Saturday, April 1, 2023, 5:19 AM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)
M

MAT-04.NBT.06

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

Number and Operations - Fraction

Narrative for (NF) Number and Operations - Fractions

Grade 4 students learn a fundamental property of equivalent fractions: multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a fraction that represents the same number as the original fraction. This property forms the basis for much of their other work in Grade 4, including the comparison, addition, and subtraction of fractions and the introduction of decimals.

Grade 4 students use their understanding of equivalent fractions to compare fractions with different numerators and different denominators. Students use area models and number line diagrams to reason about equivalence.  Students also compare decimals using the meaning of a decimal as a fraction, making sure to compare fractions with the same denominator. For example, to compare 0.2 and 0.09, students think of them as 0.20 and 0:09 and see that 0.20>0.09 because 20/100 > 9/100.

Using the understanding gained from work with whole numbers of the relationship between addition and subtraction, students add and subtract fractions with the same denominator. Students also compute sums of whole numbers and fractions, by representing the whole number as an equivalent fraction with the same denominator as the fraction. Grade 4 students also solve word problems involving multiplication of a fraction by a whole number.

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-04.NF.01

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Extend understanding of fraction equivalence and ordering. MAT-04.NF.01 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

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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-04.NF.02

(NF) Number and Operations - Fractions
Cluster: Extend understanding of fraction equivalence and ordering.

MAT-04.NF.03

(NF) Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.03 Understand a fraction a/b with a > 1 as a sum of unit fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. Justify decompositions by using a visual fraction model or other strategies.
c. Add and subtract mixed numbers with like-denominators.
d. Using visual fraction models and equations, solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

MAT-04.NF.03.a

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.03.a Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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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-04.NF.03.b

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.03.b Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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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-04.NF.03.c

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.03.c Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

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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-04.NF.03.d

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.03.d Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations 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.

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MAT-04.NF.04

(NF) Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b.
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
c. Using visual fraction models and equations, solve word problems involving multiplication of a fraction by a whole number.

MAT-04.NF.04.a

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

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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-04.NF.04.b

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.04.b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/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-04.NF.04.c

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. MAT-04.NF.04.c Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example: If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? 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-04.NF.05

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Understand decimal notation for fractions, and compare decimal fraction. MAT-04.NF.05 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100.

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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-04.NF.06

Under Development

 MAT-04 Targeted Standards(NF) Domain: Number and Operations - FractionsCluster: Understand decimal notation for fractions, and compare decimal fractions. MAT-04.NF.06 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 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-04.NF.07

(NF) Number and Operations - Fractions
Cluster: Understand decimal notation for fractions, and compare decimal fractions.

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 analyzing 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.

Fourth graders extend problem solving to multi-step word problems using the four operations posed with whole numbers.  Some problems might easily be represented with a single equation, and others will be more sensibly represented by more than one equation or a diagram and one or more equations. Consider two diving boards, one 40 feet high, the other 8 feet high. Students in earlier grades learned to compare these heights in an additive sense—“This one is 32 feet higher than that one”—using addition and subtraction to solve word problems. Students in Grade 4 learn to compare these quantities multiplicatively as well: “This one is 5 times as high as that one.”

Students reason about number or shape patterns, connecting a rule for a given pattern with its sequence of numbers or shapes. In examining numerical sequences and patterns, fourth graders can explore rules of repeatedly adding the same whole number or repeatedly multiplying by the same whole number.

Fourth graders also build upon earlier understandings about multiplication and division. Students examine various patterns in factor pairs by finding factor pairs for all numbers 1 to 100, and extend the idea of decomposition to multiplication and learn to use the terms multiple, prime number, composite number.

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-04.OA.01

Under Development

 MAT-04 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Use the four operations with whole numbers to solve problems. MAT-04.OA.01 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

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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-04.OA.02

Under Development

 MAT-04 Targeted Standards(OA) Domain: Operations and Algebraic ThinkingCluster: Use the four operations with whole numbers to solve problems. MAT-04.OA.02 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

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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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