NCTM Standards

Compute fluently and make reasonable estimates.

In grades 3-5

• All students should develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on a number lines, and as divisions of whole numbers.
• All students should use models, benchmarks, and equivalent forms to judge the size of fractions.
• All students should 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.
• All students should use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
• All students should understand meanings of operations and how they relate to one another.
• All students should understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Instructional programs from prekindergarten through grade 12 should enable all students to:

• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.

NCTM Focal Points

Grade 3

• Understand that the size of a fractional part is relative to the size of the whole, and they use fractions to represent numbers that are equal to, less than, or greater than 1
• Understand and use models, including the number line, to identify equivalent fractions.

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

1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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

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:

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

IEP Goals (sample)

• Given an area created with pattern blocks, the student will use onscreen pattern block models to cover areas and identify fractional amounts of the design correctly in 3 consecutive sessions.
• Given onscreen pattern block models and guided practice, the student will identify equivalent fractions for given amounts in 4 out of 5 examples on three consecutive sessions.
• Given a pattern block grid with a completed key and a calculator, the student will correctly create a design using pattern blocks that accurately depicts the fractional amounts in the key with 80% accuracy on 3 out of 5 sessions.