NCTM Standards

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

In grades 3-5

• All students should use models, benchmarks, and equivalent forms to judge the size of fractions.

In grades 6-8

• All students should compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.

Compute fluently and make reasonable estimates

In grades 3-5

• Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience.

In grades 6-8

• 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 use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

NCTM Focal Points

Grade 3

• Use fractions to represent numbers that are equal to, less than, or greater than 1. They solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or common numerators or denominators.

Grade 4

• Understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers, including numbers between 0 and 1, and 2, and so on.
• Relate their understanding of fractions to reading and writing decimals that are greater than or less than 1, identifying equivalent decimals, and estimating decimal or fractional amounts in problem solving.
• Connect equivalent fractions and decimals by comparing models to symbols and locating equivalent symbols on the number line.

Grade 5

• Make reasonable estimates of fraction and decimal sums and differences.

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.

IEP Goals (sample)

• Given a number line with 3 benchmark fractions and a proper or improper fraction, the student will estimate the size of the given fraction by selecting the correct benchmark with 90% accuracy.
• Given a number line with 3 benchmark fractions and a mixed number, along with guided practice, the student will estimate the location of the given number on the number line by selecting one of the benchmark fractions with for 3 out of 5 examples in 3 consecutive trials.
• Given a number line with 3 benchmark fractions and an addition equation with two fractions or mixed numbers, the student will correctly estimate the answer by selecting the benchmark for the sum for 5 consecutive examples in 4 out of 5 trials.