NCTM Standards

Compute fluently and make reasonable estimates.

In grades 3-5

• All students should develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience; use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

In grades 6-8

• All students should select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.
• develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.
• develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

NCTM Focal Points

Grade 5

• Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators.

Common Core Standards

Grade 5 - Number and Operations - Fractions:
Use equivalent fractions as a strategy to add and subtract fractions. 

3. 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.)

4. 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.

Vocabulary

partitioned, divided, denominator, uncommon, 'one fraction'

IEP Goals (sample)

• Given a CSR sequence and guided practice the student will add two fractions with uncommon denominators with 80% accuracy for 3 consecutive sessions.
• Given an addition equation with uncommon denominators, the student will select and create models for each fraction, use the models to find the common denominator and find the answer for 10 examples with 80% accuracy by the end of the second progress monitoring period.
• Given a model representing an addition problem of fractions with uncommon denominators, the student will create an equation, determine equivalencies and show the sum with 80% accuracy for 3 out of 5 sessions.