Module 3

Use equivalent fractions as a strategy to add and subtract fractions.

5.NF.1

• Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.2

• Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

4.NF.1

• 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.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
2. 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.
3. 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.
4. 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.

MP.1

• Make sense of problems and persevere in solving them. Students make sense of problems when they use number lines, tape diagrams, and fraction models to conceptualize and solve fraction addition and subtraction problems. Students also check their work and monitor their progress, assessing their approach and its validity within the given context and altering their method when necessary.

MP.3

• Construct viable arguments and critique the reasoning of others. As students add and subtract with fractions and mixed numbers, they make choices and reason about which like unit to choose and draw conclusions about what makes some problems simpler than others. Students analyze multiple solution strategies for given problems and draw conclusions about which method is most efficient in each case. Students also critique the reasoning of others and construct viable arguments during this analysis. They also use their understanding of fractions to assess the reasonableness of sums and differences and use these assumptions to justify their conclusions to others.

MP.5

• Use appropriate tools strategically. Students use mental computation and estimation strategies to assess the reasonableness of their answers. They decide which pictorial model to draw and label and reason about its size relative to the context of the problem. Students decide on the appropriateness of using special strategies when adding and subtracting mixed numbers.

MP.7

• Look for and make use of structure. Students discern patterns and structures as they draw fraction models and reason about the number of units represented, the size or length of those units, and the name of the fraction that each model represents. They identify patterns in sums and differences when the same fraction is added to or taken from a variety of numbers and use this understanding to generate predictions about the sums and differences.

MP.8

• Look for and express regularity in repeated reasoning. Students express regularity in repeated reasoning when they look for and use whole number general methods to add and subtract fractions. Adding and subtracting fractions requires finding like units just as it does with whole numbers, such as when adding centimeters and meters.