grade 1 mathematics curriculum document 2016-2017

1

Grade 1 Mathematics Curriculum Document

2016-2017

2

Table of Contents Cover Page Pg. 1 Table of Contents Pg. 2 Trouble Shooting Guide Pg. 3 Best Practices in the Math Classroom Pg. 4 Problem Solving 4-Square Model Pg. 6 Problem Solving with Pictorial Modeling/ Strip Diagrams Pg. 7 Number Sense/ Number Talks Pg. 9 Year at a Glance Pg. 12 Mathematics Process Standards Pg. 13 Math Instructional Resources Pg. 14 Bundle 1: Representing and Comparing Whole Numbers to 120 Pg. 15 Bundle 2: Addition and Subtraction (Fact Strategies) Pg. 24 Bundle 3: Addition and Subtraction (Problem Solving) Pg. 35 Bundle 4: Geometry and Fractions Pg. 42 Bundle 5: Measurement Pg. 52 Bundle 6: Money and Personal Financial Literacy Pg. 58 Bundle 7: Data Pg. 64

3

Trouble Shooting Guide

• The 2015-2016 Mathematics Curriculum Document for Grade 1 includes the following features:

• The NISD Curriculum Document is a TEKS-Based Curriculum.

• Year at a Glance Indicating Bundle Titles and Number of Days for Instruction

• Color Coding: Green- Readiness Standards, Yellow- Supporting Standards, Blue- Process Standards,

Purple- ELPS, Strike-Out- Portion of TEKS not Taught in Current Bundle

• NISD Math Instructional Focus Information

• The expectation is that teachers will share additional effective resources with their campus Curriculum &

Instructional Coach for inclusion in the document.

• The NISD Curriculum Document is a working document. Additional resources and information will be

added as they become available.

• **Theresourcesincludedhereprovideteachingexamplesand/ormeaningfullearningexperiencestoaddresstheDistrictCurriculum.InordertoaddresstheTEKStotheproperdepthandcomplexity,teachersareencouragedtouseresourcestothedegreethattheyarecongruentwiththeTEKSandresearch-basedbestpractices.Teachingusingonlythesuggestedresourcesdoesnotguaranteestudentmasteryofallstandards.Teachersmustuseprofessionaljudgmenttoselectamongtheseand/orotherresourcestoteachthedistrictcurriculum.

4

NISD Math Focus

Best Practices in the Math Classroom • Teaching for Conceptual Understanding: Math instruction should focus on developing a true understanding of the math concepts being

presented in the classroom. Teachers should avoid teaching “quick tricks” for finding the right answers and instead focus on developing student understanding of the “why” behind the math. Math is not a list of arbitrary steps that need to be memorized and performed, but is, rather, a logical system full of deep connections. When students see math as a set of disconnected steps to follow they tend to hold many misconceptions, make common mistakes, and do not retain what they have learned. However, when students understand the connections they have fewer misconceptions, make less errors, and tend to retain what they have learned.

• Developing Student Understanding through the Concrete-Pictorial-Abstract Approach: When learning a new math concept, students should be taken through a 3-step process of concept development. This process is known as the Concrete-Pictorial-Abstract approach. During the concrete phase, students should participate in hands-on activities using manipulatives to develop an understanding of the concept. During the pictorial phase, students should use pictorial representations to demonstrate the math concepts. This phase often overlaps with the concrete phase as students draw a representation of what they are doing with the manipulatives. During the abstract phase, students use symbols and/or numbers to represent the math concepts. This phase often overlaps with the pictorial phase as students explain their thinking in pictures, numbers, and words. If math concepts are only taught in the abstract level, students attain a very limited understanding of the concepts. However, when students go through the 3-step process of concept development they achieve a much deeper level of understanding.

• Developing Problem Solving Skills through Quality Problem Solving Opportunities: Students should be given opportunities to develop their problem solving skills on a daily basis. One effective approach to problem solving is the think-pair-share approach. Students should first think about and work on the problem independently. Next, students should be given the opportunity to discuss the problem with a partner or small group of other students. Finally, students should be able to share their thinking with the whole group. The teacher can choose students with different approaches to the problem to put their work under a document camera and allow them to talk through their thinking with the class. The focus of daily problem solving should always be Quality over Quantity. It is more important to spend time digging deep into one problem than to only touch the surface of multiple problems.

• Developing Problem Solving Skills through Pictorial Modeling: One of the most important components of students’ problem solving development is the ability to visualize the problem. Students should always draw a pictorial representation of the problem they are trying to solve. A pictorial model helps students to better visualize the problem in order to choose the correct actions needed to solve it. Pictorial modeling in math can be done with pictures as simple as sticks, circles, and boxes. There is no need for detailed artistic representations. One of the most effective forms of pictorial modeling is the strip diagram (or part-part-whole model in lower grades). This type of model allows students to see the relationships between the numbers in the problem in order to choose the proper operations.

5

• Developing Students’ Number Sense: The development of number sense is a critical part of a student’s learning in the mathematics classroom. The ability to reason about numbers and their relationships allows students the opportunity to think instead of just following a rote set of procedures. The standard algorithms for computation may provide students with a quick answer, but they do not allow for development of student thinking and reasoning. The standard algorithms should not be abandoned completely, but should be used as one of many ways of approaching a computation problem. It is, however, very important that students have the opportunity to develop their number sense through alternative computation strategies before learning the standard algorithm in order to prevent students from having a limited view of number relationships.

• Creating an Environment of Student Engagement: The most effective math classrooms are places in which students have chances to interact with their teacher, their classmates, and the math content. Students should be given plenty of opportunities to explore and investigate new math concepts through higher-order, rigorous, and hands-on activities. Cooperative learning opportunities are critical in order for students to talk through what they are learning. The goal should be for the student to work harder than the teacher and for the student to do more of the talking.

• Higher Level Questioning: The key to developing student thinking is in the types of questions teachers ask their students. Teachers should strive to ask questions from the top three levels of Bloom’s Taxonomy to probe student thinking.

6

NISD Math Focus

Developing Problem Solving through a 4-Square Model Approach • The 4-square problem solving model should be used to help guide students through the problem solving process. It is important that

students complete step 2 (pictorial modeling) before attempting to solve the problem abstractly (with computation). When students create a visual model for the problem they are better able to recognize the appropriate operation(s) for solving the problem.

Dragon Problem Solving What does the question ask me?

This is the picture in my mind.

This is how I solve the problem.

I know I am right because...

7

NISD Math Focus

Developing Problem Solving through Pictorial Modeling/ Strip Diagrams • Visual models for addition and subtraction situations help students see relationships between quantities. In the model, students place

object, then later draw dots, then later write numbers.

Joining/ Combining There are 3 birds. 2 more fly in. How many birds in all?

?

There are 3 birds. More fly in. Then there are 5 in all. How many flew in?

5

There are some birds. 2 more fly in. Then there are 5 in all. How many were there to begin with?

5

Separating There are 7 birds. 3 birds fly away. How many are left?

7 3 ?

There are 7 birds. Some fly away. Then 4 birds are left. How many flew away?

7 ? 4

There are some birds. 3 birds fly away. Then 4 birds are left. How many were there to begin with?

? 3 4

8

Part/Whole Mat

Whole

Part

Part

9

NISD Math Focus

Developing Number Sense through Number Talks What is a Number Talk? A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.

Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.

A Rationale for Number Talks

http://www.mathsolutions.com/documents/9781935099116_ch1.pdf

Number Talks 6-Weeks Strategy Focus

Operation Strategies 1st 6-Weeks Addition Counting All, Counting On, Doubles/ Near Doubles, Making Tens 2nd 6-Weeks Addition Counting All, Counting On, Doubles/ Near Doubles, Making Tens 3rd 6-Weeks Addition Counting All, Counting On, Doubles/ Near Doubles, Making Tens 4th 6-Weeks Addition Counting All, Counting On, Doubles/ Near Doubles, Making Tens 5th 6-Weeks Subtraction Counting Back, Removal (Making Landmark or Friendly Numbers, Adding Up 6th 6-Weeks Subtraction Counting Back, Removal (Making Landmark or Friendly Numbers, Adding Up

10

Number Talks

Addition and Subtraction Strategy Examples

Operation Strategy Example Addition Counting All

(Using Dot Images, Rekenreks, Double Ten Frames, and Number Sentences)

7 + 5 1,2,3,4,5,6,7,8,9,10,11,12

Addition Counting On (Using Dot Images, Rekenreks, Double Ten Frames, and Number Sentences)

7 + 5 Start on 7 and add on 5 7, 8, 9, 10, 11, 12

Addition Doubles/ Near Doubles (Using Rekenreks, Double Ten Frames, and Number Sentences)

8 + 8 = 16 so 8 + 9 = 8 + (8 + 1) = (8 + 8) + 1 = 16 + 1 = 17 and 8 + 7 = 8 + (8 – 1) = (8 + 8) – 1 = 16 – 1 = 15

Addition Making Tens (Using Rekenreks, Double Ten Frames, and Number Sentences)

6 + (4 + 3) = (6 + 4) + 3 6 + 4 = 10 10 + 3 = 13

11

Addition Making Landmark or Friendly Numbers (Using Number Sentences and Number Lines)

9 + (1 + 7) = (9 + 1) + 7 9 + 1 = 10 10 + 7 = 17

Subtraction Counting Back 14 – 7

Start on 14 and count back 7 14, 13, 12, 11, 10, 9, 8, 7

Subtraction Removal/ Making Landmark or Friendly Numbers (Using Number Sentences and Number Lines)

14 – 4 = 10 10 – 3 = 7

Subtraction Adding Up 16 – 9 = ___ or 9 + ___ = 16

9 + 1 = 10 10 + 6 = 16 9 + 7 = 16 so 16 – 9 = 7

12

Year at a Glance

First Semester Second Semester 1st 6-Weeks 4th 6-Weeks

• Bundle #1- Representing and Comparing Whole Numbers to 120 (29 days)

• Bundle #4- Geometry and Fractions (28 days)

2nd 6-Weeks 5th 6-Weeks • Bundle #2- Addition and Subtraction (Fact Strategies) (29 days) • Bundle #5- Measurement (20 days)

• Bundle #6- Money and Personal Financial Literacy (13 days)

3rd 6-Weeks 6th 6-Weeks • Bundle #3- Addition and Subtraction (Problem Solving) (29 days) • Bundle #6 (cont.)- Money and Personal Financial Literacy (10

days)

• Bundle #7- Data Analysis (18 days)

13

Mathematical Process Standards • Process standards MUST be integrated within EACH bundle to ensure the success of students.

1.1A 1.1B 1.1C 1.1D 1.1E 1.1F 1.1G apply mathematics to problems arising in everyday life, society, and the workplace

use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

create and use representations to organize, record, and communicate mathematical ideas

analyze mathematical relationships to connect and communicate mathematical ideas

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

14

Math Instructional Resources

Resource Print/Online Description EnVision Both Textbook Adoption https://www.pearsontexas.com/#/ Motivation Math Both Supplemental Curriculum https://www.mentoringminds.com/customer/account/login/ Thinking Blocks Online Online Problem Solving Practice with Strip Diagrams http://www.mathplayground.com/thinkingblocks.html 1st Grade Math Games Print Collection of Engaging and Low-Prep Math Games for Skill Practice http://maccss.ncdpi.wikispaces.net/file/view/Grade%201%20Games%20interactive-optimized.pdf/526446242/Grade%201%20Games%20interactive-optimized.pdf Epic! For Educators Online Search for Literature Connections for Math Content https://www.getepic.com/educators Number Talks (Sherry Parrish) Print Develop Number Sense Through a Daily Number Talk Routine Lessons for Learning (North Carolina) Print Collection of Engaging and Rigorous Math Lessons http://maccss.ncdpi.wikispaces.net/file/view/CCSSMathTasks-Grade1.pdf/464833108/CCSSMathTasks-Grade1.pdf Math Learning Center (Bridges) Print Collection of Engaging and Rigorous Math Lessons http://catalog.mathlearningcenter.org/catalog/supplemental-materials-elementary/lessons-activities-grade-1-free NCTM Illuminations Online Search for Engaging and Rigorous Math Lessons by Grade and Topic http://illuminations.nctm.org/ Math Coach’s Corner Online Math Blog from a Master Texas Math Teacher, Coach, and Consultant http://www.mathcoachscorner.com/ Promethean Planet Online Tools and Lessons for Interactive Whiteboard http://www.prometheanplanet.com/en-us/ Interactive Math Glossary Online TEA Interactive Math Glossary http://www.texasgateway.org/resource/interactive-math-glossary?field_resource_keywords_tid=math%20teks&sort_by=title&sort_order=ASC&items_per_page=5

TEKS Information for Teachers TEA Math Resources Online TEA Supporting Information for Math TEKS http://tea.texas.gov/Curriculum_and_Instructional_Programs/Subject_Areas/Mathematics/Resources_for_the_Revised_Mathematics_TEKS/ Lead4Ward Resources Online Math TEKS Instructional Resources and Supporting Information http://lead4ward.com/resources/ TEKS Resource System Online Math TEKS Instructional Resources and Supporting Information http://www.teksresourcesystem.net/module/profile/Account/LogOn

15

Course: Grade 1 Math Bundle 1: Representing and Comparing Whole Numbers to 120

Dates: August 22nd – September 30th (29 days)

TEKS 1.2A: recognize instantly the quantity of structured arrangements 1.2B: use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones 1.2C: use objects, pictures, and expanded and standard forms to represent numbers up to 120 1.2D: generate a number that is greater than or less than a given whole number up to 120 1.2E: use place value to compare whole numbers up to 120 using comparative language 1.2F: order whole numbers up to 120 using place value and open number lines 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or = 1.5A: recite numbers forward and backward from any given number between 1 and 120 1.5C: use relationships to determine the number that is 10 more and 10 less than a given number up to 120

ELPS

Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1B: monitor oral and written language production and employ self-corrective techniques or other resources 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs

16

Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E: share information in cooperative learning interactions 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

Vocabulary

Unit Vocabulary Backward Digit Greatest to least Ones Ten less Comparison symbol Equal to (=) Hundreds Open number line Ten more Compose Expanded form Least to greatest Place value Tens Counting words Forward Less than (<) Standard form Value of a number Decompose Greater than (>)

Cognitive Complexity Verbs: recognize, use, compose, decompose, use, represent, generate, order, recite Academic Vocabulary by Standard: 1.2A: counting words 1.2B: compose, decompose, digit, place value, hundreds, tens, ones, value of a number 1.2C: digit, expanded form, place value, hundreds, tens, ones, standard form 1.2D: counting words, digit, greater than, less than, place value, value of a number 1.2E: digit, equal to, place value, greater than, less than, hundreds, tens, ones, value of a number 1.2F: digit, least to greatest, greatest to least, open number line, place value, hundreds, tens, ones, value of a number 1.2G: comparison symbol, digit, equal to (=), greater than (>), less than (<), place value, hundreds, tens, ones 1.5A: backward, forward, counting numbers 1-120 1.5C: place value, ten more, ten less

17

Suggested Math Manipulatives

120 Charts Dice Base 10 Blocks Color Tiles Rekenreks Dominoes Interlocking Cubes Counters 10 Frames Place Value Charts Place Value Disks Cuisenaire Rods Dot Images Open Number Lines 2 Color Counters Popsicle Sticks

18

Bundle 1: Vertical Alignment

K.2D recognize instantly the quantity of a small group of objects in organized and random arrangements

1.2A: recognize instantly the quantity of structured arrangements

K.2I compose and decompose numbers up to 10 with objects and pictures

1.2B: use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones

2.2A use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones 3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

1.2C: use objects, pictures, and expanded and standard forms to represent numbers up to 120

2.2B use standard, word, and expanded forms to represent numbers up to 1,200 3.2A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

K.2F generate a number that is one more than or one less than another number up to at least 20

1.2D: generate a number that is greater than or less than a given whole number up to 120

2.2C generate a number that is greater than or less than a given whole number up to 1,200

K.2G compare sets of objects up to at least 20 in each set using comparative language K.2H use comparative language to describe two numbers up to 20 presented as written numerals

1.2E: use place value to compare whole numbers up to 120 using comparative language

2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>,<,=) 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >,<,=

1.2F: order whole numbers up to 120 using place value and open number lines

2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>,<,=) 2.2E locate the position of a given whole number on an open number line 3.2C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >,<,=

1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

2.2D use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>,<,=) 3.2D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >,<,=

K.5A recite numbers up to at least 100 by ones and tens beginning with any given number

1.5A: recite numbers forward and backward from any given number between 1 and 120

1.5C: use relationships to determine the number that is 10 more and 10 less than a given number up to 120

2.7B use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

19

Bundle 1: Teacher Notes

TEKS/Student Expectations

Instructional Implications Distractor Factors Supporting Readiness Standards

TEA Supporting Information

1.2A: recognize instantly the quantity of structured arrangements

Students learn to recognize dot arrangements on standard dice (number cube) due to the board games they have played. Similar instant recognition can be developed for other patterns as well (i.e. dominos, fingers, ten frames, etc.). Quantities up to 10 can be known and named without the routine of counting. Some students may continue to rely on physically counting using one-to-one correspondence to determine the total number of objects; however, with continuous exposure to pattern sets, students will begin to rely less on their counting skills and more on their spatial reasoning.

Being able to recognize the quantity of a structured arrangement will support students in being able to visually compare two numbers. 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

This SE extends K.2C where students are asked to recognize small quantities in organized and random arrangements. The number of items should be ten or less. When paired with 1.1G, a student may be asked to explain the thinking he or she used to subitize the number. Structured arrangements include ten frames and the arrangements of dots on random number generators. For example, when shown an arrangement with two “parts,” a student might justify his or her thinking by saying, “I recognize five, and then I added two more.”

This use of structured arrangements builds students’ conceptual understandings of the part-whole relationship of numbers (5 and 2 compose to 7) and basic facts (5 + 2 or 2 + 5).

20

1.2B: use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones

Developmentally, students may need to work with individual snapping cubes and/or bundled popsicle sticks to create sets of tens and ones. Concrete experiences will allow students to see how 10 ones are bundled in order to create a ten. As students’ progress in their understanding, instruction can move to the use of base ten blocks. Through the use of base ten blocks, students will begin to visually understand the magnitude of numbers (i.e. the ten rod is ten times more than the ones cube; the hundred flat is ten times more than the ten rod; the ones cube is ten times smaller than the ten rod; the ten rod is ten times smaller than the hundred flat). Students need to understand that the digit in a given number represents its place value which is different from the value of the number (i.e. 24; the digit two is in the tens place and is represented by two ten rods, but is valued at 20). It is critical for students to represent a number in more than one way (i.e. 24 can be represented as two tens and four ones or one ten and fourteen ones). This understanding will lend itself to regrouping in subtraction (i.e. 24 – 18 + ___; 24 would have to be regrouped into one ten and 14 ones in order to subtract).

Using concrete and pictorial models to represent various numbers will support students’ understanding of place value. The use of visual representations will allow students to develop relationships among the different place values. Being able to represent a number in more than one way will support students with the ability to rename numbers when having to subtract with regrouping. 1.2C: use objects, pictures, and expanded and standard forms to represent numbers up to 120

These concrete and pictorial models are used to compose and decompose numbers in more than one way as a means to describe the value of whole numbers. “So many hundreds, so many tens, and so many ones” may include using models to decompose 67 into 5 tens and 17 ones. It may also include models to decompose 67 into the sum of 50, 10, and 7.

1.2C: use objects, pictures, and expanded and standard forms to represent numbers up to 120

As students begin representing numbers through 120 using base ten blocks (see 1.2B), their understanding should also be associated with writing numbers in standard form (24), word form (twenty-four), and expanded form (i.e. 24 = 20 + 4). This type of representation will allow students to focus on the value of each digit and support the understanding of the place value system (i.e. two ten rods represent the value of 20; four unit cubes represent the value of 4; 20 + 4 = 24). In representing numbers in word form, be sure to emphasize the correct use of the hyphen (i.e. twenty-three).

* Students may incorrectly use the word “and” to represent numbers in words (i.e. 105 is represented as “one hundred five” not “one hundred and five). The use of the word “and” is applied in the representation of whole number and decimal values (i.e. 3.45 is represented as three and forty-five hundredths). * Students confuse the place value a digit has with its value (i.e. 105; the digit 1 is in the hundreds place value but is valued at 100). * Students may confuse “digit” with “number”.

This SE allows students to incorporate 1.1D through the use of multiple representations of a number by using concrete models, pictorial models, standard form (119), and expanded form (119= 100 + 10 + 9).

21

1.2D: generate a number that is greater than or less than a given whole number up to 120

As students become more fluid with their use of the place value system in using base-ten blocks (1.2B) and expanded notation (1.2C), instruction should include students generating a number “greater than” or “less than” a given whole number. Students should be able to explain that the position of each digit in a numeral determines the quantity of a given number (i.e. given the number 37, students understand that the digit three represents the number of ten rods and its value of 30). This Concept is important to ask of children before they begin to abstractly compare two given numbers (1.2E/G) to clarify students’ understanding of place value.

Generating a number greater than or less than a given whole number will allow students to focus on the value of various digits in a number before moving to the abstract use of the comparison symbols (<, >, =). 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

This SE extends K.2F where students are expected to generate a number that is one more or one less than another number up to 20.

1.2E: use place value to compare whole numbers up to 120 using comparative language

Students will compare two numbers using academic vocabulary correctly (i.e. 42 is greater than 26). It is important for students to recognize the inverse comparison statement as well (i.e. 26 is less than 42). Encourage students to articulate both comparison statements during activities. The use of comparative language is critical before moving to the symbolic representation (1.2G). Be sure to relate how the value of the digits determined which number was larger/smaller (i.e. the number 42 is greater than 26 because the digit 4 in 42 means there are 4 tens which is the value of 40; however, the digit 2 in 26 means there are only 2 tens which is a value of 20; therefore, 42 is greater than 26).

As students compare the value of numbers, they need to be able to relate their understanding of place value and use the appropriate academic vocabulary (greater than, less than, equal to) before moving to the abstract use of comparison symbols (< , >, =). 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

Students may be expected to use comparative language such as greater than, less than, or equal to in order to compare numbers using place value. For example, given the numbers 87 and 64, a student would describe 64 as having lesser value because the value of the 6 in the tens place is 60, while having an 8 in the tens place is 80, and 60 is less than 80. In comparing numbers up to 120, one may use the hundreds, tens, and ones places with a set of whole numbers like 118, 108, 98, and 89.

1.2F: order whole numbers up to 120 using place value and open number lines

In conjunction with 1.2E, students will order three or more numbers from least to greatest or greatest to least through the use of an open number line. An open number line does not have landmark numbers earmarked, does not have to begin at zero, and should include the use of arrows on both ends of the number line to indicate

A number line can be used as a strategy to compare/order numbers as well as develop a students’ understanding of place value, the relative position of numbers, and the magnitude of numbers. The use of this tool will be a critical support mechanism.

Students may be expected to use place value to order numbers based on the value of the digits and use an open number line, which builds to 2.2E. The use of an open number

22

how the numbers continue beyond what is marked.

Students will apply their understanding of the place value system in relation to the relative position on an open number line (i.e. the number 52 would fall between 50 and 60 on a number line as 52 can be expressed as 50 + 2 or the number 52 has 5 tens and 2 ones). By locating three or more numbers on an open number line, you will be able to assess students’ understanding of place value (i.e. students place the number 52 between 50 and 60), the position of numbers (i.e. the number 50 would be indicated first and the number 60 would be indicated second on the open number line), and the magnitude of numbers (i.e. students physically place the number 52 closer to 50 than 60).

Students will need to associate their understanding of how numbers increase from left to right on a number line to ordering from least to greatest and how numbers decrease from right to left on a number line to ordering from greatest to least.


line supports student understanding related to the magnitude of number and the place-value relationship among numbers when locating a given number.


As students become more comfortable with how to compare two numbers using the correct academic language of greater than, less than, or equal to (see 1.2E), instruction can then introduce the comparison symbols. It is important for students to recognize how their language can be communicated using symbols (>, <, =) just like we use the symbols (+/-) to represent joining, separating, and comparing problems (see 1.3B). It is critical that students do not learn how to read each of the symbols using a trick to remember directionality of the symbols (i.e. the

* Students that rely on a trick to determine directionality may not be able to read comparison symbols correctly. * Students may view a comparison statement and its inverse as two different comparison statements (i.e. 45 > 41 is the same as 41 < 45). * Students may confuse the place value a digit is in with its value (i.e. 45; the digit 4 is in

Students are expected to extend their understanding of comparing numbers using comparative language in 1.2E. In this SE, students are expected to compare two numbers using the symbols >, <, or =. This SE complements 1.2D, 1.2E, and 1.2F.

23

alligator’s mouth eats the bigger number). It is important for students to read the number sentence from left to right. Encourage students to write and articulate two comparison statements during activities (i.e. 54>36 and 36<54).

the tens place value but is valued at 40).

1.5A: recite numbers forward and backward from any given number between 1 and 120

The counting sequence is a rote procedure; however, asking students to begin counting at a particular number relates to the understanding of relative position (37 comes before 38) and asking a student to count forward or backward connects to their understanding of the magnitude of numbers (as I recite numbers forward, the numbers become larger; as I recite numbers backward, the become smaller).

Counting numbers backward and forward from any given number supports the contextual understanding of the value of numbers. This understanding can be associated to the representations of numbers on a number line. The number line can be used as a strategy to compare/order numbers and develop a students’ understanding of place value, the relative position of numbers, and the magnitude of numbers. The use of this tool is a critical support mechanism. 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

This SE extends K.5 where students are expected to recite numbers up to at least 100 by ones and tens beginning with any given number. When reciting by tens, kindergarten students counted only multiples of 10: 60, 70, 80….


In order to adhere to the standard, students must be able to determine 10 more/10 less of a given number (i.e. ten more than 34 is 44; ten less than 34 is 24). Instruction might begin with the use of a 100s chart to recognize the patterns of 10 more/ 10 less. Students should begin relating how the digit in the tens place is changing by one with each adding/subtracting of 10. The standard requires students to determine 10 more/less through 120. In accordance with the TEKS, students also need to connect their finding through the use of properties of numbers and operations (i.e. ten more than 34 is 44 because 34 + 10 =; 30 + 4 + 10 = ___; 30 + 10 + 4 = 44). This understanding is also reiterated in 1.3A.

Students will begin identifying patterns in determining 10 more/less than a given number. Recognizing the change in the digits will reinforce the tens place value. This standard will reinforce the concept of place value which is critical for comparing and ordering while numbers. 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

The relationship that students use should focus on place value. For example, 99= 90 + 9. If a student wants a number that is 10 more than 99, the student can think (90 + 10) + 9 or 100 + 9 or 109. This SE supports 1.2D and builds to 2.7B

24

Course: Grade 1 Math Bundle 2: Addition and Subtraction (Fact Strategies)

Dates: October 4th-November 11th (29 days)

TEKS 1.3A: use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99 1.3C: compose 10 with two or more addends with and without concrete objects 1.3D: apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10 1.3E: explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences 1.5B: skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set 1.5C: use relationships to determine the number that is 10 more and 10 less than a given number up to 120 1.5E: understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s) 1.5F: determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation 1.5G: apply properties of operations to add and subtract two or three numbers

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication

25

3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E: share information in cooperative learning interactions 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary Addends Equal sign Make 10 Skip count Tens Addition Equation Multiple of ten Strategy Think addition/ count on Combining Equivalent Number sentence Subtraction Twos Count back Expression One-digit number Sum Unknown Difference Fives Place value Ten less Value Doubles/near doubles Joining Properties of operations Ten more

Cognitive Complexity Verbs: use, determine, compose, apply, explain, skip count, understand Academic Vocabulary by Standard: 1.3A: addition, joining, combining, multiple of ten, one-digit number, sum 1.3C: addends, number sentence, sum 1.3D: count back, doubles/ near doubles, make 10, think addition/count on 1.3E: addition, difference, number sentence, strategy, subtraction, sum 1.5B: skip count, twos, fives, tens 1.5C: place value, ten more, ten less 1.5E: equal sign, expression, value, equivalent 1.5F: addition, difference, number sentence/equation, subtraction, sum, unknown 1.5G: add, difference, properties of operations, sum, subtract

26


120 Charts Dice 2 Color Counters Popsicle Sticks Rekenreks Dominoes Color Tiles Part/Whole Mats 10 Frames Open Number Lines Counters Dot Images Interlocking Cubes Cuisenaire Rods

27


1.3A: use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99

2.4C solve one-step and multistep word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

K.3B solve word problems using objects and drawings to find sums up to 10 and differences within 10

1.3C: compose 10 with two or more addends with and without concrete objects

3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

1.3D: apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10

2.4A recall basic facts to add and subtract within 20 with automaticity 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

K.3C explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentence

1.3E: explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences

2.4B add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

1.5B: skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set

2.7A determine whether a number up to 40 is even or odd using pairings of objects to represent the number


2.7B use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

28

1.5E: understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s)

2.7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem 3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

1.5F: determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation

2.7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem 3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.

1.5G: apply properties of operations to add and subtract two or three numbers

3.5D determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product

29





1.3A: use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99

As students become comfortable with representing numbers with base ten blocks and associating the concrete representation with the expanded notation of a number (see 1.2B/C), instruction will extend this understanding to addition. Through continued use of the base ten blocks, provide students ample opportunities to act out various addition story problems in which students are joining various tens and ones (i.e. Margarita collected 30 sea shells from the beach on Monday. She found 6 more sea shells on Tuesday. How many sea shells did Margarita collect during those two days at the beach?). In adherence to the standard, instruction is limited to problems with a multiple of ten for one addend (30 sea shells) and a one-digit number for the second addend (i.e. 6 sea shells). Be sure to connect the given number sentence to the base ten representation (i.e. 30 + 6 = 36; three ten rods represents the number of sea shells she collected on Monday; six unit cubes represents how many sea shells she collected on Tuesday; the total value of the sea shells is 36).

Using concrete and pictorial models (i.e. base ten blocks) to represent the sum of a multiple of ten and a one-digit number (30 + 6 = 36) will support students in developing algorithms based on place values. 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5G apply properties of operations to add and subtract two and three numbers

Students may use concrete and pictorial models to add whole numbers with sums up to 99. For example, to determine the sum of 60 + 7, a student would use a model to represent 6 tens and 7 ones. This SE supports student understanding of place value and expanded form.

1.3C: compose 10 with two or more addends with and without concrete objects

Instruction should begin with two different colored manipulatives where students can create as many different color patterns for a train of ten (i.e. ten blue; ten yellow; one blue and 9 yellow; two blue and 8 yellow; etc.). Students should then associate a given number sentence for each of the different representations (i.e. seven blue and three yellow represents 7 + 3 = 10 and/or 10 = 7 + 3). Students may begin to informally discover

Being able to compose 10 in more than one way will support the students’ flexible use of numbers. Becoming fluid with manipulating numbers is critical in moving students toward developing strategies for solving addition and subtraction problems.

The focus is on flexible thinking with composing 10 with two or more addends to support basic fact strategies such as “making 10.” For example, a student may compose 10 without objects using addends such as 4 + 6 = 10 or 4 + 1 + 5 = 10.

30

the commutative property (i.e. I can build a train of 7 blue and 3 yellow to represent 7 + 3 = 10, but I can flip the train and reflect 3 yellow and 7 blue to represent 3 + 7 = 10). As students become comfortable with understanding the many ways the sum of 10 can be represented with two colors (addends), provide students with a set of another color and ask them to now build different color patterns with three different colors (i.e. ten red; ten green; ten yellow; 1 red, 1 green, and 8 yellow; 2 red, 1 green, and 7 yellow, etc.). Again, students should associate a given number sentence for each of the different representations (i.e. 1 red, 1 green, and 8 yellow represents 1 + 1 + 8 = 10 and or 10 = 1 + 1 + 8). Challenge students to create as many different number sentences with three addends for the sum of 10. Students will begin developing their own variations without the use of the manipulatives.

1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

1.3D: apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10 (new this unit)

In order to adhere to the standard, students must use their basic facts in order to solve problems through 20. Instruction may include some of the following strategies: Addition: - Make Ten with the use of two tens frames as a model

(i.e. 9 + 8 = ___; can be rewritten as

9 + 1 + 7 = ___; 10 + 7 = 17)

Being flexible to applying basic fact strategies is critical in moving students toward developing algorithms for solving addition and subtraction problems. 1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

This SE supports 1.3C by asking students to apply their understanding of composing 10 to solving problems based upon the basic facts of addition. For example, given the fact 7 + 8, a student may decompose 8 into 3 and 5 so that the 3 may be added to the 7 to make 10, then add 10 and 5 to equal 15. When paired with 1.1A, students may be asked to apply these basic facts to solve word problems.

31

- Make Ten with the use of an open number line

(i.e. 9 + 8 = ___; 9 + 1 + 7 = ___; 10 + 7 = ___; 10 + 7 = 17) - Doubles: (i.e. 6 + 8 = 6 + 6 + 2 = ___; 12 + 2 = ___; 12 + 2 = 14) - Count On: (i.e. 3 + 8 = ___; 8, 9, 10, 11; 3 + 8 = 11) Subtraction: - Think Addition/ Count One: (i.e. 12 – 9 = ___; 9 + ___ = 12; 9 + 3 = 12). - Make Ten: (i.e. 12 – 9 = 12 – 2 – 7 = 10 – 7 = 3). - Compensation (i.e. 12 – 9 = 12 - 10 + 1 = 2 + 1 = 3). - Count Back: (i.e. 12 – 3 = ___; 12, 11, 10, 9; 12 – 3 = 9)


In conjunction with 1.3D, it is essential that students not only apply the appropriate basic fact strategy, but explain their thought processes (i.e. student made use of an open number line to solve the problem 12 – 9 + ___; student marked an “x” on the numbers 9 and 12 on the open number line; students demonstrated how there are three spaces between the number 9 and 12, so the difference between the two numbers is 3; 12 – 9 = 3). Students need to also explain which of the strategies is most appropriate in different contexts (i.e. 12 – 3 = ___; count back would not be as efficient as make 10).

Being able to relate the manipulation of concrete objects to pictorials to a number sentence is a critical transition to moving students from concrete to abstract understanding of addition and subtraction. 1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

When paired with 1.1E and 1.1G, students are expected to explain and record observations, which may include strategies.

32

1.5B: skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set

Students use skip counting by twos, fives, and tens to count the number of objects more efficiently (i.e. a bag of candy counted by twos; the total number of sides for six pentagons can be more efficiently determined by skip counting of fives; the value of a handful of dimes can be quickly determined by skip counting by tens). Instruction should move between skip counting by tens, fives, and twos (i.e. counting the value of a set of 4 ten rods and 8 unit cubes; 10, 20, 30, 40, 42, 44, 46, 48 or counting a collection of unlike coins; 2 dimes, 4 nickels, and 6 pennies; 10, 20, 25, 30, 35, 40, 42, 44, 46).

Associating skip counting by twos, fives, and tens is a foundational skill to determining the value of a collection of coins. 2.5A determine the value of a collection of coins up to one dollar

The focus of the counting is on determining the total number of objects in a set. This SE supports 1.4C where students skip count to find the value of a collection of coins.


In order to adhere to the standard, students must be able to determine 10 more/10 less of a given number (i.e. ten more than 34 is 44; ten less than 34 is 24). Instruction might begin with the use of a 100s chart to recognize the patterns of 10 more/ 10 less. Students should begin relating how the digit in the tens place is changing by one with each adding/subtracting of 10. The standard requires students to determine 10 more/less through 120. In accordance with the TEKS, students also need to connect their finding through the use of properties of numbers and operations (i.e. ten more than 34 is 44 because 34 + 10 =; 30 + 4 + 10 = ___; 30 + 10 + 4 = 44). This understanding is also reiterated in 1.3A.

Students will begin identifying patterns in determining 10 more/less than a given number. Recognizing the change in the digits will reinforce the tens place value. This standard will reinforce the concept of place value which is critical for comparing and ordering while numbers. 1.2G: represent the comparison of two numbers to 100 using the symbols >, <, or =

The relationship that students use should focus on place value. For example, 99 = 90 + 9. If a student wants a number that is 10 more than 99, the student can think (90 + 10) + 9 or 100 + 9 or 109. This SE supports 1.2D and builds to 2.7B.

1.5E: understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s)

If number sentences are limited to only one type of representation (i.e. 7 + 4 = 11), students develop the misconception that the equal sign stands for “the answer is coming.” Therefore, it is essential for instruction to vary the representation of number sentences (i.e. 7 + 4 = 11; 11 = 7 + 4). Students need to understand that the equal sign is a symbolic representation of how one side of the equation “is the same”

Understanding that the equal sign represents equivalent values is foundational to representing and identifying number sentences/equations in more than one way (i.e. 23 – 9 = ___; ___ = 23 – 9; 9 + ___ = 23; 23 = ___ + 9). 1.5D represent word problems

This SE requires students to understand that the equal sign does not necessarily mean “find the answer.” For example, in the problem 4 + 2 + 3=___, the relationship may be 4 + 2 + 3 = 9 or 4 + 2 +

33

value as the other side of the equation (i.e. 10 + 1 = 7 + 4; 9 + 2 + 2 = 4 + 4 + 1 + 4). As students begin to solve multi-step problems, it is essential for them to understand the representation of their work. (I.e. 5 + 4 + 3 = ___; 5 + 4 ≠ 9 + 3 = 12 does not show equality. However, students can show 5 + 4 + 3 = 9 + 3 = 12).

involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences 1.5G: apply properties of operations to add and subtract two or three numbers

3 = 6 + 3. In both of these number sentences, the expressions on each side of the equal sign have a value of 9. The understanding of this SE helps support 1.5F, as students are asked to determine the unknown equation (number sentence). When paired with 1.1G, students may be expected to explain that 4 + 2 + 2 = 4 + 4 because the sum of each side of the equal sign is 8.

1.5F: determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation

In conjunction with 1.5E, students will apply their understanding of equality to determine the unknown value of a given equation (i.e. ___ = 7 + 4; 7 + 4 = ___ + 6; 15 = 4 + 3 + ___; ___ - 7 = 6). The use of a part-part-whole mat may provide structure to student understanding.

Whole 15

Part 4

Part 3

Part ?

Relating addition and subtraction number sentences/ equations supports a student’s ability to represent and solve addition and subtraction problems. 1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

This SE allows students to apply their understanding of 1.5E. Examples of equations with three terms and one unknown include 6 + ___ = 14, 14 - ___ = 6, or 14 – 6 = ___.

1.5G: apply properties of operations to add and subtract two or three numbers

Properties of operations include the commutative, associative, and inverse operational properties. Although instruction may not include the formal academic language, the use of the underlying concepts will be used to solve addition and

* Students may try to apply the commutative property in subtraction. * Students may not recognize how applying

This SE may require students to apply the understanding of properties of operations to problem situations when incorporating 1.1A

34

subtraction problems. Commutative Property: 4 + 3 + 6 = ___ (to employ the make ten strategy, one could change the order of the addends and not change the sum); 4 + 6 + 3 = 13. Associative Property: 12 + 6 = ___ (to employ the make ten strategy, one could decompose 12 and it will not change the sum); (10 + 2) + 6 = ___; 10 + (2 + 6) = 18. Inverse Operational Property: 12 – 9 = ___ (to employ the think addition method, one could employ the inverse property); 9 + ___ = 12; 9 + 3 = 12.

addition to solve a subtraction problem may be easier.

and 1.1C. For example, there are 2 books on Ms. Smith’s desk. After lunch, she placed 9 more books on her desk. How many books are on Ms. Smith’s desk now? A student may solve this problem using the commutative property of addition. The problem may be solved as 2 + 9 = 11, or a student may understand that 9 + 2 = 11 and could use this to solve the problem. A student may also use a place value strategy such as “make 10.” For example, 2 + 9 = 2 + (8 + 1) = (2 + 8) + 1 = 10 + 1 = 11. The SE also includes the addition and subtraction of three numbers. For example, students may be expected to add 3 + 8 + 6 as 3 + (7 + 1) + 6 = (3 + 7) + 1 + 6 = 10 + (1 + 6) = 10 + 7 = 17. The application of the properties of operations allow for the grouping and regrouping of numbers to develop a strong sense of place value and for creating groups of tens and ones.

35

Course: Grade 1 Math Bundle 3: Addition and Subtraction (Problem Solving)

Dates: November 14th-January 12th (29 days)

TEKS 1.3B: use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3

1.3E: explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences 1.3F: generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 1.5D: represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1B: monitor oral and written language production and employ self-corrective techniques or other resources 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) 1F: use accessible language and learn new and essential language in the process Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3B: expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication 3C: speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics 3H: narrate, describe, and explain with increasing specificity and detail as more English is acquired

36

Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4D: use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

Vocabulary

Unit Vocabulary Addition Difference Number sentence Subtraction Combining Distance Separating Sum Comparing Joining Strategy

Cognitive Complexity Verbs: use, solve, explain, generate, represent Academic Vocabulary by Standard: 1.3B: comparing, addition, subtraction, distance, joining, combining, number sentence, separating, subtraction 1.3E: addition, difference, number sentence, strategy, subtraction, sum 1.3F: addition, joining, combining, difference, number sentence, subtraction, separating, comparing, distance, sum 1.5D: addition, joining, combining, difference, number sentence, subtraction, separating, comparing, distance, sum


120 Charts Dice 2 Color Counters Popsicle Sticks Rekenreks Dominoes Color Tiles Part/Whole Mats 10 Frames Open Number Lines Counters Dragon Problem Solving Model Dot Images Interlocking Cubes Cuisenaire Rods

37


K.3A model the action of joining to represent addition and the action of separating to represent subtraction

1.3B: use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3

3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

K.3C explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentence


2.4B add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

1.3F: generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 (new this unit)

2.4D generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000 3.4A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

1.5D: represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

2.7C represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem 3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

38


TEKS/Student Expectations Instructional Implications Distractor Factors Supporting Readiness Standards


1.3B: use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3

Students will use their manipulatives to act out joining (i.e. Margarita collected 11 sea shells on Monday and 8 sea shells on Tuesday. How many sea shells did Margarita collect during those two days?), separating (i.e. Margarita found 11 sea shells at the beach. Eight of them were cracked so she threw them back in the ocean. How many sea shells did Margarita keep?), and comparing (i.e. Margarita collected 11 sea shells on Monday and 8 sea shells on Tuesday. How many more sea shells did Margarita find on Monday than Tuesday?). Instruction should include how the subtraction symbol represents distance (i.e. 11 – 3 = ___; how far away is 3 from 11 on the number line?) This understanding of how subtraction represents distance lays the foundation for future learning of subtraction of integers (i.e. 11 – (-3) = 14; the number -3 is 14 spaces away from 11 on the number line). Students should write at least two different number sentences for each type of problem: (i.e. joining: 11 + 8 = ___; 8 + 11 = ___; ___ = 11 + 8; ___ = 8 + 11; separating: 11 – 8 = ___; ___ = 11 – 8; comparison/distance: 11 – 8 = ___; ___ = 11 – 8; 8 + ___ = 11; ___ + 8 = 11). Joining, separating, and comparing word problems should include a variety of contexts: Joining: Sarah had 8 pencils. Juan gave her 3 more pencils. How many pencils does Sarah have now? Sarah had 8 pencils. Juan gave her some more pencils. Now Sarah has 11 pencils. How many pencils did Juan give her? Sarah had some pencils. Juan gave her

The use of concrete objects and pictorial models to demonstrate joining, separating, and comparison situations will support students’ understanding of the context of addition and subtraction problems. Connecting such actions to their corresponding number sentence will support students as they move from concrete to abstract understanding. 1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

This SE extends K.3A where students solve joining and separating problems with the result unknown. It also provides a context for 1.5F. For example, 3 + [ ] = 7. There were 3 birds in a tree. Some more birds came to join them. Now, there are 7 birds in the tree. How many birds came to join the birds that were there at the start? Students would then be asked to use objects or pictures to solve the problem.

39

3 pencils. Now Sarah has a total of 11 pencils. How many pencils did Sarah have to begin with? Separating: Sarah had 11 pencils. She gave 3 pencils to Juan. How many pencils does Sarah have now? Sarah had a total of 11 pencils. She gave some to Juan. Now she only has 3 pencils. How many pencils did she give to Juan? Sarah had some pencils. She gave 3 to Juan. Now Sarah has 8 pencils left. How many pencils did Sarah have before? Comparing: Juan has 11 pencils and Sarah has 8 pencils. How many more pencils does Juan have than Sarah? Sarah has 3 fewer pencils than Juan. If Sarah has 8 pencils, how many pencils does Juan have? Juan had 3 more pencils than Sarah. If Juan has 12 pencils, how many pencils does Sarah have? If Juan has 17 and Sarah has 11, how many more does Sarah need to have the same amount as Juan?


In conjunction with 1.3D, it is essential that students not only apply the appropriate basic fact strategy, but explain their thought processes (i.e. student made use of an open number line to solve the problem 12 – 9 + ___; student marked an “x” on the numbers 9 and 12 on the open number line; students demonstrated how there are three spaces between the number 9 and 12, so the difference between the two numbers is 3; 12 – 9 = 3). Students need to also explain which of the strategies is most appropriate in different contexts (i.e. 12 – 3 = ___; count back would not be as efficient as make 10).

Being able to relate the manipulation of concrete objects to pictorials to a number sentence is a critical transition to moving students from concrete to abstract understanding of addition and subtraction. 1.3F : generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20 1.5G: apply properties of operations to add and subtract two or three numbers

When paired with 1.1E and 1.1G, students are expected to explain and record observations, which may include strategies.

40

1.3F: generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20 (new this unit)

In adherence to the standard, students not only have to solve word problems that are provided for them, but they must also create their own story problems when given a number sentence. In conjunction with 1.3B, this standard will assess students’ conceptual understanding of joining (+), separating (-), or comparison situations (+/-) and how it applies to the appropriate operation. Instruction should provide students opportunities to write story problems with multiple representations of various number sentence (i.e. 12 – 8 = ___; ___ = 12 – 8; 8 + ___ = 12; ___ + 8 = 12).

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem. * Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 = 18 + ___ is the same thing as 18 + ___ = 42). * Students may substitute the term “take away” for “minus,” creating a misconception that subtraction is only about separating.

Students must be provided with a mathematical number sentence (equation) in order to generate and then solve a problem situation. To build upon SEs 1.3B and 1.5F, the unknown may be in any one of the terms in the problem.

1.5D: represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

In conjunction with 1.3, students continue to demonstrate their understanding of joining, separating, comparing and distance types of problem solving with associated operations. In adherence to the standard, instruction should require students to act out, draw, and write number sentences for various story problems. Students should be able to articulate the components of the word problem, to the presented manipulative/ drawing, to the values in their number sentence (i.e. 11 + 8 = 19 or 19 = 8 + 11. These eleven blue birds in the picture stand for the 11 in the number sentence. These eight red birds in the picture joined the blue birds, which is the +8 in my number sentence; there is now a total of 19 birds sitting in the tree which is the same as 19 in the number sentence). Real world

* Students may try to apply “key words” to select the appropriate operation instead of understanding the context of the problem. * Students may not recognize a number sentence and its inverse as being equivalent (i.e. 42 – 18 = ___ is the same thing as 18 + ___ = 42). * Students may gravitate to one subtraction structure (i.e. comparing or distance).

For this SE, the student is not asked to solve the word problem. The student is asked to represent the context of the word problem using objects, pictures, and number sentences (equations). Based upon 1.3B, these word problems may include the unknown as any one of the terms. For example, Phoung has 12 pencils. She has some red pencils and 8 yellow pencils. How many red pencils does Phoung have? 12 = 8 + ?

41

situations should be extended beyond two addends (i.e. There were 9 blue birds, 5 red robins, and 6 hummingbirds in the tree. How many birds are in the tree?). Instruction should vary the context of +/- type problems provided to students (see 1.3B for examples).

42

Course: Grade 1 Math Bundle 4: Geometry and Fractions

Dates: January 17th-February 24th (28 days)

TEKS 1.6A: classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language 1.6B: distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape 1.6C: create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons 1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language 1.6E: identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language 1.6F: compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible 1.6G: partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words 1.6H: identify examples and non-examples of halves and fourths

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English 1D: speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known) Listening 2C: learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions Speaking 3D: speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics

43

Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

Vocabulary

Unit Vocabulary Attributes Examples Irregular Regular Square

(as special rectangle) Circle Face Non-examples Rhombus Three-dimensional Cones Fair share/ equal parts Polygon Shape Triangle Cubes (as special rectangular prisms)

Fourths Quadrilateral Sides Triangular prisms

Curved side Half/halves Rectangle Solids Two-dimensional Cylinders Hexagon Rectangular prisms Spheres Vertex/vertices Edge Examples

Cognitive Complexity Verbs: classify, sort, distinguish, create, identify, compose, produce, partition, describe Academic Vocabulary by Standard: 1.6A: attributes, irregular, regular, shape, circle, hexagon, polygon, quadrilateral, rectangle, rhombus, square (as special rectangle), triangle, sides, two-dimensional, vertex/vertices 1.6B: polygon, shape, two-dimensional, attributes, sides, vertex/vertices, three-dimensional, attributes, edge, face 1.6C: attributes, sides, vertex/vertices, shapes, circle, hexagon, polygon, quadrilateral, rectangle, rhombus, square (as special rectangle), triangle, two-dimensional 1.6D: attributes, curved side, sides, vertex/vertices, irregular, shapes, circle, hexagon, polygon, quadrilateral, rectangle, rhombus, square (as special rectangle), triangle, regular, two-dimensional 1.6E: attributes, edges, faces, vertex/vertices, solids, cones, cubes (as special rectangular prisms), cylinders, rectangular prisms, spheres, triangular prisms, three-dimensional 1.6F: polygon, two-dimensional, shapes, circle, hexagon, polygon, quadrilateral, rectangle, rhombus, square (as special rectangle), triangle 1.6G: fair share/ equal parts, half/halves, polygon, shapes, circle, hexagon, polygon, quadrilateral, rectangle, rhombus, square (as special rectangle), triangle, two-dimensional 1.6H: examples, non-examples, fourths, half/halves

44


Plane figures (regular and irregular)

3-dimensional figures AngLegs Pattern Blocks Geoboards

45


K.6E classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size

1.6A: classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language

2.8C classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices 3.6A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

K.6C identify two-dimensional components of three-dimensional objects

1.6B: distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape

K.6A identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles

1.6C: create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons

2.8A create two-dimensional shapes based on given attributes, including number of sides and vertices 3.6B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

K.6D identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably

1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

2.8A create two-dimensional shapes based on given attributes, including number of sides and vertices 3.6B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

K.6B identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world

1.6E: identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language

2.8B classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language 3.6A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

K.6F create two-dimensional shapes using a variety of materials and drawings

1.6F: compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible

2.8D compose two-dimensional shapes and three-dimensional solids with given properties or attributes 2.8E decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

46

1.6G: partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words

3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

1.6H: identify examples and non-examples of halves and fourths

3.6E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

47




1.6A: classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language

Students must be given a variety of two-dimensional shapes to sort based on their attributes. Students need to be exposed to both regular (i.e. equilateral triangle) and irregular (i.e. right, scalene, isosceles types of triangles) two-dimensional figures. Although students may describe a given two-dimensional shape as having “three lines” and/or “three pointy corners,” teacher should paraphrase student responses with “three sides and three vertices.” With exposure, students will begin to use the formal vocabulary on their own. Students will recognize that circles have curves, and triangles and rectangles have straight sides. The teacher should model the term polygon for those two-dimensional shapes that are enclosed with straight sides. As students begin to recognize how a rectangle, square, and rhombus all have four sides, the teacher should model the term quadrilateral.

* Students may interchange the terms side referencing two-dimensional shapes and edge referencing a three-dimensional shape. * Students may not view a square as a rectangle.

Students are expected to classify and sort two-dimensional shapes, including rectangles, squares as special rectangles, rhombuses, hexagons, and regular and irregular triangles. Shapes may include figures with curved edges and hexagons other than regular hexagons. The language of the SE does not exclude these figures. Students may use informal language such as corners, sides, curved, straight, etc. as they classify and sort figures.

1.6B: distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape

Geometric attributes include the study of sides/edges, vertices and faces. Color, orientation, and size do not define a geometric figure. It is possible to have a triangle (a geometric figure that has three sides and

Defining geometric attributes that define a figure (i.e. number of sides/edges and vertices) and understanding those attributes that do not define a figure (i.e. color, size, orientation) is critical in supporting the

When paired with 1.6D, the expectation is that students distinguish between attributes in order to identify two-dimensional shapes.

48

three vertices) of a different color (i.e. green, blue, yellow, etc.), different orientation (i.e. on its side, upside down, etc.), and a different size (i.e. thick/thin, big/small, long/short, etc.). Therefore, students sorting shapes based on color or size are not describing the geometric differences.

appropriate sorting and classifying of two- and three-dimensional figures. 1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language 1.6E: identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language

For example, a closed figure with three sides is a triangle. A triangle is not defined by its orientation or color. When paired with 1.6E, the expectation is that students distinguish between attributes in order to identify three- dimensional shapes. For example, a solid with exactly six rectangular faces is a rectangular prism. A prism is not defined by its orientation or color.

1.6C: create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons

This standard requires students to take their ability to identify attributes of two-dimensional shapes (1.6A) and create them (i.e. given the attributes of a polygon with six sides and six vertices, students use materials to represent a hexagon). Instruction should vary the materials (i.e. spaghetti, straws, toothpicks, pennies, string, etc.) in order to observe student selection of appropriate materials (i.e. will students recognize that six straws would be easier to demonstrate a hexagon than pennies). Instruction should extend the study of attributes by taking an already created shape and asked to modify it to create a new shape (i.e. students made a rectangle out of clay; student is now asked to modify the

Creating two-dimensional figures given attributes (i.e. the number of sides and vertices) and properties (i.e. all sides are of different lengths) allow students to focus on the geometric attributes of a figure. This attention to specific attributes and properties will support the classification and sorting of various figures. 1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

Students may create two-dimensional figures by using materials, sketching figures, cutting figures out of paper, etc. This SE provides a foundation for 2.8A in which students create two-dimensional figures based on given attributes.

49

rectangle and make it a square and explain how the attributes/ properties of the two shapes were similar yet different).

1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

Students should use the attributes of a given two-dimensional figure to correctly identify a shape. A variety of shapes (i.e. equilateral triangle, scalene triangle, right tringle, etc.) and a variety of orientation, color, and size should be used to ensure that students use the geometric attributes (number of sides/vertices; length of sides) to identify a shape. Instruction should identify a square as a rectangle (opposite sides are of equal length) and a rhombus (all four sides are of equal length).

* Students may interchange the terms side refereeing two-dimensional shapes and edge referencing a three-dimensional shape. * Students may not view a square as a rectangle. * Students may only recognize the more common equilateral triangle (i.e. green triangle pattern block) as a triangle.

The SE adds rhombuses and hexagons to the list of two-dimensional geometric shapes found in K.6A. Students are expected to use formal geometric language such as “vertex/vertices” and “side.”

1.6E: identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language

Students should use the attributes (i.e. number of edges, vertices, and faces) of a given three-dimensional figure to correctly identify a solid. Instruction should clearly identify a cube as a rectangular prism as the faces have four sides and four vertices. It is a special rectangular prism as the lengths of all the edges are equal. To distinguish a triangular prism from a rectangular prism, students should recognize that the shape found at the base of the figure defines the type of prism.

* Students may interchange the terms side refereeing two-dimensional shapes and edge referencing a three-dimensional shape. * Students may not view a cube as a rectangular prism. * Students may identify a triangular prism as a rectangular prism because it is comprised of rectangular faces. * Students may confuse the identification of a three-dimensional shape by its two-dimensional attribute (i.e. a cube is mistakenly identified as a square).

Students are expected to identify and describe attributes of specified three-dimensional geometric figures. The SE adds triangular prisms to the list of three-dimensional geometric solids found in K.6B. Students are expected to use formal geometric language such as vertex/vertices, edge, and face.

50

1.6F: compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible

As students begin to recognize and describe the attributes of given two-dimensional figures, instruction will lead to more spatial reasoning development. Students will be given a targeted two-dimensional shape (i.e. a trapezoid) and asked to use their manipulatives (i.e. pattern blocks, tangram pieces, etc.) to create the targeted shape. Encourage students to find more than one way (i.e. a trapezoid could be made out of three triangle pattern blocks, one square and one triangular pattern block, four triangular pattern blocks, etc.).

Joining various two-dimensional shapes to create a target shape (i.e. given a right angles trapezoid as the target shape, students use their pattern blocks to create the shape. Encourage students to find more than one way of creating a given target shape. The attention to the critical attributes to create a target shape will support the appropriate sorting and classification of two-dimensional figures (i.e. enable to learner to focus on the attributes of the target shape and the joining parts). 1.6D: identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

This SE provides a foundation for 2.8D where students are asked to compose a shape with given properties or attributes. For example, a student may be asked to produce a rectangle as the target shape. A student may join two square tiles to make a rectangle or may join four square tiles to make a rectangle.

1.6G: partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words

The study of fractions will unveil itself through the lens of geometry. Students will take a two-dimensional shape (i.e. a square) and divide the figure into two and/or four equal parts. Encourage students to find more than one way to divide a given shape into equal parts (i.e. a square can be divided in two equal parts vertically, horizontally, or diagonally). This will develop a students’ understanding of how it is possible for different shapes to represent the same fair share of the whole. In adherence to the

2.3B explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

For this SE, two-dimensional figures include circles and rectangles. The student may be expected to partition the figures into two or four equal parts as opposed to being given a shape that is already partitioned and being asked to describe the fraction. Students may be expected to describe the parts using words such as halves, fourths, or quarters and phrases such as half of.

51

standard, instruction should include irregular two-dimensional shapes. The use of geoboards will support the trial and error process of dividing an irregular shape into two and four equal parts. Students should then be able to describe the equal parts in words (i.e. one of two equal parts; one of two fair shares; one-half; and halves).

1.6H: identify examples and non-examples of halves and fourths

In conjunction with 1.6G, as students are partitioning figures into two and four equal parts and identifying them as halves/fourths, students recognize examples (i.e. regular and irregular shapes divided equally) and non-examples of such partitions (i.e. whole objects divided unequally). With the use of geoboards, students verify examples of halves and fourths by comparing the amount of area in each part.

Identifying examples and non-examples of fractional parts of the same whole will support students in understanding the part-to-whole relationship and the equal size of the parts. This knowledge provides the foundation for visually comparing two fractions and/or concretely representing equivalent fractions. 2.3B explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

The focus of this SE is on the fair sharing or equal parts of the two-dimensional figure. A non-example of a half would be a two-dimensional figure that has been partitioned into two unequal parts.

52

Course: Grade 1 Math Bundle 5: Measurement

Dates: February 27th-March 31st (20 days)

TEKS 1.7A: use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement 1.7B: illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other 1.7C: measure the same object/distance with units of two different lengths and describe how and why the measurements differ 1.7D: describe a length to the nearest whole unit using a number and a unit 1.7E: tell time to the hour and half hour using analog and digital clocks

ELPS Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 2E: use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3E: share information in cooperative learning interactions Reading 4E: read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language

53

Vocabulary

Unit Vocabulary Analog clock End to end Hour Measurement tool Shorter than Colon Fewer Hour hand Minute hand Time Digit Gaps Length More Unit of measure Digital clock Half hour Longer than Overlaps Whole unit Distance

Cognitive Complexity Verbs: use, measure, illustrate, describe, tell time Academic Vocabulary by Standard: 1.7A: length, measurement tool 1.7B: end to end, gaps, overlaps, length, unit of measure 1.7C: distance, fewer, more, length, longer than, shorter than, unit of measure 1.7D: length, unit of measure, whole unit 1.7E: analog clock, colon, digit, digital clock, hour hand, minute hand, time, half hour, hour


Clocks Color Tiles Interlocking Cubes Cuisenaire Rods Non-standard measurement tools

54


K.7A give an example of a measurable attribute of a given object, including length, capacity, and weight

1.7A: use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement

2.9D determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes 2.9E determine a solution to a problem involving length, including estimating lengths


1.7B: illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other

2.9A find the length of objects using concrete models for standard units of length 2.9E determine a solution to a problem involving length, including estimating lengths


1.7C: measure the same object/distance with units of two different lengths and describe how and why the measurements differ

2.9B describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object 2.9E determine a solution to a problem involving length, including estimating lengths


1.7D: describe a length to the nearest whole unit using a number and a unit

2.9A find the length of objects using concrete models for standard units of length 2.9E determine a solution to a problem involving length, including estimating lengths

1.7E: tell time to the hour and half hour using analog and digital clocks

2.9G read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m. 3.7C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

55





1.7A: use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement

As students begin to measure the length of various objects, it is important to understand that linear measurements are continuous in nature (i.e. measurement tools need to be aligned back to back with no gaps or overlaps in between). Instruction should begin with aligning non-standard units of measure (i.e. paper clips, snap cubes, index cards, unit cubes, color tiles, etc.) in order for students to grasp the concept of linear measurement being continuous. This will be important when students begin to measure with rulers.

Understanding that linear measurement is continuous in nature provides the foundational understanding of the functionality of the ruler. 1.7D: describe a length to the nearest whole unit using a number and a unit

This SE includes non-standard measuring tools that illustrate the continuous nature of length. Examples of tools may include real-world objects such as adding machine tape, ribbon, or string.

1.7B: illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other

In conjunction with 1.7A, students need to decipher between the object being measured (i.e. length of an index card) and the unit of measure (i.e. paper clips). As students begin to measure the length of various objects, they need to understand where the measurement begins and ends (i.e. to determine the length of the index card we will only measure one side), the unit of measure must be consistent (i.e. paper clips must be the same length; cannot mix smaller paper clips with larger ones), and manipulatives need to be aligned back-to-back with no gaps or overlaps. As non-standard units of measure will also be used to determine area in grade 2 (see 2.9F), it is critical to identify that

Understanding the appropriate process for measuring objects is a critical foundation component before introducing the use of formal measurement tools such as a ruler. 1.7D: describe a length to the nearest whole unit using a number and a unit

Units of length may include manipulatives such as proportional rods and objects such as paperclips and craft sticks.

56

only the length of one of the sides of the manipulatives is used, not the entire object (i.e. when utilizing color tiles, draw a line along one side to visually demonstrate that we will only use this component of the measuring tool to determine length).

1.7C: measure the same object/distance with units of two different lengths and describe how and why the measurements differ

Students should measure a give object with more than one unit of measure (i.e. measure the length of an index card using paper clips, unit cubes, color tiles, etc.). Instruction leads the students to discover that the longer the unit of measure, the fewer units of measure is needed; the shorter the units of measure, the more unit of measure are needed. This concept leads to future understanding of how an object measuring 2 yards in length is not shorter than an object measuring 6 feet in length.

Measuring the length of objects with a variety of concrete objects supports the understanding that objects can be measured with various units. This supporting standard allows the learner to experience that the shorter the unit of measure the more units are needed to measure the length; the longer the unit of measure, the fewer units needed to measure the length. As students move to measuring with a ruler, this non-standard unit of measurement experience supports their understanding of how objects can be measured in centimeters and inches and the inverse relationship between the size of the units and the number of units needed to equal the length of the object. 1.7D: describe a length to the nearest whole unit using a number and a unit

In describing how and why the measurements differ, students are expected to describe the relationship between the size of the unit and the number of units needed to measure the length of an object. For example, a student may say, “I measured the distance with the white rods and the yellow rods. It took more of the white rods to measure the distance than yellow rods. The white rods are shorter, so I had to use more to measure the length.” This SE provides support for 2.9E where students are asked to describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object.

1.7D: describe a length to the nearest whole unit using a number and a unit

As with most measurements, the length of objects will not always be exact. Students will measure the length of objects to the nearest whole unit of measure (i.e. students will not record measurements as 3 ½ unit cubes). Beware of students that will want to fill in the missing length with

* Students may not align the zero marking of the ruler appropriately. * Students may think that an object measuring 12 inches in length is longer than an object measuring one foot because 12 is bigger than 1.

When students measure length using manipulatives or objects that are linear in nature, they should use a number and a label to identify the length, such as 5 yellow rods or 5 craft sticks.

57

smaller units of measure. Remind them that units of measure cannot be mixed (see 1.7B). This standard also requires students to record their measurements using a number and unit (i.e. 6 color tiles; 5 small paper clips; 16 rainbow cubes, etc.).

* Students may not estimate a measurement reasonably because they do not have a solid understanding of the size of various measures.

1.7E: tell time to the hour and half hour using analog and digital clocks

Relate the clock to a circular, closed number line (see 1.2F). Create a number line identifying the whole numbers 0-12. Demonstrate how to connect both ends of the number line to create a circular number line pointing out how hour numerals on the clock relate to those on a number line. The telling of time to the nearest hour with only the hour hand shown on the face of the clock will allow students to focus on the positioning of the hour hand and determine the hour when in-between numerals. As instruction moves to telling time to the half hour, associate the concept to fractions (see 1.6G). Be sure to relate the hour and minutes hand from the analog clock to the digits represented on a digital clock. Instruction should clarify the use of the color (:) on the digital clock to separate the hours (whole) from the minutes (part).

* Students may misidentify the hour and minute hands, confuse how to read each one, and/or not understand what each hand measures. * Students may not be able to accurately read the hour hand as it falls between two hour points. * Students may be able to read time accurately but struggle when asked to represent a given time on a clock.

The phrase “half hour” also indicates that students would recognize that 1:27 is closer to 1:30 than 1:00, so the time would be estimated as 1:30. When looking at an analog clock, students may compare the location of the minute hand between 12 and 6 to determine if a time is closer to an hour, such as 1:00, or closer to a half hour, such as 1:30. Because students begin work with fraction concepts such as halves in grade 1, it is appropriate to focus on 30 minutes as an indicator of a half hour.

58

Course: Grade 1 Math Bundle 6: Money and Personal Financial Literacy

Dates: April 3rd- May 5th (23 days)

TEKS 1.4A: identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them 1.4B: write a number with the cent symbol to describe the value of a coin 1.4C: use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes 1.9A: define money earned as income 1.9B: identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs 1.9C: distinguish between spending and saving 1.9D: consider charitable giving

ELPS

Learning Strategies 1A: use prior knowledge and experiences to understand meanings in English Listening 2D: monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed Speaking 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4C: develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

59

Vocabulary

Unit Vocabulary Cent symbol Fives Needs Saving Twos Charitable giving Goods Nickels Services Value Coins Income Pennies Spending Wants Dimes Money earned Quarters Tens

Cognitive Complexity Verbs: identify, write, describe, use, determine, define, distinguish, consider Academic Vocabulary by Standard: 1.4A: coins, pennies, nickels, dimes, quarters, value 1.4B: cent symbol, coins, pennies, nickels, dimes, quarters, value 1.4C: coins, dimes, nickels, pennies, cents, twos, fives, tens 1.9A: money earned, income 1.9B: goods, income, needs, services, wants 1.9C: saving, spending 1.9D: charitable giving


Coins: pennies, nickels, dimes, quarters

60


K.4A identify U.S. coins by name, including pennies, nickels, dimes, and quarters

1.4A: identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them

1.4B: write a number with the cent symbol to describe the value of a coin

2.5B use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins

1.4C: use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

2.5A determine the value of a collection of coins up to one dollar 3.4C determine the value of a collection of coins and bills

K.9A identify ways to earn income 1.9A: define money earned as income 3.9A explain the connection between human capital/labor and income

K.9D distinguish between wants and needs and identify income as a source to meet one's wants and needs

1.9B: identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs

1.9C: distinguish between spending and saving 2.11A calculate how money saved can accumulate into a larger amount over time 2.11B explain that saving is an alternative to spending

1.9D: consider charitable giving 3.9F identify decisions involving income, spending, saving, credit, and charitable giving

61





1.4A: identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them

Students need to be able to identify the coin and its value whether the heads or tails side of the coin is visible. Instruction must also address how various coins are related to each other (i.e. five pennies = one nickel; two nickels = one dime; five nickels = one quarter). The TEKS also requires the students to recognize the need for coins in monetary transactions (i.e. when would we need to know that value of coins; why would it be important to know the relationship between the coins).

Being able to identify U.S. coins and describe the relationship between them is critical in solving monetary transactions. 1.4C: use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

This SE extends K.4A by asking students to describe the relationship among the coins. For example, a quarter may be thought of as having the same value as 5 nickels or 25 pennies. Students should be familiar with the basic attributes of each coin regardless of if the coin has traditional or other images.

1.4B: write a number with the cent symbol to describe the value of a coin

In conjunction with 1.4A, as students begin to identify U.S. coins and their value, they will use the cent symbol to represent the value.

Being able to symbolically represent the value of a coin is critical in solving monetary transactions. 1.4C: use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes 2.5A determine the value of a collection of coins up to one dollar

The SE expects students to label the value of a coin with the cent symbol, such as a dime has a value of 10¢.

1.4C: use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

In conjunction with 1.5B, students are able to apply their knowledge of skip counting to determine the value of a collection of coins (i.e. skip count by two to count a collection of pennies; skip count by fives to count a collection of nickels; skip count by tens to count a collection of dimes). As students become comfortable with determining the value of a collection of like coins, instruction should then address a mixture of

* Students may not recognize the heads and/or tails side of a coin. * Students may not recognize non-traditional coins. * Students may confuse the size of the coin with its value (i.e. a nickel is worth more than a dime because it is larger in size). * When adding a collection of

To use the relationships among the coins with connections to skip counting, one may count nickels by fives and dimes by tens. One may count two pennies together to count by twos. A collection of coins used for skip counting should not include quarters in grade 1.

62

unlike coins. Again, associating a child’s understanding of skip counting will allow them to add the value with ease (i.e. given 3 dimes, 4 nickels and 6 pennies, students will skip count by tens to add the value of dimes 10, 20, 30; continuing skip counting by fives to add the value of the nickels 35, 40, 45, 50; then skip count by two to add the value of the pennies; 52, 54, 56).

unlike coins, students may struggle to determine which coins to begin with when skip counting.

With a collection of pennies, nickels, and dimes, a student may begin counting by tens to determine the value of the dimes, continue from that amount counting by fives to determine the values of the dimes and the nickels, and count by ones or twos to include the pennies in the value of the collection. The maximum value of the collection is 120 cents.

1.9A: define money earned as income

Students in Kindergarten (see K.9B), discussed the difference between money received as income and money received as a gift. In Grade 1, students learn that money that is earned from goods and labor are classified as income. Doing chores to earn money is income; money received from family/friends for birthdays/holidays is a gift. Story problems involving real world situations of money being earned could be incorporated into the Number and Operations strand (see 1.2E/F/G and 1.3F).

Defining money earned as income will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

Emphasis for this SE should be on the idea that income is “earned.” This SE builds on K.9A and supports 1.9B.

1.9B: identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs

Students in Kindergarten see (K.9D) discussed the difference between wants (i.e. video games, computers, vacations, etc.) and needs (i.e. water, food, shelter, etc.) and how income is needed to obtain both. In Grade 1 students continue that understanding with an emphasis on making choices between the two (i.e. when my income is limited, I will have to make choices between what is a necessity and what is luxury). Perhaps story problems involving real world situations of money being earned and/or money being spent on goods (i.e. video games, computer, candy, etc.) and services (i.e. manicures, cable television, dry

Identifying income and distinguishing between wants and needs will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds on K.9D as well as 1.9A.

63

cleaning, etc.) could be incorporated into the Number and Operations strand (see 1.2E/F/G and 1.3F).

1.9C: distinguish between spending and saving

Students will need to decipher between spending money (on either wants or needs) and saving. Future grade level discussions extend this learning to why both are necessary. Perhaps story problems involving real world situations of money being spent and earned could be incorporated into the Number and Operations strand (see 1.2E/F/G and 1.3F).

Distinguishing between spending and saving will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 2.11A and 3.9E.

1.9D: consider charitable giving Instruction should include discussions about what is a charity, identifying types of charities, and benefits of giving to a charity. Perhaps story problems involving real world situations of charitable giving could be incorporated into the Number and Operations strand (see 1.2E/F/G and 1.3F).

Understanding charitable giving will support one’s ability to manage financial resources more effectively for a lifetime of financial security.

This SE builds to 3.9F.

64

Course: Grade 1 Math Bundle 7: Data

Dates: May 8th- June 1st (18 days)

TEKS 1.8A: collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts 1.8B: use data to create picture and bar-type graphs 1.8C: draw conclusions and generate and answer questions using information from picture and bar-type graphs

ELPS Learning Strategies 1F: use accessible language and learn new and essential language in the process Listening 2I: demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs Speaking 3F: ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments 3G: express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics Reading 4F: use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language 4G: demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs

65

Vocabulary

Unit Vocabulary Bar-type graphs Data Information Picture graphs t-charts Categories Graph title Labels Tally marks

Cognitive Complexity Verbs: collect, sort, organize, use, create, draw conclusions, generate, answer Academic Vocabulary by Standard: 1.8A: categories, data, graph title, labels, tally marks, t-charts 1.8B: bar-type graphs, data, graph title, labels, picture graphs 1.8C: bar-type graphs, information, picture graph


Chart Paper Grid Paper Pocket Charts Collapsible Sorting Rings

66


K.8A collect, sort, and organize data into two or three categories

1.8A: collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts

K.8B use data to create real-object and picture graphs 1.8B: use data to create picture and bar-type graphs 2.10B organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more 3.8A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

K.8C draw conclusions from real-object and picture graphs

1.8C: draw conclusions and generate and answer questions using information from picture and bar-type graphs

2.10D draw conclusions and make predictions from information in a graph 2.10C write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one 3.8B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

67




1.8A: collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts

It is imperative for students to generate a question before a unit of study on data (i.e. What types of flowers grow in my grandmother’s garden?). Instruction should encourage students to extend beyond two categories (i.e. roses, carnations, and daffodils), yet restrict the sorting to within three categories (i.e. sorting by the different color of flowers may yield too many categories). Students collect their own data, so they have a personal connection. Students will use tally marks to collect the data and the information will be organized in T-charts in order to better interpret the data. Ensure that students title and label their models/ representations of tally marks and T-chart.

Having students collect, sort, and organize their own data allows students to interpret data on a graph more effectively. 1.8C: draw conclusions and generate and answer questions using information from picture and bar-type graphs

Students are expected to collect data, sort, and organize the data using models and representations such as T-charts and tally marks. The data collection takes place in response to a question. Pairing with 1.8B, the student will use the organized data to create a picture of bar-type graph.

1.8B: use data to create picture and bar-type graphs

In conjunction with 1.8A, students will represent the data they have collected in a picture and/or bar-type graph. Ensure that students title and label their graphs appropriately. At this stage of development, one-to-one correspondence should be employed for the picture representations and scales on the bar-type graphs. Instruction should emphasize the importance of a title and labeling the categories of the graph.

Having students collect, sort, and organize their own data assists them in drawing conclusions and making reasonable predictions. Representing student collected data on picture and bar-type graphs enables them to interpret the information more accurately. 1.8C: draw conclusions and generate and answer questions using information from picture and bar-type graphs

A picture graph is a graph that uses one picture to represent each piece of data. A bar-type graph may be partitioned into sections so that first graders may use one-to-one correspondence to count the spaces as opposed to using the length of the bar as required in 2.10A. The limitations of three categories found in 1.8A applies to this SE. Students extend to 4 categories in grade 2. Data values should align to the Number and Operations standards for grade 1.

68

1.8C: draw conclusions and generate and answer questions using information from picture and bar-type graphs

As students have collected their own data and organized it into graphs (see 1.8A/B), they should reflect on what type of information the graphs provide. Students will be able to better articulate the type of information when it is personal. Students will naturally give factual responses (i.e. My grandmother has 18 daffodils, 4 roses, and 16 carnations in her garden, etc.) and inferential responses (i.e. Roses must not grow very well in that type of soil). Instruction should lead students to create their own questions from the data they collected (i.e. how many more daffodils did my grandmother have in her garden than roses? How many roses and carnations are there in Grandma’s garden?) and inferential questions that require students to draw conclusions (Which flower do you think my grandmother likes the most and why?). Students could then exchange their graphs and ask fellow classmates to answer their self-generated questions.

* When representing the same set of data on the two types of graphs, students may interpret the data as different because of the difference in the visual representations. * When representing the same set of data vertically or horizontally, students may interpret the data as different because of the difference in the visual representations. * When using real-objects to represent data, students may associate the larger object with representing more data (i.e. two king size candy bars aligned next to four snack size candy bars appears as if there are more king size than snack size candy bars).

Answers to questions should align to the Number and Operations standards for grade 1.

grade 1 mathematics curriculum document 2016-2017

Documents