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 3 - Number and Operations - Fractions:
Develop understanding of fractions as numbers. 

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

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

1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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.

Vocabulary

equivalent, value, multiple, 'one fraction'

IEP Goals (sample)

• Given the use of fraction models and a procedural strategy, the student will accurately create at least 1 equivalent fraction for each given fraction with 100% accuracy for 2 out of 3 sessions.
• Given a fraction model and an instructional routine with feedback, the student will create two additional models which are equivalent and write the fraction number for each for 8 out of 10 examples in 3 consecutive sessions.
• Given a fraction and a calculator, the student will find two additional fractions which are equivalent and record their answers with 80% accuracy over 10 sessions.