Los Angeles Unified School District Grade 2012-13.pdf · Los Angeles Unified School District . ... grade), in which textbook ... 9 = Instructional Block in which the standard is taught

Los Angeles Unified School District Office of Curriculum, Instruction, and School Support

2012-2013 Elementary Mathematics Instructional Guide (MIG) Introduction to the Document: Welcome to the Los Angeles Unified School District’s Elementary Mathematics Instructional Guide (MIG). This MIG ensures the teaching and assessment of all grade level standards by the California Standards Testing dates. Additionally, the MIG is intended to be a one-stop tool for teachers, administrators, parents, and other school support personal. It blends CST blueprints, California State Mathematics Standards, enVisionMATH Topics which address those standards, and Instructional Blocks into one easy-to-read resource. The MIG is a living document—it is neither set in stone for all time nor is it perfect. Teachers and other users are encouraged to provide on-going feedback as to its accuracy, usability, and content. Organization of the Document: This Instructional Guide for Mathematics has been organized in several ways to provide flexibility to teachers in planning instruction. Teachers and other users are encouraged to review the various versions and to choose the one that best fits their instructional planning needs. Under the section Organized by Standards, the standards are listed as they are found in the Mathematics Framework for California Public Schools. In this section, teachers and other users will be able to see at a glance the mathematics standard number and wording for the grade level, the number of questions on the CST for each standard (applicable for 2nd through 6th grade), in which textbook topics (chapters) the standards can be found, and in which Instructional Block(s) the standard will be taught and assessed. For quick identification, the essential key standards, as determined by the Mathematics Framework, are noted by bold type and a key symbol. Under the section Organized by Instructional Block, the standards are listed in a developmental sequence. A significant difference with this section versus the organization by standards is that, in some cases, portions of the standards are lined-out or modified for that particular Instructional Block (IB) as that part of the standard is not taught during that time. While the entire standard will be taught and assessed by the time the CST is given, some longer, more complex standards are parsed out over multiple IB’s to allow students time to develop their understanding of the concept and the essential skills they will need in order to be successful. Please note the following examples:

OCISS PreK-12 Mathematics Revised: 5/11/2012 i

Second Grade example:

Number Sense 1.2 asks student to: Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent

numbers (to 1,000). How NS1.2 will look in IB#1: Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent

numbers (to 1,000 100). How NS1.2 will look in IB#3: Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent

numbers (to 1,000). Fourth Grade example: Number Sense 2.1 asks students to: Estimate and compute the sum or difference of whole numbers and positive

decimals to two places. How NS2.1 will look in IB#1: Estimate and compute the sum or difference of whole numbers and positive

decimals to two places. How NS2.1 will look in IB#2: Estimate and compute the sum or difference of whole numbers and positive

decimals to two places. As in the organized by standards section, this section allows teachers and other users to be able to see at a glance the mathematics standard number and wording for the grade level, the number of questions on the CST for each standard (applicable for 2nd through 6th grade), in which textbook topics (chapters) the standards can be found, and in which Instructional Block(s) the standard will be taught and assessed. Again for quick identification, the essential key standards, as determined by the Mathematics Framework, are noted by bold type and a key symbol. Symbols and Footnotes: Additional key information has been embedded into this guide to assist teachers and others in instructional decision-making. Next to the numbers listed in the enVisionMATH topics section, occasionally there will be a symbol indicating that a topic has lessons that address standards outside of the targeted grade level. This is designed to assist in instructional decision-making when choosing lessons to prepare and present based on student needs. Please note the following examples:

OCISS PreK-12 Mathematics Revised: 5/11/2012 ii

First Grade example: 2† indicates that this topic contains lessons that include Kindergarten standards, whereas 18‡ indicates that this topic contains lessons that include Second grade standards. Fifth Grade example: 5‡ indicates that this topic contains lessons that include Fourth grade standards, whereas 14 indicates that this topic contains lessons that include Sixth grade standards. All symbols used in the guide are defined in the footnote section of the document on every page. General Calendar for Instruction and Assessment: The first three Instructional Blocks (IB) and their periodic assessments reflect the standards or portions of the standards as indicated in the Organized by Instructional Block portion of the guide. The guide is designed to ensure full instruction and assessment of the grade level standards by the CST window. The fourth IB is scheduled for after the CST window. This block of time is intended for teachers to use, based on student data, to strengthen areas of weakness the students may still have (intervention) or to “step up” to the next grade level. This is where out-of-grade-level lessons which may have been skipped could be taught or other mathematical concepts could be deepened to support the students’ success in the next grade level. Grade Level Expectations: Included on the first page of each grade level guide is a boxed statement of grade level expectations. This is taken directly from the Mathematics Framework for California Public Schools. This provides teachers, parents, students, administrators, and other instructional support staff an overview of what students should accomplish by the end of the targeted grade level. Using the Mathematics Instructional Guide: The guide can be thought of as a menu. It cannot be expected that one would do every lesson and activity from the instructional resources provided. To try to teach every lesson or use every activity would be like ordering everything on a menu for a single meal. It is not a logical option. Nor is it possible given the number of instructional days and the quantity of resources. That is why the

OCISS PreK-12 Mathematics Revised: 5/11/2012 iii

OCISS PreK-12 Mathematics Revised: 5/11/2012 iv

document is called a "Mathematics Instructional Guide" and not a "Mathematics Pacing Plan." And, like a menu, teachers select, based on instructional data, which lessons best fit the needs of their students – sometimes students need more time with a concept and at other times, less. An effective way to use this guide is to review the mathematical concepts to be taught in each Instructional Block. From there, teachers would map out how much time they feel is needed to teach the concepts within the block based on the data of their students’ needs. For example, some classes may need more time devoted to developing division concepts, while another class at the same grade level may need more focused time on understanding the functions of fractions within an Instructional Block. The starting point for instructional planning is the standards. The textbook resources are just the first tools for teachers in helping to build mathematical understanding. Like going to a restaurant specializing in customer service, there may be times one wishes to order “off-the-menu”. There are hundreds of resources available, both publisher- and teacher-created, that may be used to best teach a concept or skill. Collaborative planning, both within and among grade levels, is strongly encouraged in order to design effective instructional programs for students.

SECOND GRADE

* based on enVisionMATH Overview and Implementation Guide. **fractional values indicate rotated standards (e.g., 1/2 = rotated every 2 years; 1/3 = rotated every 3 years). ***not assessable in a multiple-choice format

Bold standards are essential Key Standards for the grade level. These comprise 70% of the CST. Double lined through are portions of the standard not taught in that topic. Full coverage of the standard will occur in later topics. Italics indicate partial coverage of a longer standard. Full coverage of the standard will occur in later topics.

= Instructional Block in which the standard is taught according to LAUSD Mathematics Instructional Guide. †Topics 2 and 3 include First grade standards. OCISS PreK-12 Mathematics 1 Revised: 5/11/2012

ORGANIZED BY STANDARDS 2012-13 MIG Topics and Instructional Components

By the end of grade two, students understand place value and number relationships in addition and subtraction, and they use simple concepts of multiplication. They measure quantities with appropriate units. They classify shapes and see relationships among them by paying attention to their geometric attributes. They collect and

analyze data and verify the answers. NOTES: enVisionMATH Topic 2 & 3 include lessons covering First grade standards

CST # of

Items

Grade 2 Standard Number

Grade 2 Standard Wording

enVisionMATH TOPIC* IB 1 IB 2 IB 3 After

CST

--- NS 1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000: 15

3 NS 1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit. 4, 15

1 NS 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000). 4, 15

4 NS 1.3 Order and compare whole numbers to 1,000 by using the symbols <, =, >. 4, 15

--- NS 2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers: 6, 7, 9

2 ½** NS 2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 3†, 7, 10

SECOND GRADE




CST # of

Items




CST

14 is 14 - 6 = 8) to solve problems and check solutions.

4 NS 2.2 Find the sum or difference of two whole numbers up to three digits long. 9, 10, 15, 17

NA*** NS 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. 6, 7

--- NS 3.0 Students model and solve simple problems involving multiplication and division: 18, 20

2 NS 3.1 Use repeated addition, arrays, and counting by multiples to do multiplication. 18, 19, 20

3 NS 3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division. 20

3 NS 3.3 Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory. 19

--- NS 4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole: 12

3 NS 4.1 Recognize, name, and compare unit fractions from 1/12 to 1/2. 12

3 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). 12

3 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. 12

--- NS 5.0 Students model and solve problems by representing, adding, and subtracting amounts of money: 16

3 NS 5.1 Solve problems using combinations of coins and bills. 16

SECOND GRADE




CST # of

Items




CST

3 NS 5.2 Know and use the decimal notation and the dollar and cent symbols for money. 16

--- NS 6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places:

8, 17

1/2 ** NS 6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch). 11

--- AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction: 1, 2†, 7, 9, 10

4 AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. 1, 2†, 7

1 AF 1.2 Relate problem situations to number sentences involving addition and subtraction. 1, 2†, 3†, 6, 8, 9, 10

1 AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. 1, 2†, 3†, 6, 9, 14

--- MG 1.0 Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:

11

1 MG 1.1 Measure the length of objects by iterating (repeating) a nonstandard or standard unit. 11

1 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. 11

3 MG 1.3 Measure the length of an object to the nearest inch and/ or 11

SECOND GRADE




CST # of

Items




CST

centimeter.

2 MG 1.4 Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). 13

1 MG 1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.). 13

--- MG 2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space: 5

3 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.

5

3 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).

5

--- SDAP 1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:

4, 16

2 SDAP 1.1 Record numerical data in systematic ways, keeping track of what has been counted. 14, 16

2 SDAP 1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies). 14, 17

2 SDAP 1.3 Identify features of data sets (range and mode). 14 1 SDAP 1.4 Ask and answer simple questions related to data representations. 4, 6, 14, 17, 18, 20

SECOND GRADE




CST # of

Items




CST

--- SDAP 2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways: 6, 19, 20

NA*** 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).

4, 6, 9, 15, 20

NA*** SDAP 2.2 Solve problems involving simple number patterns. 4, 6, 18, 20

SECOND GRADE




ORGANIZED BY INSTRUCTIONAL BLOCK Revision for 2012-13 MIG Topics and Instructional Components

By the end of grade two, students understand place value and number relationships in addition and subtraction, and they use simple concepts of multiplication. They measure quantities with appropriate units. They classify shapes and see relationships among them by paying attention to their geometric attributes. They collect and

analyze data and verify the answers. NOTES: enVisionMATH Topic 2 & 3 include lessons covering First grade standards

CST # of Items



enVisionMATHTOPIC* IB 1 IB 2 IB 3 After

CST

--- AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction: 1

4 AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. 1

1 AF 1.2 Relate problem situations to number sentences involving addition and subtraction. 1

1 AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. 1

--- AF 1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction: 2†

4 AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. 2†

SECOND GRADE




CST # of Items




CST

1 AF 1.2 Relate problem situations to number sentences involving addition and subtraction. 2†

1 AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. 2†

2 1/2** 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.

3†

1 AF 1.2 Relate problem situations to number sentences involving addition and subtraction. 3†

1 AF 1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences. 3†

3 NS 1.1 Count, read, and write whole numbers to 1,000 100 and identify the place value for each digit. 4

1 NS 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000 100). 4

4 NS 1.3 Order and compare whole numbers to 1,000 100 by using the symbols <, =, >. 4

--- SDAP 1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations: 4

1 SDAP 1.4 Ask and answer simple questions related to data representations. 4


4

SECOND GRADE




CST # of Items




CST

NA*** SDAP 2.2 Solve problems involving simple number patterns. 4

--- MG 2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space: 5

3 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.

5

3 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).

5

--- NS 2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers: 6

NA*** NS 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. 6




--- SDAP 2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways: 6

NA*** 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 6

SECOND GRADE




CST # of Items




CST

horses, three horses, four horses). NA*** SDAP 2.2 Solve problems involving simple number patterns. 6



7

NA*** NS 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. 7


4 AF 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. 7


8



4 NS 2.2 Find the sum or difference of two whole numbers up to three two digits long. 9

--- AF 1.0 Students model, represent, and interpret number relationships to create 9

SECOND GRADE




CST # of Items




CST

and solve problems involving addition and subtraction:




9


10

4 NS 2.2 Find the sum or difference of two whole numbers up to three two digits long. 10



1/2** NS 6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch). 11

--- MG 1.0 Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:

11

1 MG 1.1 Measure the length of objects by iterating (repeating) a nonstandard or 11

SECOND GRADE




CST # of Items




CST

standard unit.

1 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. 11

3 MG 1.3 Measure the length of an object to the nearest inch and/ or centimeter. 11

--- NS 4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole: 12

3 NS 4.1 Recognize, name, and compare unit fractions from 1/12 to 1/2. 12

3 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). 12

3 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. 12

2 MG 1.4 Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). 13

1 MG 1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.). 13


2 SDAP 1.1 Record numerical data in systematic ways, keeping track of what has been counted. 14

2 SDAP 1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies). 14

2 SDAP 1.3 Identify features of data sets (range and mode). 14

SECOND GRADE




CST # of Items




CST


--- NS 1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000: 15

3 NS 1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit. 15

1 NS 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000). 15

4 NS 1.3 Order and compare whole numbers to 1,000 by using the symbols <, =, >. 15

4 NS 2.2 Find the sum or difference of two whole numbers up to three digits long. 15


15

--- NS 5.0 Students model and solve problems by representing, adding, and subtracting amounts of money: 16

3 NS 5.1 Solve problems using combinations of coins and bills. 16

3 NS 5.2 Know and use the decimal notation and the dollar and cent symbols for money. 16

--- SDAP 1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations: 16

2 SDAP 1.1 Record numerical data in systematic ways, keeping track of what has been counted. 16

SECOND GRADE




CST # of Items




CST

4 NS 2.2 Find the sum or difference of two whole numbers up to three digits long. 17


17

2 SDAP 1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies). 17


--- NS 3.0 Students model and solve simple problems involving multiplication and division: 18

2 NS 3.1 Use repeated addition, arrays, and counting by multiples to do multiplication. 18

1 SDAP 1.4 Ask and answer simple questions related to data representations. 18 NA*** SDAP 2.2 Solve problems involving simple number patterns. 18

2 NS 3.1 Use repeated addition, arrays, and counting by multiples to do multiplication. 19

3 NS 3.3 Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory. 19


--- NS 3.0 Students model and solve simple problems involving multiplication and division: 20

2 NS 3.1 Use repeated addition, arrays, and counting by multiples to do 20

SECOND GRADE




CST # of Items




CST

multiplication.

3 NS 3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division. 20




20

NA*** SDAP 2.2 Solve problems involving simple number patterns. 20

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Los Angeles Unified School District Grade 2012-13.pdf · Los Angeles Unified School District . ... grade), in which textbook ... 9 = Instructional Block in which the standard is taught