(NF) Number and Operations - Fractions Categories All categories Not categorized Prioritized (G) Geometry (MD) Measurement and Data (NBT) Number and Operations in Base Ten (NF) Number and Operations - Fractions (OA) Operations and Algebraic Thinking

# Number and Operations - Fraction

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

In Grade 4, students have some experience calculating sums of fractions with different denominators.  They understand the process as expressing both quantities in terms of the same unit fraction so that they can be added. Grade 5 students extend this reasoning to situations where it is necessary to re-express both fractions in terms of a new denominator. Students make sense of fractional quantities when solving word problems, estimating answers mentally to see if they make sense.

Grade 4 students connected fractions with addition and multiplication. In Grade 5, students connect fractions with division, understanding a fraction as division of the numerator by the denominator.  Using the relationship between division and multiplication, students start working with simple fraction division problems. They solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Grade 5 work with multiplying by unit fractions, and interpreting fractions in terms of division, enables students to see that multiplying a quantity by a number smaller than 1 produces a smaller quantity. This work - interpreting multiplication as scaling (resizing), prepares students for Grade 6 work in ratios and proportional reasoning.

## 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-05.NF.01

(NF) Number and Operations - Fractions
Cluster: Use equivalent fractions as a strategy to add and subtract fractions.

#### MAT-05.NF.02

(NF) Number and Operations - Fractions
Cluster: Use equivalent fractions as a strategy to add and subtract fractions.

#### MAT-05.NF.03

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.03 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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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-05.NF.04

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 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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#### MAT-05.NF.04.a

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.04.a Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.) 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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#### MAT-05.NF.04.b

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.04.b Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 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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#### MAT-05.NF.05

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.05 Interpret multiplication as scaling (resizing), by:

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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-05.NF.05.a

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.05.a Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

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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-05.NF.05.b

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.05.b Interpret multiplication as scaling (resizing), by: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (nxa)/(nxb) to the effect of multiplying a/b by 1.

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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-05.NF.06

(NF) Number and Operations - Fractions
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

#### MAT-05.NF.07

(NF) Number and Operations - Fractions
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

##### MAT-05.NF.07 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
b. Interpret division of a whole number by a unit fraction, and compute such quotients.
c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using visual fraction models and equations to represent the problem.

#### MAT-05.NF.07.a

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.07.a Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.

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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-05.NF.07.b

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.07.b Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.

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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-05.NF.07.c

Under Development

 MAT-05 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. MAT-05.NF.07.c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.

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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.