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 Understand a fraction a/b with a > 1 as a sum of 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 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.

c) 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.

d) 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.

Student Learning Targets:

Knowledge Targets

Reasoning Targets

I can understand adding and subtracting fractions involves joining and separating parts of the same whole.

Skills (Performance) Targets

I can decompose a fraction in more than one way and represent each with an equation.

I can use visual fraction models to justify and explain my thinking.

I can write equations when adding and subtracting fractions.

I can add and subtract fractions <1 with like denominators.

I can solve word problems involving fractions and mixed numbers with like denominators.

Product Targets

Rubric / Proficiency Scale

Score

Description

Sample Activity

4.0

Student is able to add and subtract mixed numbers with unlike denominators to solve word problems.

Traveled 5 1/4 miles + 1 3/8 miles. If traveling 10 miles in all, how much farther?

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

Student is able to demonstrate understanding of fraction concepts involving decomposing fractions, using fraction models, and can solve word problems involving addition and subtraction of mixed numbers having like denominators.

I can use visual fraction models to justify and explain my thinking.

I can write equations when adding and subtracting fractions.

I can solve word problems involving fractions and mixed numbers with like denominators.

2 1/3 cups of sugar - 2/3 cups of sugar

2.5

No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content.

2.0

Student is able add fractions <1 with like denominators to solve word problems in which the sum results in a mixed number , use visual models to support thinking, and write equations.

I can use visual fraction models to justify and explain my thinking.

I can write equations when adding and subtracting fractions.

I can solve word problems involving fractions and mixed numbers with like denominators.

5/8 of a pie + 4/8 of a pie

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 add and subtracts fractions <1 with like denominators.

I can understand adding and subtracting fractions involves joining and separating parts of the same whole.

I can add and subtract fractions <1 with like denominators.

1/4+ 2/4

5/6 - 3/6

0.5

Limited or no understanding of the skill is demonstrated.