Primary Standard(s):
MAFS.5.NF.1.1: 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.)
MAFS.5.NF.1.2: 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.
Content Knowledge:
In 4th grade, students added and subtracted fractions with like denominators, and explored the process for creating equivalent fractions. In this Unit, students will extend and merge these skills to add and subtract fractions with unlike denominators.
Exploring addition and subtraction with visual models provides a foundation for adding and subtracting fractions with unlike denominators. For example, when adding 1/2 and 1/3, students may be challenged in how the sum will be expressed. By using a model such as pattern blocks, they can decide that using the equivalent sixths works with both halves and thirds, and can be used to express the sum. This is the basic understanding behind the use of common denominators used to express the sum or difference.
Once again, encouraging students to use benchmark fractions and estimation prior to computing a sum or differences allows them to check their answers for reasonableness. This fraction sense will allow them to quickly notice any common errors, such as add the numbers in the denominator. Setting fraction computations in a context allows our students to become familiar with situations that call for adding and subtracting fractions. Using fraction models allows them to visualize and show their understanding of the problem, and building equations challenges them to represent the problem situation with numbers and symbols.
GCG 1 – Learning Goal: As a Mathematician, I will be able to Add Fractions with Unlike Denominators MAFS.5.NF.1.1, MAFS.5.NF.1.2
- Step 1: Use concrete models or pictures to understand the need for common denominators
- Step 2: Represent Addition of fractions with unlike denominators in written form
- Step 3: Explain how to determine the denominator to use to notate the whole when regrouping with mixed numbers
- Step 4: Problem Solving with fractions and mixed numbers (Addition only)
GCG 2 – Learning Goal: As a Mathematician, I will be able to Subtract Fractions with Unlike Denominators MAFS.5.NF.1.1, MAFS.5.NF.1.2
- Step 1: Use concrete models or pictures to subtract fractions with unlike denominators
- Step 2: Represent subtraction of fractions with unlike denominators in written form
- Step 3: Use models and connect to written fraction notation to determine when and why regrouping of wholes with mixed numbers may be needed when subtracting fractions
- Step 4: Problem solving with fractions and mixed numbers
