12 SOL 2.12: The student will tell time and write time to the nearest five minutes, using analog and digital clocks. Learning Target: I can tell and write time to the nearest five minutes, using analog and digital clocks.




Advanced Proficient

I can tell time, using analog and digital clocks, and justify examples of appropriate activities for different time periods (ie. It takes 20 minutes to walk a mile, I wake up at 6:30am, etc.)

Proficient

I can tell and write time to the nearest five minutes, using analog and digital clocks.

Intermediate

I can match a written time to a time shown on a clock to the nearest 5 minutes.

Beginner

I can use skip counting by 5s to help me tell and write time to the nearest five minutes.


a) determine past and future days of the week; and b) identify specific days and dates on a given calendar.


Learning Target: I can use a calendar to determine specific days and dates in the past, present, and in the future.



Advanced Proficient

I can determine the amount of time between two events on a calendar, in terms of days, weeks, and/or months. (i.e. there is one week between each of our Homework Club meetings, there is one month between our Bowling club meetings, there is 3 weeks and 2 days between my doctor’s appointments).

Proficient


Intermediate

I can use a calendar to determine specific days/dates up to one week in the past and in the future. I can use the terms yesterday, tomorrow, next week, and last week correctly to describe specific days/dates.

Beginner

I understand that the calendar is a tool used to measure time. I can use a calendar to identify the months of the year, identify the seven days of the week, and identify today’s date and day.

LP 2.14 SOL 2.14: The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees.


Learning Target: I can use a Celsius and Fahrenheit thermometer to tell temperature to the nearest 10 degrees.



Advanced Proficient

I can estimate and predict the Celsius and Fahrenheit temperature for a given situation (without measuring the temperature) and connect it to a similar classroom experience. (i.e. Q: What do you think is the temperature of this glass of soda that was left out in our classroom overnight? A: I am guessing the temperature is about 70o Fahrenheit. Yesterday, we measured the temperature of a glass of water that was left out in our classroom. The temperature of the water was about 70o Fahrenheit.)

Proficient


Intermediate

I know how to use a Celsius and Fahrenheit thermometer to measure the temperature. I can show which part of the thermometer I need to look at to read the temperature.* *This is about the procedure for using a thermometer to measure temperature in different situations. This level is also about identifying the parts of a thermometer they focus on in order to read the temperature.

Beginner

I can identify the thermometer (both Celsius and Fahrenheit) as a tool to measure temperature.

LP 2.15


SOL 2.15: The student will: a) draw a line of symmetry in a figure; and b) identify and create figures with at least one line of symmetry.

Learning Target: I can develop strategies to identify line(s) of symmetry in a figure, create symmetrical figures, and draw line(s) of symmetry using

a variety of math tools.



Advanced Proficient

I can create a figure to fit a set of clues (for example: Draw a figure with zero lines of symmetry and three vertices. Draw a figure with exactly six lines of symmetry.).

Proficient

I can develop strategies to identify line(s) of symmetry in a figure, create symmetrical figures, and draw line(s) of

symmetry using a variety of math tools.

Intermediate

I can use a variety of strategies to identify lines of symmetry in a figure.

Beginner

I can identify symmetrical and non-symmetrical figures.


LP 2.16 SOL 2.16: The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism). Learning Target: The student describe, identify, compare and contrast related plane and solid figures.



Advanced Proficient

I can justify my identifications and comparisons of plane and solid figures.

Proficient

I can describe, identify, compare and contrast related plane and solid figures.

Intermediate I can relate numbers of edges, vertices, and angles to faces and bases of solid figures.

Beginning I can trace faces of solid figures and identify the plane figures related to the solid figure.


LP 2.17 SOL 2.17: The student will use data from experiments to construct picture graphs, pictographs, and bar graphs. Learning Target: I can collect and organize data to construct picture graphs, pictographs, and bar graphs. I can read the information presented on these data graphs (representations).



Advanced Proficient

I can take existing data graphs (representations) and create a different representation on a picture graph, pictograph, and bar graph (i.e. using different pictures to represent the same data, using a different increment for a bar graph, using a different key for a pictograph, or organizing the data into different categories).

Proficient

I can collect and organize data to construct picture graphs, pictographs, and bar graphs. I can read the information presented on these data graphs (representations).

Intermediate

I can compare data graphs (representations) and tell the similarities and differences between picture graph, pictograph, and bar graphs.

Beginner

I can use counting and tallying, informal surveys, observations, and voting to collect data in everyday situations.


LP 2.18 SOL 2.18: The student will use data from experiments to predict outcomes when the experiment is repeated. Learning Target: I can use data from my experiments to predict outcomes when I repeat my experiment.



Advanced Proficient

I can predict which of two experiments is more likely to occur if an experiment is repeated.

Proficient I can use data from my experiments to predict outcomes when I repeat my experiment.

Intermediate I can record the outcomes of my probability experiments using tables, charts, and tally marks and interpret the results of the experiments.

Beginning I can conduct experiments about probability using spinners, color tiles, number cubes.


LP 2.19 SOL 2.19: The student will analyze data displayed in picture graphs, pictographs, and bar graphs. Learning Target: I can analyze data displayed in picture graphs, pictographs, and bar graphs in order to answer questions posed, make predictions and generalizations.



Advanced Proficient

I can select the best analysis of a graph from a set of possible analyses of the graph and justify my selection in writing.

Proficient

I can analyze data displayed in picture graphs, pictographs, and bar graphs in order to answer questions posed, make predictions and generalizations.

Intermediate I can describe the categories of data and the data as a whole, and identify parts of the data that have special characteristics.

Beginning I can read the key used in graphs.


LP 2.20 SOL 2.20: The student will identify, create, and apply a wide variety of patterns. Learning Target: I can identify, create, and apply a wide variety of patterns.



Advanced Proficient

I can identify real world situations that reflect one of the patterns we used in class.

Proficient


Intermediate

I can extend a variety of patterns (including patterns with numbers, geometric figures, pictures, symbols, or objects).

Beginner

I can identify and describe the pattern in a variety of patterns (numerical or geometric pattern).


LP 2.21 SOL 2.21: The student will solve problems by completing numerical sentences involving the basic facts for addition and subtraction. The student will create story problems, using the numerical sentences. Learning Target: I can use mathematical models to represent basic addition and subtraction number sentences and create story problems for those

sentences.



Advanced Proficient

I can create multiple story problems for each addition or subtraction fact and justify models used to represent each situation.

Proficient

I can use mathematical models to represent basic addition and subtraction number sentences and create story problems for

those sentences.

Intermediate

I can model an addition and subtraction problem using manipulatives.


Beginner

I understand that addition means a part plus a part equals a whole and that subtraction means that a whole minus a part equals a part.


LP 2.22 SOL 2.22: The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ≠ indicates that quantities are not equivalent. Learning Target: I can demonstrate that some number sentences are balanced (=) and some are not balanced (≠).



Advanced Proficient

I can create multiple models and real-life contexts to represent balanced and unbalanced number sentences.

Proficient

I can demonstrate that some number sentences are balanced (=) and some are not balanced (≠).

Intermediate

I can use models to represent that a number sentence is balanced.

Beginner

I can recognize that a number sentence represents a mathematical relationship.

Grade 2 Math Intervention Ideas

Unit 2 – Extending Place Value

Hands-On Standards Book Grades 1-2 Every Day Counts Partner Games

Number and Operations Lessons 1-5, 14 Algebra Lessons 4-8

Game #2: Odd and Even? Game #3: Teen Concentration Game #4: Make The Sum Game #5: Two More, Two Less Neighbors Game #8: Get Them In Order Game #11: Go For 100, One Way or Another Game #12: Track Race Game #13: Try for 100

Unit 3 – Computational Fluency


Number and Operations Lessons 9-21 Algebra Lessons 4-8

Game #4: Make The Sum Game #5: Two More, Two Less Neighbors Game #6: 1-12 Crossout Game #7: Keep The Difference Game #9: Doubles and Doubles Plus 1 Search Game #10: Fast Ten – Yes or No? Game #11: Go For 100, One Way or Another Game #14: Double Digit Addition Game #15: Penny Give Away Game #16: Double Trouble Game #17: Teen Take-Away Game #20: Pyramid Ten

Unit 4 – Applying Place Value to Computation/Problem Solving


Number and Operations Lessons 5-21

Game #4: Make The Sum Game #5: Two More, Two Less Neighbors Game #6: 1-12 Crossout Game #7: Keep The Difference Game #8: Get Them In Order Game #9: Doubles and Doubles Plus 1 Search Game #10: Fast Ten – Yes or No? Game #11: Go For 100, One Way or Another Game #13: Try for 100 Game #14: Double Digit Addition Game #15: Penny Give Away Game #16: Double Trouble Game #17: Teen Take-Away Game #20: Pyramid Ten

Unit 5 – Probability & Data


Number and Operations Lessons 22-24 Data Analysis and Probability Lessons 1-6

Game #19: Pizza Maker

Unit 6 – Data & Problem Solving


Data Analysis and Probability Lessons 5-6

Unit 7 – Time & Temperature


Measurement Lessons 12-13

Unit 8 – Geometry & Fractions


Number and Operations Lessons 23-24 Geometry Lesson 4

Game #19: Pizza Maker

Unit 9 – Measuring My World


Measurement Lessons 1-7, 10-13

Unit 10 – Skip Counting & Money


Algebra Lessons 4-8

Game #1: Coin Collector

Resources available in all LCPS Elementary Schools

Hands-On Standards books Every Day Counts Partner Games

NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)

VA SOL Alignment

Kindergarten Math

Domino Addition and Subtraction

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Activity

SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

Counting Sheep

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.

Activity SOL K.3 The student, given an ordered set of ten objects and/or

pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.

How Big is Your Foot?

Launch & Activity

SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.

1st Grade Math

Bunny Hip Hop

Launch

SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;

and b) group a collection of up to 100 objects into tens and ones and

write the corresponding numeral to develop an understanding of place value.

Activity

SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.

When does it Happen?

Launch & Activity

SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.

Ten is our Friend!

Launch

SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.

Activity SOL 1.6 The student will create and solve one-step story and picture

problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.

2nd Grade Math

Creative Cards

Launch & Activity

SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).

Piggy Banks

Launch & Activity

SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and

quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and

decimal point (.).

Show What You Know!

Launch

SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an

ordered set of objects; and b) write the ordinal numbers.

Activity

SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.

SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.

Pies for Sale

Launch SOL 2.19 The student will analyze data displayed in picture graphs,

pictographs, and bar graphs.

Activity

SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.

SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.

3rd Grade Math

Playful Puppies

Launch

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Activity

SOL 3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.

SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Correcting the Calculator

Launch & Activity

SOL 3.1 The student will a) read and write six-digit numerals and identify the place value

and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,

hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using

symbols (>, <, or = ) and words (greater than, less than, or equal to).

SOL 3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.

Fraction Reactions

Launch & Activity

SOL 3.3 The student will a) name and write fractions (including mixed numbers)

represented by a model; b) model fractions (including mixed numbers) and write the

fractions’ names; and c) compare fractions having like and unlike denominators, using

words and symbols (>, <, or =).

4th Grade Math

Bugs, Giraffes, Elephants, and More

Launch

SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.

SOL 4.7 The student will a) estimate and measure length, and describe the result in

both metric and U.S. Customary units; and b) identify equivalent measurements between units within

the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Activity

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Does it Make Sense?

Launch

SOL 4.3 The student will a) read, write, represent, and identify decimals expressed

through thousandths; b) round decimals to the nearest whole number, tenth, and

hundredth; c) compare and order decimals; and

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

Activity

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

The Bigger Half

Launch & Activity


Harry’s Hike

Launch


Activity

SOL 4.5 The student will a) determine common multiples and factors, including least

common multiple and greatest common factor; b) add and subtract fractions having like and unlike

denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving

addition and subtraction with fractions and with decimals.

5th Grade Math

Packed Parking

Launch

SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Activity

SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers

expressed as decimals through thousandths (divisors with only one nonzero digit); and

b) create and solve single-step and multistep practical problems involving decimals.

SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Finding Fractions

Launch

SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form

and vice versa; and b) compare and order fractions and decimals in a given set from

least to greatest and greatest to least.

Activity

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Varying Volumes

Launch & Activity

SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify

whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;

c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.

Customary and metric units; and e) choose an appropriate unit of measure for a given situation

involving measurement using U.S. Customary and metric units.

SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and b) investigate and describe the results of combining and

subdividing plane figures.

Location, Location, Location

Launch

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

Activity

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Mathematics Literature Connections Organized by Curriculum Units

Grade K Math Literature Connections

Unit 2: Counting

One, Two, Skip a Few: First Number Rhymes by Roberta Arenson

98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater

Unit 3: Comparing Sets

20 Hungry Piggies: A Number Book by Trudy Harris

Ten Little Rubber Ducks by Eric Carle

Ten Little Caterpillars by Bill Martin Jr

Henry the Fourth by Stuart J. Murphy

One Monday Morning by Uri Shulevitz

The Napping House by Audrey Wood

Tally O’Malley by Stewart J. Murphy

So you want to be President? By Judith St. George

The Great Graph Contest By Loreen Leedy

Unit 4: Geometry & Sorting

Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy

Unit 5: Shapes in Space

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 6: Geometry & Fractions

Give Me Half by Stuart J. Murphy

Full House by Dayle Ann Dodds

Unit 7: Measuring My World

Measuring Up by J.E. Osborne

Dumpling Soup by Jama Kim Rattigan

How Big is a Foot by Rolf Myller

Big and Little by Steven Jenkins

Time to… by Bruce McMillan

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

Telling Time with Big Mama Cat by D. Harper

Biggest, Strongest, Fastest by Steven Jenkins

Inch by Inch by Leo Lionni

Before and After: A Book of Nature Timescapes by Jan Thornhill

Unit 8: Skip Counting & Money

Arctic Fives Arrive by Elinor J. Pinczes

26 Letters and 99 Cents by Tana Hoban

Unit 9: Combining & Separating

More or Less by Stuart J. Murphy

Animals on Board by Stuart J. Murphy

A Quarter from the Tooth Fairy by Caren Holtzman

Grade 1 Math Literature Connections

Unit 2: Sorting, Ordering, & Patterns

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 3: Developing a Base Ten System

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Is It Larger? Is It Smaller? By T. Hoban

One Hundred Hungry Ants by Elinor J. Pinczes

Ten Sly Piranhas: A Counting Story in Reverse by William Wise

How Many, How Many, How Many by Rick Walton

98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater

Stay in Line by Teddy Slater


Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone

Flat Stanley by J. Brown

The Shapes We Eat by Simone T. Ribke

Give Me Half! By Stuart J. Murphy

Gator Pie by L. Mathews

Unit 5: Time & Fractions


Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Unit 6: Working With Data

Probably Pistachio by Stuart J. Murphy

So You Want to be President? By Judith St. George

The Great Graph Contest by Loreen Leedy

Ready, Set, Hop! By Stuart J. Murphy

Bunches and Bunches of Bunnies by Mathews and Bassett

Unit 7: Combining & Separating

Rooster’s Off to See the World by Eric Carle

Round Trip by A. Jonas

Lemonade For Sale by Stuart J. Murphy


How Do You Measure Weight? by Thomas K. and Heather Adamson

The Greedy Triangle by Marilyn Burns


How Big is a Foot? by Rolf Myller


Biggest, Strongest, Fastest by Steven Jenkins



Best Bug Parade by Stuart J. Murphy

Me and the Measure of Things by J. Sweeney

Unit 9: Applying Place Value

Shoes, Shoes, Shoes by A. Morris

Unit 10: Whole Number Computation

Animals on Board by Stuart J. Murphy

Elevator Magic by Stuart J. Murphy

Ten Black Dots by Donald Crew

Rooster’s Off to See the World by Eric Carle


How High Can a Dinosaur Count? by V. Fisher


The Penny Pot by Stuart J. Murphy


Unit 2: Extending Place Value

The Crayon Counting Book by Pam Munoz

Underwater Counting: Even Numbers by Jerry Pallotta

Unit 3: Computational Fluency

Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell

Mission: Addition by Loreen Leedy

Each Orange Had 8 Slices: A Counting Book by Paul Giganti


Unit 4: Applying Place Value to Computation/Problem Solving

Great Estimations by Bruce Goldstone

How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas

How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns

Sam and the Lucky Money by K. Chinn

Balancing Act by Ellen Stoll Walsh

Betcha by Stuart J. Murphy

Unit 5: Probability & Data

Frog and Toad are Friends by A. Lobel

Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel

Get Up and Go! By Stuart J. Murphy

Unit 6: Data & Problem Solving

So You Want to be President? By Judith St. George

Unit 7: Time & Temperature

Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema

The Grouchy Lady Bug by Eric Carle

Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel

What Time Is It? A Book of Math Riddles by Sheila Keenan


Eating Fractions by Bruce McMillan


Full House by Dayle Ann Dodds

The Patchwork Quilt by Valerie Flournoy



How Big is a Foot? By Rolf Myller



Biggest, Strongest, and Fastest by Steven Jenkins



Jelly Beans for Sale by Bruce McMillan

The Penny Pot by Stuart J. Murphy

The Coin Counting Book by Rosanne Lanczak Williams

Once Upon a Dime by Nancy Kelly Allen


Unit 2: Place Value

Many Is How Many? By Illa Pondendorf

A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein

Counting on Frank by Rod Clement

How Much Is a Million? by David M. Schwartz

If You Made a Million by David M. Schwartz

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Unit 3: Computation With Whole Numbers (addition/subtraction)

Ten Black Dots by Donald Crews

Dealing with Addition Lynette Long

One Duck Stuck by Phyllis Root

One Gorilla by Atsuko Morozumi

A Three Hat Day by Laura Geringer

Unit 4: Money

Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Penny: The Forgotten Coin by Denise Brenna-Nelson

The Coin Counting Book by Rozanne Lanczak Williams

The Penny Pot by Stuart Murphy

Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod

Unit 5: Computation With Whole Numbers (multiplication/division)

Amanda Bean’s Amazing Dream by Cindy Neuschwander

A Remainder of One (*extension) by Elinor J. Pinczes

One Hundred Angry Ants by Elinor J. Pinczes

2 x 2 = Boo by Loreen Leedy

7 x 9 Trouble by Claudia Mills

Too Many Kangaroo Things to Do by Stuart Murphy

Divide and Ride by Stuart Murphy

Bananas Jacqueline Farmer

Centipede’s 100 Shoes by Tony Ross

Ten Times Better by Richard Michelson

Unit 6: Patterns & Data

Emma’s Christmas by Irene Trivias

The Doorbell Rang by Pat Hutchins

One Hundred Angry Ants by Elinor Pinczes

She Came Bringing Me That Little Baby Girl by Eloise Greenfield

Knots on a Counting Rope by Bill Martin Jr.

Berries, Nuts, and Seeds by Diane L. Burns

Lemonade for Sale by Stuart Murphy

Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda

Grapes of Math by Greg Tang

The Quilting Bee by Gail Gibbons

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

Unit 7: Geometry

The Important Book by Margaret Wise Brown

Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone

Pablo’s Tree Pat Mora

If You Were a Polygon Marcie Aboff

It Looked Like Spilt Milk by Charles G. Shaw

Mummy Math by Cindy Neuschwander

Shape Up by David Adler

A Cloak for the Dreamer by Aileen Friedman

Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions

Eating Fractions by Bruce McMillan

Seven Little Hippos by Mike Thaler

Shoes, Shoes, Shoes by Ann Morris

Biggest, Strongest, Fastest Steve Jenkins

The Wolf’s Chicken Stew Keiko Kasza

A Very Improbably Story: A Math Adventure by Edward Einhorn

The Thirteen Days of Halloween Carool Greene

The Doorbell Rang Pat Hutchins

Whole-y Cow, Fractions are Fun! by Taryn Souders

Apple Fractions by Jerry Pallotta

The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta

Fraction Action by Loreen Leedy

Unit 10: Elapsed Time and Temperature

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

What Time is it, Mr. Crocodile? By Judy Sierra

Chimp Math by Ann Whitehead Nagda

Unit 11: Measurement

Spaghetti and Meatballs for All by Marilyn Burns

Perimeter, Area, and Volume David A. Adler

Pastry School in Paris Cindy Neuschwander

Measuring Penny (length) by Loreen Leedy

Biggest, Strongest, Fastest by Steve Jenkins

Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells

Polly’s Pen Pal by Stuart L. Murphy


Room for Ripley by Stuart Murphy


Unit 2: Number Sense: Whole Numbers

A Million Fish…More or Less by Patricia C. McKissack

Unit 3: Whole Number Operations & Applications (adding & subtracting)

Math Curse by Jon Scieszka and Lane Smith

The $1.00 Word Riddle Book by Marilyn Burns

Esio Trot by Roald Dahl

From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine

Giesecke

Anno’s Magic Seeds by Mitsumasa Anno

Equal Shmequal by Virginia Kroll

Unit 4: Whole Number Operations & Applications (multiplication & division)

The King’s Chessboard by David Birch

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Math Curse by Jon Scieszka and Lane Smith

Hottest, Coldest, Highest, Deepest by Steve Jenkins

In the Next Three Seconds…Predictions for the Millenium by Comp. Rowland Morgan

Ten Times Better by Richard Michelson

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

A Remainder of One by Elinor J. Pinczes

Counting on Frank by Rod Clement

Unit 5: Data & Statistics

The Great Graph Contest by Loreen Leedy

Unit 6: Number Sense: Rational Numbers

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

One Riddle, One Answer by Lauren Thompson

Icebergs and Glaciers by Seymour Simon

Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel

Unit 7: Rational Number Operations

Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley

Pizza Counting by Christina Dobson

Piece=Part=Portion by Gifford and Thaler

Fractions=Trouble! By Claudia Mills

Unit 8: Probability & Data Using Rational Numbers

Jumanji by Chris Van Allsburg

A Very Improbable Story by Edward Einhorn and Adam Gustavson

Pigs at Odds by Amy Axelrod and Sharon Nally

Unit 9: Patterns & Measurement

G is for Googol: A Math Alphabet Book by David M. Schwartz

How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen

Nolan

Icebergs and Glaciers by Seymour Simon

If You Hopped Like a Frog by David M. Schwartz

Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells

Biggest, Strongest, Fastest by Steve Jenkins

Unit 10: Plane Geometry & Transformations

Marvelous Math by Lee Bennett Hopkins

The Warlord’s Puzzle by Virginia Walton Pilegard

Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin

Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley

Chickens on the Move (Math Matters!) by Pamela Pollack


Unit 2

A Remainder of One by Elinor Pinczes

My Even Day by Doris Fisher

The Grapes of Math by Greg Tang

Math Appeal by Greg Tang

Among the Odds and Evens by Prescilla Turner


Unit 3

Germs Make Me Sick by Melvin Berger

Bats on Parade by Kathi Appelt

Unit 4

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Fraction Fun by David Adler

Unit 5

Measuring Penny by Loreen Leedy

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Counting On Frank by Rod Clements

How Long? How Wide? by Brian Cleary

Millions to Measure by David Schwartz

Fractions, Decimals, and Percents by David Adler

Unit 6

The Greedy Triangle by Marilyn Burns

Sir Cumference and the Dragon of Pi by Cindy Neuschwander

Unit 7

Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda

A More Perfect Union by Betsy Maestro

Model Performance Indicator Information for Curriculum Guides

Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).

These tables will be useful as you differentiate instruction for all of your learners, but they are especially

helpful for English Language Learners. Below are frequently asked questions about MPI.

What is a Model Performance Indicator (MPI)?

An MPI is a tool that can be used to show examples of how language is processed or produced within a

particular context, including the language with which students may engage during classroom instruction and

assessment.

Each MPI contains three main parts:

Language Function: The first part of an MPI, this shows how students are processing/producing

language at each level of language proficiency

Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge

and skills of the state’s content standards

Support: The final part of an MPI, this highlights the differentiation that should be incorporated for

students at each language level by suggesting appropriate instructional supports for students at each

level of language proficiency

The samples provided also include an example context for language use that provides a brief descriptor of the

activity or task in which students would be engaged, while the inclusion of topic-related language helps to

support the emphasis on imbedding academic language instruction into our content-area teaching practices.

How can these sample MPIs help me?

Educators can use MPI strands in several ways:

to align students’ performance to levels of language development

as a tool for creating language objectives/targets that will help extend students’ level of language

proficiency

as a means for differentiating instruction that incorporates the language of the content area in a way that

meets the needs of students’ levels of language proficiency

An MPI strand helps illustrate the progression of language development from one proficiency level to the next

within a particular context. As these strands are examples, they represent one of many possibilities; therefore,

they can be transformed in order to be made more relevant to the individual classroom context.

Where can I get more information about WIDA, MPIs, etc.?

See My Learning Plan for several WIDA training modules

Introduction to the WIDA ELD Standards

Transforming the WIDA ELD Standards

Interpreting the WIDA ACCESS Score Report

The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at

www.wida.us

http://www.wida.us/

SOL Strand and Bullet: 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.

Example Context for Language Use: Students will create and interpret data in graphs or in a variety of graphs (e.g., picture graphs, pictographs, bar

graphs).

COGNITIVE FUNCTION: Students of all levels of English language proficiency will ANALYZE data in graphs or in a variety of graphs.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Select single words to

identify data in graphs

in a small group (e.g.,

more, less, or fewer….)

Interpret data in graphs

using sentence frames

(e.g. ______ is the most

liked food)

Compare data in graphs

with a partner (e.g., more

students like basketball

than football )

Explain data in graphs

with a partner (e.g.,

soccer is the most

popular because 10 out of

15 voted for it)

Discuss data in graphs

collected from

experiments and

present with a partner

(e.g., Do you think

basketball and soccer

are equally liked?)

RE

AD

ING

Discover the relationship

of data in graphs using a

simple tally chart in a

small group (e.g., teacher

gives students a data

chart and asks them to

match the data chart with

the correct graph)

Examine data in graphs

(pictographs or bar

graphs) with a partner

(e.g., find the graph that

shows the data presented

by the tally chart)

Organize data in graphs

(pictographs or bar

graphs) in a small group

(e.g., read the data from a

graph and decide as a

group on the type of graph

that should be used to

represent the data)

Organize data in graphs

(pictographs or bar

graphs) with a partner

(e.g., read the data from a

graph and decide as a

group on the type of

graph that should be used

to represent the data)

Evaluate data in

graphs and compare

with a partner

WR

ITIN

G

Build a variety of

graphs, using data from

a chart in a small group

Build a variety of

graphs using data from

a chart with a partner

Compose sentences about

a variety of graphs using a

sentence frame with a

partner

Compose sentences about

a variety of graphs using

a sentence frame

Compose answers to

questions about the

data on a variety of

graphs with a partner

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade-level words and expressions, such as:

graph, chart, data, line graph, picture graph, pictographs, bar graphs, pie graph, table, less, fewer, more, least, most, chart, tally, interpret.

WR

ITIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging Lev

el 6-R

each

ing

Categorize pictures of the

data from a simple

probability experiment as a

class

Record the results of data

from a simple probability

experiment in a small

group using a data chart

Create a graph to show the

data results from a simple

probability experiment in a

small group using a template

for a pictograph

Design a graph to show the

data results from a simple

probability experiment with

a partner using a template

for a bar graph

Compose a four-sentence

written prediction about

the outcomes of

repetitions of a simple

probability experiment

using a data chart, bar

graph, or pictograph

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade-level words and expressions, such as:

table(s), object(s), pictorial representations, tally marks, chart(s), graph(s), pictographs, bar graphs, data, axes, probability, outcome(s) impossible,

unlikely, likely, equally likely, certain, categorize, record, create, design, compose

SOL Strand and Bullet: 2.18 The student will use data from experiments to predict outcomes when the experiment is repeated.

Example Context for Language Use: Students will work in small groups to conduct a simple probability experiment with colored objects, record

the data, and use the data to predict outcomes when the experiment is repeated.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will EVALUATE data from a simple probability experiment to

predict outcomes of repeated experiments.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Analyze yes/no questions

about data from a simple

probability experiment in a

small group (e.g., “Do you

think the red color will be

picked the most?)

Examine patterns in data


experiment using sentence

starters with a partner

(e.g., I predict that

____color will _______ be

picked the least.)

Compare results of data


experiment using a data

chart with a partner

Explain observations of

data from a simple


using a data chart with a

partner

Predict and discuss the

outcomes of repetitions of

a simple probability

experiment using a data

chart

R

EA

DIN

G

Identify the graph that

correctly shows the data


experiment as a class (e.g.

Teacher shows the students

different graphs and asks

students to identify the

graph that shows the date

correctly.)

Examine the data from a

simple probability

experiment in a small

group using illustrated text

Draw conclusions about the

data from a simple


a partner using content terms

(e.g., “unlikely,” “likely,”

“most likely,” “impossible,

and “certain.”)

Analyze data from a simple


a partner using a question

cube

Formulate a prediction

about the outcomes of

repetitions of a simple


using a data chart

SOL Strand and Bullet: 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs

Example Context for Language Use: After students conduct a classroom survey and record data from tally marks on a picture graph, pictograph,

and bar graph, students will explore graphs as a whole group. Students will then work in small groups or with a partner to analyze each graph.

Students will work as a class to select the best analysis of the data on a graph.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE data displayed in picture graphs, pictographs,

and bar graphs.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify categories of data

displayed in picture graphs,

pictographs, and bar graphs

as a class (e.g., the parts of

a graph, the key to reading

the graph, etc.)

Describe data displayed in

picture graphs,

pictographs, and bar

graphs in a small group

(e.g., how many students

picked red as their favorite

color)

Compare the data displayed

in picture graphs,


in a small group (e.g., which

color has the most, least,

fewest)

Compare and contrast the

data displayed in picture

graphs, pictographs, and

bar with a partner (e.g.,

how does each graph show

the data)

Explain the data

displayed in picture

graphs, pictographs, or

bar graphs with a partner

RE

AD

ING

Associate tally marks from

the classroom survey with

the data displayed in picture


bar graphs as a class

Classify data displayed in

picture graphs,

pictographs, and bar

graphs to answer questions

about survey results as a

class (e.g., each graph

shows that 10 boys

selected soccer)

Develop questions about


graphs, pictographs, or bar

graphs with a partner (e.g.,

“Which sport is the most

favorite?” “Which is the

least favorite?”)

Draw a conclusion about

the classroom survey

results from data displayed

in picture graphs,

pictographs, or bar graphs

with a partner (e.g., “Boys

like to play soccer.”)

Make a general inference

about the survey results

based on data displayed

in picture graphs,

pictographs, or bar graphs

with a partner (e.g.,

“Boys will always want

to play outside during

recess.”)

WR

ITIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Connect ideas about the



bar graphs as a class using a

word/picture bank

Describe the categories of

data displayed on a picture

graph, pictograph, and bar

graph in a small group

using sentence strips

Explain in complete

sentences the data displayed

in picture graphs,

pictographs, or bar graph

with a partner

Create a display board

showing a written

explanation about the

classroom survey results

data on picture graphs,


with a partner

Formulate a written

conclusion about the

survey results as shown

on data displayed in a

picture graph, pictograph,

or bar graph with a

partner

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade-level words and expressions, such as: graph, chart,

data, line graph, picture graph, pictographs, bar graphs, pie graph, table, less, fewer, more, least, most, chart, tally marks, interpret, identify, describe, compare,

contrast, explain, associate, classify, develop, conclusion, inference, organize, create, formulate.

grade 2 mathematics curriculum guide · to navigate the curriculum guide, click on the hyperlink...

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