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 - Fractions
Cluster: 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.

Student Learning Targets:

Knowledge Targets

I can

Reasoning Targets

I can

Skills (Performance) Targets

I can

Product Targets

I can

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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Vocabulary

List

MAT-04.NF.02

4^th Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Extend understanding of fraction equivalence and ordering.

MAT-04.NF.02 By creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 , compare two fractions with different numerators and different denominators.
Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Proficiency Scale

MAT-04.NF.03

4^th Grade (MAT) Targeted Standard
(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.

Proficiency Scale

MAT-04.NF.03.a

Under Development

MAT-04 Targeted Standards
(NF) Domain: 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.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.