NCTM Standards

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

In grades 3-5

• Use models, benchmarks, and equivalent forms to judge the size of fractions

NCTM Focal Points

Grade 3: solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or common numerators or denominators.

Common Core Standards

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

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

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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.

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.

Vocabulary

small, large, compare, greater than, less than, larger, smaller

IEP Goals (sample)

• Given two fractions with common or uncommon denominators and pictorial representations of each, the student will label each using terms smaller and larger with 90% accuracy for 3 out of 5 trials.
• Given three fractions with common or uncommon denominators, the student will create a model for each fraction and order them by size using labels of small, medium and large with 80% accuracy for 3 consecutive trials.
• Given guided practice with and without the use of models the student will compare two fractions using the symbols <>= with 90% accuracy for three consecutive trials.