NCTM Standards

Understand the meaning of operations and how they relate to one another.

In grades 3-5

• All students should use models, benchmarks, and equivalent forms to judge the size of fractions.
• Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

In grades 6-8

• All students should work flexibly with fractions, decimals, and percents to solve problems.

NCTM Focal Points

Grade 4

• Students earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.

Common Core Standards

Grade 4 - Number and Operations - Fractions:
Extend understanding of fraction equivalence and ordering. 

2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. 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.

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

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.)

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.

Vocabulary

partitioned, divided, numerator, denominator, multiple, 'one fraction'

IEP Goals (sample)

• Given a model of two fractions with uncommon denominators and teacher modeling, the student will change the models and write the fractions with common denominators with 80% accuracy for 5 consecutive sessions.
• Given two fractions with uncommon denominators and a calculator, the student will rewrite one fraction so that it has the same denominator (common) as the second for three out of four examples in 5 consecutive sessions.
• Given two fractions with uncommon denominators and controlled practice with feedback, the student will find and write the fractions with common denominators with 90% accuracy for 5 consecutive sessions.