rationale for second grade instructional guide · rationale for second grade instructional guide...

Rationale For Second Grade Instructional Guide

Organizational Highlights All power standards are being assessed. Second grade has twenty power standards. There was an attempt made to reduce the number of standards being assessed by only focusing on assessing the power standards. However, in discussions with teachers and coaches, it was felt that some standards needed to be benchmarked over several quarters. In addition, it was felt that there were nonpower standards that also needed to be assessed because they are on the Blueprint for the California Standards Assessment. Also, there was a concern that certain standards needed to be assessed more than one time. For these reasons, the number of assessed standards is high for each quarter in the second grade. Recommended lessons from Harcourt Math, Second Grade are listed for each of the content standards The mathematics program in second grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives during mathematics. Manipulatives enables the students to create models which facilitate their understanding of the mathematics being taught. Throughout Harcourt Math the publisher includes manipulatives when introducing a lesson. Use of the teaching suggestions labeled “Getting Started Options” as well as the Intervention and Extension Resources, is strongly recommended. Lessons listed in Additional Resources by Marilyn Burns and from LUCI also provide activities using manipulatives. It is recommended that the use of manipulatives extend beyond the introduction of a lesson. The teacher resource pages of the teacher edition provide a number of activities that involve the use of manipulatives. However, manipulatives should not be used in isolation. It is important that a link be created between the manipulative and the paper and pencil representations. The Problem of the Day should be included as part of the daily routine when teaching mathematics. The Instructional Guide lists the recommended Lesson Resource pages and accompanying lessons for each of the content standards. Harcourt Math also provides various resources such as literature connections, strategies for English Language Learners, the Family Involvement Activities, Activities and Games for Home and School, and Intervention Strategies and Activities.

Quarter One This quarter begins with a focus on Graphing and Interpreting Data. The writers of the 2nd grade instructional guide felt that

the beginning of school is a time when data about the class is collected and can be integrated with mathematics instruction. Addition and Subtraction strategies reinforce learnings from the 1st grade and emphasize the inverse relationship between the two operations. Teachers need to continue to emphasize these understandings to encourage more flexible methods of thinking about and solving problems. Time is taught over the first two quarters to provide more time for mastery. Telling time emphasizes counting by fives which will support learning the five times table. Number Sense, Place Value, and Patterns are spread over the first three quarters to enable a focus on a portion of these key standards that spiral in difficulty from quarter to quarter.

Quarter Two This quarter introduces the content standards relating to money. The focus in only on coins which provides students an

opportunity to reinforce addition facts when adding a five or a ten or when adding ten to a two-digit number. The Quarter continues with a review of the inverse relationship of addition and subtraction that was taught in the First Quarter before beginning addition and subtraction of two-digit numbers with and without regrouping. Geometry is added with a focus on attributes of plane and solid figures. While concepts of symmetry and congruency are introduced, students will have another opportunity to work on these concepts in Quarter Four. Place Value is continued from Quarter One and is extended through 500. Time is reinforced and assessed in this quarter. Attention needs to be paid to time equivalencies. Patterns are again revisited to reinforce previous learning and provide time for mastery.

Quarter Three This Quarter begins with instruction in the content standards of measurement. In teaching measurement, there should be an

emphasis on estimation before actual measurement. Lesson planning should include experiences with measuring real world objects. It should first begin with non standard measurement before the introduction of standard measurement to provide opportunities for students to understand why standards units are needed. Understanding how to measure the length of objects and lines will be expanded in 3rd grade as students learn about perimeter. Instruction continues in place value building on concepts learned in Quarters 1 and 2 and extends to 1000. Fractions begin and focus on parts of a whole and parts of a group as well as fractions equal to one. Addition and subtraction with and without regrouping builds on the learning from Quarter 2 and extends to using three-digit numbers. Money continues with a review of coins and expands to include bills. At this time, the decimal notation for coins and bills are also introduced as students add and subtract problems with decimal notation. Multiplication and division begin in this Quarter and extend to Quarter Four. These concepts build on the addition and subtraction concepts taught in the first three Quarters. The emphasis is on learning the concepts of multiplication and division and memorizing the facts of 2, 5, and 10. By learning these facts in the second grade prepares students for learning additional multiplication facts in the third grade.

Quarter Four This Quarter continues developing measurement concepts with an emphasis on mass, capacity and temperature and extends

linear measurement to perimeter. These topics are not 2nd grade standards but are key standards in 3rd grade. The remainder of this quarter is spent Reviewing 2nd Grade Number Sense Standards. These standards prepare students for the first Quarter of the third grade. Student data should be used to determine differentiated concepts for review. Additional resources such as Marilyn Burns’ material and LUCI investigations can provide a rich experience for students to grasp a deeper understanding of mathematical concepts.

LOS ANGELES UNIFIED SCHOOL DISTRICT Second Grade

Mathematics Instructional Guide: Quarter One

DATA ANALYSIS NUMBER SENSE PLACE VALUE PATTERNS TIME Standards: 100 * NS 1.1 Count, read, and write numbers to 1000 and identify place value for each digit. 100 * NS 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000). 100 * NS 1.3 Order/ compare whole numbers to 1000 by using the symbols <, =, >. * NS 2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 – 6 = 8) to solve problems and check solutions. NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places. AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction. * AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. AF 1.2 Relate problem situations to number sentences involving addition and subtraction. * AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. MG 1.4 Tell time to nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). MG 1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.) * SDAP 1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations. SDAP 1.1 Record numerical data in systematic ways, keeping track of what has been counted. SDAP 1.2 Represent the same data set in more than one way (e.g. bar graphs and charts with tallies). * SDAP 1.3 Identify features of data sets (range and mode). * SDAP 1.4 Ask and answer simple questions related to data representations. * SDAP 2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways. SDAP 2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12…; the number of ears on one horse, two horses, three horses, four horses). SDAP 2.2 Solve problems involving simple number patterns. MR 1.0-3.0 Embedded

Key: Power Standard * Assessed Standard Strikethrough: Topic not taught or assessed this quarter ** Dates to be determined at school site

LAUSD Mathematics ProgramInstructional Guide, Grade 2

Quarter One, 2003-2004



DATA ANALYSIS NUMBER SENSE PLACE VALUE PATTERNS TIME

Dates ** Standard # Concepts Harcourt Additional Resources AF 1.3

SDAP 1.0 SDAP 1.1 SDAP 1.2 SDAP 1.3 SDAP 1.4 MR 1.0 MR 2.0 MR 2.2

Graphing: • Collect, record and represent data • Solve problems using data

Lesson Planning: 75A – 82A Lessons: 6.1 - 6.6

About Teaching Mathematics, Marilyn Burns: • Graphing in the Classroom, P. 75-78, 180, 184 A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Estimating Beans, Pp 41- 46

NS 2.1AF 1.0 AF 1.1 AF 1.2

Addition • Mental Strategies • Commutative and Associative Rules

Lesson Planning: 3A – 14A Lessons: 1.1- 1.6

About Teaching Mathematics, Marilyn Burns: • Cross Out Singles, Pg 191, • How Many Reds? Pp 162-163 A Collection of Math Lessons, Grades 1-3, Marilyn Burns: •The Game of Pig, Pg 188







Dates ** Standard # Concepts Harcourt Additional Resources

NS 2.1 AF 1.1

Subtraction • Mental Strategies • Fact families


NS 2.1AF 1.0 AF 1.1 MR 1.1

Addition & Subtraction • Inverse relationship

Lesson Planning: 33A – 40A Lessons: 3.1 – 3.4

NS 1.1 NS 1.2 NS 6.0 MR 2.0 MR 3.0

Numbers to 100 • Tens and ones • Reasonable estimates


About Teaching Mathematics, Marilyn Burns: • How Many Pockets? P. 174 A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Making Tens and Ones, P. 63-70 • Five Tower Game, P. 80 • Fill the Cube, P 81 • Handfuls, P 82 •Fill the Boxes, P 82







Dates ** Standard # Concepts Harcourt Additional Resources NS 1.3

SDAP 2.2

Compare and Order Numbers

Lesson Planning: 61A -64A Lessons: 5.2 & 5.3

SDAP 2.0 SDAP 2.1 SDAP 2.2 MR 3.0

Number Patterns • Even and Odd • Skip Count


About Teaching Mathematics, Marilyn Burns: • Introducing Patterns, P. 112-113 • Arrow Arithmetic, Pg 135 A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Making Necklaces, P. 11-19

MG 1.4 MG 1.5

Telling Time • Nearest quarter hour • Intervals of time • Relationships of time

Lesson Planning: 125A – 132A; 137A – 144A Lessons: 9.1 – 9.4; 10.1 – 10.4

A S S E S S M E N T E N R I C H M E N T / R E T E A C H I N G





Mathematics Instructional Guide: Quarter Two

MONEY ADDITION SUBTRACTION GEOMETRY PLACE VALUE TIME Standards: 500 * NS 1.1 Count, read, and write numbers to 1000 and identify place value for each digit. 500 * NS 1.2 Use words, models, and expanded forms (e.g. 45= 4 tens + 5) to represent numbers (to 1,000). 500 * NS 1.3 Order/ compare whole numbers to 1000 by using the symbols <, =, >. * NS 2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 – 6 = 8) to solve problems and check solutions. * NS 2.2 Find the sum or difference of two whole numbers up to three digits long. NS 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. NS 5.0 Students model and solve problems by representing, adding, and subtracting amounts of money. * NS 5.1 Solve problems using combinations of coins and bills. NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places. AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction. * MG 1.4 Tell time to nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). MG 1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.). * MG 2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space. * MG 2.1 Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices. * MG 2.2 Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle). * SDAP 1.4 Ask and answer simple questions related to data representations. * SDAP 2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways. SDAP 2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12…; the number of ears on one horse, two horses, three horses, four horses). SDAP 2.2 Solve problems involving simple number patterns. MR 1.0-3.0 Embedded



Quarter Two, 2003-2004



MONEY ADDITION SUBTRACTION GEOMETRY PLACE VALUE TIME


NS 5.1 SDAP 1.4

Counting Money • Fewest coins • Make change • Decimal notation

Lesson Planning: 101A – 106A; 111A – 120A Lessons: 7.1 - 7.5; 8.1 - 8.5

About Teaching Mathematics, Marilyn Burns: • Coin Riddles, Pg 130 • Billy Goes Shopping, Pg 190 • Making Change, Pg 130 • Race for $1.00, Pg 75

NS 2.1 Review: Addition and Subtraction • Inverse relationship

Refer to Instructional Quarter 1 for additional resources.

NS 2.2NS 2.3 NS 6.0

2-Digit Addition • Estimate and compute • Add 2 and 3 digit numbers

Lesson Planning: 157A - 166A; 171A - 178A Lessons: 11.1 - 11.5; 12.1 - 12.4

About Teaching Mathematics, Marilyn Burns: • Addition Table Explorations, Pg 132 A Collection of Math Lessons, Grades 1-3 Marilyn Burns: • Activities with Base 10 Blocks, Pp 83-95

NS 2.2NS 2.3 AF 1.0

2-Digit Subtraction • Estimate and compute

Lesson Planning: 195A - 204A; 209A - 218A; 223A - 226A Lessons: 14.1 to 14.5; 15.1 to 15.5; 16.1 to 16.2

A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Clear the Board, Pp 92-95 • The Subtraction Game, Pp 181-183, 188






MONEY ADDITION SUBTRACTION GEOMETRY PLACE VALUE TIME Dates ** Standard # Concepts Harcourt Additional Resources

MG 2.0 MG 2.2 MR 1.2 MR 2.0 MR 2.1

Plane Shapes • Attributes of common figures • Putting together and taking apart shapes


A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • The Four Triangle Problem, Pp 99-105 • Explorations with Four Toothpicks, Pg 129 – 138 About Teaching Mathematics, Marilyn Burns: • Tangram Puzzle, P. 83 • Explorations with Four Toothpicks, P. 92 • The Four Triangle Problem, Pg 93

MG 2.0MG 2.1 MR 1.2

Solid Figures • Attributes of common figures • Faces, vertices, edges


A Collection of Math Lessons, Grades 1-3 Marilyn Burns: • Box Sorting, Pp 117 - 128

NS 1.1 NS 1.2 MR 1.0 MR 1.2 MR 2.0 MR 3.0

Place Value to 500 • Count, read, and write • Order and compare numbers


A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • A Place Value Menu, Pp. 71-82 • Activities with Base 10 Blocks, P. 83-95 • Place Value Game , Pp.167 - 172






MONEY ADDITION SUBTRACTION GEOMETRY PLACE VALUE TIME

Dates ** Standard # Concepts Harcourt Additional Resources MG 1.4

MG 1.5 Review: Time Concepts

Refer to Instructional Quarter 1 for additional resources

NS 1.3SDAP 2.0 SDAP 2.1 SDAP 2.2

Review: Patterns • Order and compare numbers

Lesson Planning: 321A – 322A; 325A – 326A 329A – 330A Lessons: 22.1 - 22.3 & 23.5






Mathematics Instructional Guide: Quarter Three

MEASUREMENT NUMBER SENSE FRACTIONS ADDITION/SUBTRACTION MULTIPLICATION DIVISION MONEY

Standards: * NS 1.1 Count, read, and write numbers to 1000 and identify place value for each digit * NS 1.3 Order/ compare whole numbers to 1000 by using the symbols <, =, >. * NS 2.2 Find the sum or difference of two whole numbers up to three digits long. NS 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. * NS 3.0 Students model and solve simple problems involving multiplication and division. * NS 3.1 Use repeated addition, arrays, and counting by multiples to do multiplication. * NS 3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division * NS 3.3 Know the multiplication tables of 2s, 5s, and 10s (to “times 10”) and commit them to memory. * NS 4.1 Recognize, name and compare unit fractions from 1/12 to 1/2. * NS 4.2 Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls). * NS 4.3 Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one NS 5.0 Students model and solve problems by representing, adding, and subtracting amounts of money. * NS 5.1 Solve problems using combinations of coins and bills * NS 5.2 Know and use the decimal notation and the dollar and cent symbols for money. NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places NS 6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch). AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. MG 1.1 Measure the length of objects by iterating (repeating) a nonstandard or standard unit. MG 1.2 Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used. * MG 1.3 Measure the length of an object to the nearest inch and/or centimeter. MR 1.0-3.0 Embedded



Quarter Three, 2003-2004





NS 6.1 MG 1.1 MG 1.2 MG 1.3

Measurement • Length


A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Exploring Ratio, Pp 107-116

NS 1.1 NS 1.3

Comparing and Ordering Numbers to 1,000

Lesson Planning: 323A – 324A; 327A – 328A Lessons: 22.2 & 22.4

A Collection of Math Lessons, Grade 1-3, Marilyn Burns: • Activities with Base 10 Blocks, Pp 83-95 • The Place Value Game, Pp 167-172

NS 4.1 NS 4.2 NS 4.3 MR 1.2 MR 2.0 MR 3.0

Parts of a Whole • Identify fractions • Compare fractions • Fractions Equal to One


About Teaching Mathematics, Marilyn Burns: • Sharing Cookies, P. 230 • The Fraction Kit, P. 226 • Put in Order, P 231 A Collection of Math Lessons, Grades 3-6, Marilyn Burns: • Fractions with Cookies, Pp 37-43

NS 4.1 NS 4.2 MR 1.2

Parts of a Group • Identify fractions • Compare fractions • Fractions Equal to One


About Teaching Mathematics, Marilyn Burns: • Introducing Fractions as Parts of Sets, Pg 225 • Fractions with Two Color Counters, Pg 225








NS 2.2 NS 2.3 NS 6.0 MR 1.2 MR 2.2

3 – Digit Addition • Estimate and compute


About Teaching Mathematics, Marilyn Burns: • Palindromes, Pp 127-128 • Decision Making, Pg 106

NS 2.2 MR 1.2 MR 2.1 MR 2.2

3 – Digit Subtraction


AF 1.3

Addition and Subtraction • Problems using data from graphs

Lesson Planning: 189A – 190A Lesson: 13.4

NS 5.0NS 5.1 NS 5.2 NS 6.0

Add and Subtract Money

Lesson Planning: 227A – 230A; 377A-378A; 399A – 402A Lessons: 16.3 & 16.4; 25.5, 27.1 - 27.2








NS 3.0 NS 3.1 NS 3.3 MR 1.2 MR 3.0

Multiplication: • Repeated addition • Arrays • Counting by multiples • Tables: 2, 5, 10

Lesson Planning: 411A – 420A; 425A-430A Lessons: 28.1- 28.5; 29.1 – 29.3

About Teaching Mathematics, Marilyn Burns: • The Chopstick Problem, P. 195 • Circles and Stars, P. 196 • Candy Boxes, P. 197 • Things That Come in Groups, Pg 195 A Collection of Math Lessons, Grades 3-6, Marilyn Burns: • Introducing Multiplication, Pg 21-35

NS 3.0 NS 3.2 NS 3.3 MR 1.1

Division Concepts: • Repeated subtraction • Equal sharing • Equal groups with remainders


About Teaching Mathematics, Marilyn Burns: • Investigations with Raisins, Pp 129 • Leftovers, P. 208 A Collection of Math Lessons, Grades 1-3, Marilyn Burns: • Sharing Problems, Pp 47-59 A Collection of Math Lessons, Grades3-6, • Explorations with Raisins, Pp 11-19






Mathematics Instructional Guide: Quarter Four

MEASUREMENT REVIEW 2nd GRADE STANDARDS Standards: * NS 1.3 Order/ compare whole numbers to 1000 by using the symbols <, =, >. * NS 2.2 Find the sum or difference of two whole numbers up to three digits long. * NS 3.0 Students model and solve simple problems involving multiplication and division. * NS 3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division. * NS 3.3 Know the multiplication tables of 2s, 5s, and 10s (to “times 10”) and commit them to memory. NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places NS 6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch). * AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. * MG 1.3 Measure the length of an object to the nearest inch and/or centimeter * MG 2.2 Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle). MR 1.0-3.0 Embedded


MG 1.3 MR 1.0 MR 1.2 MR 2.2

Perimeter Lesson Planning: 277A – 280A Lessons: 19.5 & 19.6

MG 1.0 MG 1.2 MR 1.1 MR 1.2 MR 3.0

Capacity, Weight and Temperature


AF 1.1 Review: Commutative and Associative Rules




Quarter Four, 2003-2004


Mathematics Instructional Guide: Quarter Four

MEASUREMENT REVIEW 2nd GRADE STANDARDS


NS 6.0 MR 3.0

Review: Addition and Subtraction • Review estimation strategies


NS 3.0 NS 3.3 MR 3.0

Review: Memorize the Facts • 2’s, 5’s, 10’s

Lesson Planning: 431A – 432A Lesson: 29.4 Refer to Instructional Quarter 3 for additional resources

NS 3.2

Review: Division Concepts


NS 1.3 Review: Order and Compare Numbers

Refer to Instructional Quarters 1, 2, 3 for additional resources

MG 2.2 Review Plane Shapes: • Put Shapes Together; Take them Apart





Quarter Four, 2003-2004

rationale for second grade instructional guide · rationale for second grade instructional guide...

Documents