rationale for first grade instructional guide · involve the use of manipulatives and include...

Rationale for First Grade Instructional Guide Organizational Highlights The mathematics program in First grade includes the use of manipulatives. All students should have access to concrete objects and/or manipulatives during mathematics. This enables the students to create models which facilitate their understanding of the mathematics being taught. Throughout Harcourt Math the publisher included manipulatives when introducing a lesson. 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 and include ELL/SDAIE strategies. However, manipulatives should not be used in isolation. It is important that a link be created between the manipulative and the symbolic representations. Calendar Activities, such as Mary Baratta-Lorton’s Mathematics Their Way “Opening Activities” and “Problem of the Day” should be part of the daily routine in mathematics. In the Instructional Guide is listed the Lesson Resource pages and accompanying lessons for each of the content standards.

Quarter One

The first instructional period builds upon content standards of sorting and classifying that was first introduced in Kindergarten. This is a mathematically sound way to begin the teaching and learning of mathematics concepts in the first grade. Lessons supporting the language needed to describe patterns provide students with the appropriate vocabulary. Students build upon their prior experiences with numbers in Kindergarten. The content standards of number sense help the students continue to develop their understanding of addition and subtraction started in Kindergarten. The students are also exposed to strategies to help them remember the basic facts in addition and subtraction.

Quarter Two

The second instructional period continues the study of the content standards dealing with numbers and the concepts of addition and subtraction. Building upon the students’ Kindergarten experiences with plane and solid geometric figures, these shapes are formally re-introduced in this quarter. In addition to the students’ Kindergarten experiences, the inclusion of shapes in the sorting, classifying and patterning activities in quarter one also laid the foundation for the geometry the students will encounter in this quarter. The representation and comparison of data were introduced in Kindergarten. Sorting and classifying activities in quarter one provides the basis for the study of data.

Quarter Three

In the third instructional period, students continue to develop an understanding of addition and subtraction. They explore money and the concepts of length, weight, and capacity. Money was placed in this quarter because the students needed time to have sufficient counting and place value experiences before dealing with the value of coins. During the previous two quarters, the students were actively involved in sorting and classifying. By incorporating the attributes of length, weight, and capacity in the sorting and classifying activities, students are ready for a more formal study of these attributes.

Quarter Four

This quarter provides an opportunity to revisit skills and concepts which students have not yet mastered. Prior to standardized testing, teachers and coaches may want to develop instructional plans based on student needs identified in the periodic assessment data. If first grade students have achieved the mathematics content goals for first grade as stated in The Mathematics Framework for California Public Schools Kindergarten through Grade Twelve, then time can be spent previewing beginning concepts for second grade. Therefore lessons which were skipped throughout the year because they were addressing second grade standards are listed here. They are not in any particular order.

LOS ANGELES UNIFIED SCHOOL DISTRICT First Grade

Mathematics Instruction Guide: Quarter One

GEOMETRY NUMBER SENSE PATTERNS SORTING Standards: * SDAP 1.0 Students organize, represent, and compare data by category on simple graphs and charts: SDAP 1.1 Sort objects and data by common attributes and describe the categories. * SDAP 2.1 Describe, extend, and explain ways to get to a next element in simple repeating patterns (e.g., rhythmic, numeric, color, and shape). MG 2.3 Give and follow directions about locations. MG 2.4 Arrange and describe objects in space by proximity, position, and direction (e.g., near, far, below, above, up, down, behind, in front of, next to, left or

right of). NS 1.0 Students understand and use numbers up to 100 50. * NS 1.1 Count, read, and write whole numbers to 100 50. * NS 1.2 Compare and order whole numbers to 100 50 by using the symbols for less than, equal to, or greater than (<,=,>). NS 1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20 10) (e.g., 8 may be represented as 4+4, 5+3, 2+2+2+2, 10-2, 11-3). NS 1.4 Count and group objects in ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 + 4). * NS 2.1 Know the addition facts (sums to 20 10) and the corresponding subtraction facts and commit them to memory. NS 2.2 Use the inverse relationship between addition and subtraction to solve problems. * NS 2.3 Identify one more than, one less than, 10 more than, and 10 less than a given number. NS 2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference). AF 1.2 Understand the meaning of the symbols +, -, =. MR 1.0-MR 3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources NS 1.0

NS 1.1 NS 1.2

Numbers Getting Ready pp xviii-xx About Teaching Mathematics, Marilyn Burns pp. 168-169

NS 2.5 Addition, Subtraction Geometry

Getting Ready pp xxi-xxiv

SDAP 1.0 Sort Objects SDAP 1.1

Lesson Resources 213A-214A Lesson 15.1

SDAP 2.1 Patterns Lesson Resources 315A-320A Lessons 22.1-22.3

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 1

Quarter One, 2003-2004



GEOMETRY NUMBER SENSE PATTERNS SORTING Dates** Standard # Concepts Harcourt Additional Resources

MG 2.3 MG 2.4

Give and Follow Directions; Locate Objects

Lesson Resources 305A-310A Lessons 21.3-21.5

NS 1.0NS 1.1 NS 1.2 NS 1.3 NS 2.3 NS 2.5 AF 1.2

Numbers, Addition

Lesson Resources 3A-12A Lessons 1.1-1.5 Lesson Resources 17A-24A Lessons 2.1-2.3

About Teaching Mathematics, Marilyn Burns pp 168-169

NS 1.0NS 1.1 NS 1.2 NS 1.3 NS 2.5 AF 1.2

Numbers, Subtraction Lesson Resources 31A-35A Lessons 3.1-3.5 Lesson Resources 45A-54A Lesson 4.1-4.5

NS 1.3NS 2.1 NS 2.3 NS 2.5 SDAP 2.1 AF 1.2 MR 1.0 to MR 3.0

Addition Lesson Resources 65A-74A Lessons 5.1-5.5

About Teaching Mathematics, Marilyn Burns p 170

NS 2.2 Inverse Relationship of Addition and Subtraction

Use additional resources.






GEOMETRY NUMBER SENSE PATTERNS SORTING Dates** Standard # Concepts Harcourt Additional Resources NS 1.4 Make Tens and Ones Use additional resources. About Teaching Mathematics,

Marilyn Burns p 179 A Collection of Math Lessons From Grade 1-3, Marilyn Burns Chapter 6, pp 63-70

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





Mathematics Instruction Guide: Quarter Two

GEOMETRY NUMBER SENSE DATA TIME Standards: AF 1.1 Write and solve number sentences from problem situations that express relationships involving addition and subtraction. * NS 1.1 Count, read, and write whole numbers to 100. * NS 1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<,=,>). * NS 1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20 10) (e.g., 8 may be represented as 4+4, 5+3, 2+2+2+2, 10-2, 11-3). * NS 1.4 Count and group objects in ones and tens. * NS 2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory. NS 2.2 Use the inverse relationship between addition and subtraction to solve problems. * NS 2.3 Identify one more than, one less than, 10 more than, and 10 less than a given number. * NS 2.4 Count by 2s, 5s, 10s to 100. * NS 2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference). * SDAP 1.2 Represent and compare data (e.g., largest, smallest, most, often, least often). * MG 1.2 Tell time to the nearest half hour and relate time to events (e.g., before/after, shorter/longer). * MG 2.1 Identify, describe, and compare triangles, rectangles, squares, and circles including the faces of three dimensional objects. MG 2.2 Classify familiar plane and solid objects by common attributes, such as color, position, shape, size, roundness, or number of corners, and explain which attributes are being used for classification. MR 1.0-MR 3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources

NS 2.1 NS 2.2 NS 2.3 NS 2.5 AF 1.1 MR 1.0 to MR 3.0

Addition and Subtraction

Lesson Resources 79A-88A Lessons 6.1-6.5 Lesson Resources 93A-100A Lessons 7.1-7.4 Lesson Resources 105A-114A Lessons 8.1-8.6

A Collection of Math Lessons, Marilyn Burns, Chapters 2, pp 19-20

NS 1.3 Equivalent Forms Use Additional Resources NS 1.4

Place Value Lesson Resources 127A-138A Lessons 9.1-9.5

A Collection of Math Lessons, Marilyn Burns, Chapters 7-8 pp 71-95



Quarter Two, 2003-2004


Mathematics Instruction Guide: Quarter Two

GEOMETRY NUMBER SENSE DATA TIME Dates** Standard # Concepts Harcourt Additional Resources

NS 1.1 NS 1.2 NS 1.1

Counting and Comparing Numbers Ordinal Numbers

Lesson Resources 143A-154A Lessons 10.1-10.6 Lesson Resources 159A-160A Lessons 11.1

About Teaching Mathematics, Marilyn Burns pp 131, 176-181

NS 1.2NS 1.4 NS 2.4 MR 1.0- 3.0

Counting and Comparing Numbers

Lesson Resources 161A- 164A Lessons 11.2- 11.3

MG 1.2 MR 1.0 to 3.0

Time Lesson Resources 253A, 254A Lesson 18.1 Lesson Resources 257A-262A Lessons 18.3-18.5

MG 1.2SDAP 1.2

Relate Time to Events Lesson Resources 267A-272A Lessons 19.1- 19.3 Lesson Resources 275A- 276A Lesson 19.5

MG 2.2MG 2.1

Plane and Solid Figures Lesson Resources 287A-296A Lessons 20.1-20.5 Lesson Resources 301A-302A Lessons 21.1

SDAP 1.1 Represent and Compare Data SDAP 1.2

Lesson Resources 215A-222A Lessons 15.2-15.5

About Teaching Mathematics, Marilyn Burns, pp 74-78




Quarter Two, 2003-2004


Mathematics Instruction Guide: Quarter Three

NUMBER SENSE MEASUREMENT Standards: * NS 1.1 Count, read, and write whole numbers to 100. * NS 1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<, =, >). * NS 1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented

as 4+4, 5+3, 2+2+2+2, 10-2, 11-3) NS 1.4 Count and group objects in ones and tens. * NS 1.5 Identify and know the value of coins and show different combination of coins that equal the same value. * NS 2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory. * NS 2.2 Use the inverse relationship between addition and subtraction to solve problems. NS 2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference). * NS 2.6 Solve addition and subtraction problems with one- and two-digit numbers (e.g., 5 + 58 = ___). * NS 2.7 Find the sum of three one-digit numbers. * NS 2.3 Identify one more than, one less than, 10 more than, and 10 less than a given number. * NS 2.4 Count by 2s, 5s, and 10s to 100 * MG 1.1 Compare the length, weight, and volume of two or more objects by using direct comparison or a nonstandard unit. MR 1.0-MR 3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources

NS 1.1 NS 1.2 NS 1.3 NS 1.4

Numbers Use additional resources.

NS 2.1NS 2.2 NS 2.5 NS 2.6 NS 2.7 MR 1.0 to MR 3.0

Addition and Subtraction Strategies

Lesson Resources 171A-178A Lessons 12.1-12.4 Lesson Resources 183A-190A Lessons 13.1-13.4 Lesson Resources 195A-202A Lessons 14.1-14.4

About Teaching Mathematics, Marilyn Burns pp 126, 162-165, 191

NS 2.3 1 More, 1 Less Than, 10 More,10 Less Than a number

Lesson Resources 149A-154A



Quarter Three, 2003-2004


Mathematics Instruction Guide: Quarter Three

NUMBER SENSE MEASUREMENT Dates** Standard # Concepts Harcourt Additional Resources

NS 1.5 NS 2.4

Money Lesson Resources 227A-234A Lessons 16.1-16.4 Lesson Resources 239A-248A Lessons 17.1-17.5

About Teaching Mathematics, Marilyn Burns pp 130, 190

MG 1.1 MG 1.1

Length Weight and Capacity

Lesson Resources 327A-330A Lessons 23.1-23.2 Lesson Resources 335A-336A Lesson 23.5 Lesson Resources 341A-346A 24.1-24.3

About Teaching Mathematics, Marilyn Burns, pp. 46-48, 50-52, 189

NS 2.1NS 2.7

Addition and Subtraction Facts and Strategies

Lesson Resources 373A-382A Lessons 26.1-26.5 Lesson Resources 389A-394A Lessons 27.1-27.4 Lesson Resources 401A- 406A Lessons 28.1- 28.3

NS 2.1NS 2.6

One- and Two-digit Addition Lesson Resources 415A-416A Lesson 29.2 Lesson Resources 419A-422A Lesson 29.4-29.5

NS 2.6 One-digit from Two-digit Subtraction

Lesson Resources 429A-430A Lesson 30.2 Lesson Resources 433A-438A Lesson 30.4-30.6




Quarter Three, 2003-2004


Mathematics Instruction Guide: Quarter Four

DATA ANALYSIS NUMBER SENSE PATTERN Standards: * NS 1.1 Count, read, and write whole numbers to 100. * NS 1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<, =, >). NS 3.1 Makes reasonable estimates when comparing larger or smaller numbers. * NS 1.4 Count and group object in ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 + 4). * NS 2.4 Count by 2s, 5s, and 10s to 100. * NS 2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference). * NS 2.2 Use the inverse relationship between addition and subtraction to solve problems. * NS 2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory. NS 2.6 Solve addition and subtraction problems with one- and two-digit numbers (e.g., 5 + 58 =____). * SDAP 2.1 Describe, extend, and explain ways to get to a next element in simple repeating patterns (e.g., rhythmic, numeric color, and shape). * SDAP 1.2 Represent and compare data (e.g., largest, smallest, most often, least often) by using pictures, bar graphs, tally charts, and picture graphs. MR 1.0-MR 3.0 Embedded Dates** Standard # Concepts Harcourt Additional Resources

NS 1.1 NS 1.2 NS 1.4 NS 3.1 NS 2.4

Numbers Use additional resources

NS 2.5MR 1.2

Addition Lesson Resources 23A- 26A Lesson 2.4- 2.5

NS 2.2NS 2.1

Addition and subtraction

Lesson Resources 99A-100A, 113A-114A Lesson 7.5 Use additional resources.

NS 2.1NS 2.5

Subtraction Lesson Resources185-188AUse additional resources

SDAP 2.1 Odd and Even Lesson Resources 164A- 166A Lesson 11.4 Use additional resources.



Quarter Four, 2003-2004


Mathematics Instruction Guide: Quarter Four

DATA ANALYSIS NUMBER SENSE PATTERN Dates** Standard # Concepts Harcourt Additional Resources

SDAP 1.2 Represent andCompare Data

Use additional resources.

MG 1.2 Estimating Time Lesson Resources 255A- 256A Lesson 18.2

MG 2.2 Symmetry Lesson Resources 303A- 304A Lesson 21.2

M.R 1.2 Measurement Lesson Resources 331A- 334A Lesson 23.3- 23.4

MR 1.2, 2.1, 3.0

Fractions Lesson Resources 353A- 358A Lessons 25.1- 25.3

MR 1.2NS 2.1

Tally Charts Lesson Resources 407A- 408A Lesson 28.4

NS 2.1NS 2.6

Add tens Lesson Resources 413A- 414A Lesson 29.1 Lesson Resources 417A- 418A Lesson 29.3

NS 2.6 Subtraction Lesson Resources 431A- 432A Lesson 30.3 Lesson Resources 435A- 436A Lesson 30.5




Quarter Four, 2003-2004

rationale for first grade instructional guide · involve the use of manipulatives and include...

Documents