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#### MAT-03.MD.07.c

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.c Relate area to the operations of multiplication and addition: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.

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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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#### MAT-03.MD.07.d

Under Development

 MAT-03 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. MAT-03.MD.07.d Relate area to the operations of multiplication and addition: Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

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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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#### MAT-03.MD.08

(MD) Measurement and Data
Cluster: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

# Number and Operation in Base Ten

## Narrative for (NBT) Number and Operations in Base Ten

At Grade 3, the major focus is multiplication, so students’ work with addition and subtraction is limited to maintenance of fluency within 1000 for some students and building fluency to within 1000 for others.  They achieve fluency with strategies and algorithms that are based on place value, properties of operations, and/or the relationship between addition and subtraction. Such fluency can serve as preparation for learning standard algorithms in Grade 4, if the computational methods used can be connected with those algorithms.

For students in grade 3, the special role of 10 in the base-ten system is important in understanding multiplication of one-digit numbers with multiples of 10. For example, the product of 3 x 50 can be represented as 3 groups of 5 tens, which is 15 tens, which is 150.

## 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-03.NBT.01

Under Development

 MAT-03 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to perform multi­digit arithmetic. MAT-03.NBT.01 Use place value understanding to round whole numbers to the nearest 10 or 100.

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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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#### MAT-03.NBT.02

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

#### MAT-03.NBT.03

 MAT-03 Targeted Standards(NBT) Domain: Number and Operations in Base TenCluster: Use place value understanding and properties of operations to perform multi­digit arithmetic. MAT-03.NBT.03 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

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## Rubric / Proficiency 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 is demonstrated.

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# Number and Operations - Fraction

## Narrative for (NF) Number and Operations - Fractions

In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares. In Grade 3, they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision and measurement. In Grade 4, this is extended to include wholes that are collections of objects.

Grade 3 students do some preliminary reasoning about equivalent fractions, in preparation for work in Grade4. As students experiment on number line diagrams they discover that many fractions label the same point on the number line, and are therefore equal; that is, they are equivalent fractions.

Previously, in Grade 2, students compared lengths using a standard measurement unit. In Grade 3 they build on this idea to compare fractions with the same denominator. They see that for fractions that have the same denominator, the underlying unit fractions (fractions with numerator1) are the same size, so the fraction with the greater numerator is greater because it is made of more unit fractions.

## 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-03.NF.01

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.01 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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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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#### MAT-03.NF.02

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02 Understand a fraction as a number on the number line; represent fractions 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.

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#### MAT-03.NF.02.a

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02.a Understand a fraction as a number on the number line; represent fractions on a number line diagram: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

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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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#### MAT-03.NF.02.b

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.02.b Understand a fraction as a number on the number line; represent fractions on a number line diagram: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

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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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#### MAT-03.NF.03

(NF) Number and Operations - Fractions
Cluster: Develop understanding of fractions as numbers.

##### MAT-03.NF.03 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent using a visual fraction model.
c. Recognize fractions, a/1 or a/a, that are equivalent to whole numbers. Express whole numbers as fractions, a/1 or a/a.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size.
e. Recognize that comparisons are valid only when the two fractions refer to the same whole.
f. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions by using a visual fraction model.

#### MAT-03.NF.03.a

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.a Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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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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#### MAT-03.NF.03.b

Under Development

 MAT-03 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Develop understanding of fractions as numbers. MAT-03.NF.03.b Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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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.