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# Geometry

## Narrative for the (G) Geometry

Grade 2 students learn to name and describe the defining attributes of categories of two-dimensional shapes, including circles, triangles, squares, rectangles, rhombuses, trapezoids, and the general category of quadrilateral. They describe pentagons, hexagons, octagons, and other polygons by the number of sides. Because they have developed both verbal descriptions of these shapes and their defining attributes and a rich store of associated mental images, they are able to draw shapes with specified attributes, such as a shape with five sides or a shape with six angles.

Students in Grade 2 also explore decompositions of shapes into regions that are congruent or have equal area. For example, two squares can be partitioned into fourths in different ways. Any of these fourths represents an equal share of the shape (e.g., “the same amount of cake”) even though they have different shapes.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-02.G.01

Under Development

 MAT-02 Targeted Standards(G) Domain: GeometryCluster: Reason with shapes and their attributes. MAT-02.G.01 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.G.02

Under Development

 MAT-02 Targeted Standards(G) Domain: GeometryCluster: Reason with shapes and their attributes. MAT-02.G.02 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.G.03

2nd (MAT) Targeted Standard
(G) Domain: Geometry
Cluster: Reason with shapes and their attributes

# Measurement and Data

## Narrative for the (MD) Measurement and Data

Second graders learn to measure length with a variety of tools, such as rulers, meter sticks, and measuring tapes. To learn measurement concepts and skills, students might use both simple rulers (e.g., having only whole units such as centimeters or inches) and physical units (e.g., manipulatives that are centimeter or inch lengths). Second graders also learn the concept of the inverse relationship between the size of the unit of length and the number of units required to cover a specific length or distance. For example, it will take more centimeter lengths to cover a certain distance than inch lengths because inches are the larger unit.

In Grade 2, students learn to combine and compare lengths using arithmetic operations to solve word problems. That is, they can add two lengths to obtain the length of the whole and subtract one length from another to find out the difference in lengths.

After experience with measuring, second graders learn to estimate lengths. Real-world applications of length often involve estimation. Skilled estimators move fluently back and forth between written or verbal length measurements and representations of their corresponding magnitudes on a mental ruler (also called the “mental number line”).

As students work with data in Grades K–5, they build foundations for their study of statistics and probability in Grades 6 and beyond, and they strengthen and apply what they are learning in arithmetic. Kindergarten work with data uses counting and order relations. First- and second-graders solve addition and subtraction problems in a data context.  Students in Grade 2 draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. They solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-02.MD.01

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure and estimate lengths in standard units. MAT-02.MD.01 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.MD.02

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure and estimate lengths in standard units. MAT-02.MD.02 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.MD.03

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure and estimate lengths in standard units. MAT-02.MD.03 Estimate lengths using units of inches, feet, centimeters, and meters.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.MD.04

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Measure and estimate lengths in standard units. MAT-02.MD.04 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.MD.05

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Relate addition and subtraction to length. MAT-02.MD.05 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.MD.06

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Relate addition and subtraction to length. MAT-02.MD.06 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.MD.07

(G) Geometry
Cluster: Work with time and money.

#### MAT-02.MD.08

(G) Geometry
Cluster: Work with time and money.

#### MAT-02.MD.09

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Represent and interpret data. MAT-02.MD.09 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.MD.10

Under Development

 MAT-02 Targeted Standards(MD) Domain: Measurement and DataCluster: Represent and interpret data. MAT-02.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.t

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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# Number and Operation in Base Ten

## Narrative for the (NBT) Number and Operation in Base Ten

At Grade 2, students extend their base-ten understanding to hundreds. They now add and subtract within 1000, with composing and decomposing, and they understand and explain the reasoning of the processes they use. They become fluent with addition and subtraction within 100.

Students extend their understanding of the base-ten system by viewing 10 tens as forming a new unit called a “hundred.” This lays the groundwork for understanding the structure of the base-ten system as based in repeated bundling in groups of 10 and understanding that the unit associated with each place is 10 of the unit associated with the place to its right.

Students also begin to work towards multiplication when they skip count by 5s, by 10s, and by 100s. This skip counting is not yet true multiplication because students don’t keep track of the number of groups they have counted.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-02.NBT.01

(NBT) Number and Operations in Base Ten
Cluster: Understand place value.

##### MAT-02.NBT.01 Demonstrate understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones, including:
a. 100 can be thought of as a bundle of ten tens called a “hundred”.
b. Multiples of 100 represent a number of hundreds, 0 tens, and 0 ones.

#### MAT-02.NBT.01.a

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-02.NBT.01.a Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a "hundred".

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

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#### MAT-02.NBT.01.b

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-02.NBT.01.b Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.NBT.02

(NBT) Number and Operations in Base Ten
Cluster: Understand place value.

#### MAT-02.NBT.03

(NBT) Number and Operations in Base Ten
Cluster: Understand place value.

#### MAT-02.NBT.04

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Understand place value. MAT-02.NBT.04 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.NBT.05

(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to add and subtract.

#### MAT-02.NBT.06

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-02.NBT.06 Add up to four two-digit numbers using strategies based on place value and properties of operations.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.NBT.07

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-02.NBT.07 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-02.NBT.08

(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to add and subtract.

#### MAT-02.NBT.09

Under Development

 MAT-02 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to add and subtract. MAT-02.NBT.09 Explain why addition and subtraction strategies work, using place value and the properties of operations.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

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# Operations and Algebraic Thinking

## Narrative for the (OA) Operations and Algebraic Thinking

Algebraic thinking is about generalizing arithmetic operations and operating on unknown quantities.  It involves recognizing and analysing patterns and developing generalizations about these patterns.  In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations - addition, subtraction, multiplication, and division - the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships.

Grade 2 students build upon their work in Grade 1 with operations and algebraic thinking in two major ways. They represent and solve situational problems which involve addition and subtraction within 100 rather than within 20, and they represent and solve two-step situational problems in which the result is unknown, the change is unknown, and the start is unknown. (20 + 15 = ___; 20 + ___ = 46; ___ + 14=26)

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-02.OA.01

(OA) Operations and Algebraic Thinking
Cluster: Use place value understanding and properties of operations to add and subtract.

#### MAT-02.OA.02

(OA) Operations and Algebraic Thinking
Cluster: Add and subtract within 20.

#### MAT-02.OA.02.a

 MAT-02 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Add and subtract within 20. MAT-02.OA.02.a Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Know from memory: The ability to compute math facts with automaticity (3-5 seconds) and confidence (ND).

## Resources

### Vocabulary

• sum
• know from memory
• plus
• equals

#### MAT-02.OA.02.b

 MAT-02 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Add and subtract within 20. MAT-02.OA.02.b Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Know from memory: The ability to compute math facts with automaticity (3-5 seconds) and confidence (ND).

## Student Learning Targets:

### Knowledge Targets

• I can answer subtraction facts to 20 quickly (3-5 seconds).

## Resources

### Vocabulary

• subtraction facts
• difference
• know from memory
• minus
• subtract
• equals

#### MAT-02.OA.03

Under Development

 MAT-02 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Work with equal groups of objects to gain foundations for multiplication. MAT-02.OA.03 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

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#### MAT-02.OA.04

Under Development

 MAT-02 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Work with equal groups of objects to gain foundations for multiplication. MAT-02.OA.04 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.