NCTM Standards

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

In grades 6-8

• All students should develop understanding of the meaning and effects of arithmetic operations with fractions, decimals, and integers.

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; use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

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 analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.
• Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

NCTM Focal Points

The Focal Points to do not explicitly mention adding fractions with common denominators, however the following points are potentially relevant:

Grade 3

• Students solve problems that involve comparing and ordering fractions by using models, benchmark fractions, or common numerators or denominators.

Grade 5

• Students develop fluency with standard procedures for adding and subtracting fractions and decimals.

Common Core Standards

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.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Vocabulary

common, addition, denominator

IEP Goals (sample)

• Given only models representing addition of fractions with common denominators, the student will create a model of the sum and accurately explain the rationale for his answer with 80% accuracy for 3 out of 5 sessions.
• Given an addition example of two fractions with common denominators and various models (circle, area, horizontal bars, vertical bars, sets) the student will accurately create each model to represent the addens, use the models to determine the sum, and correctly record the sum for 5 or more examples on three consecutive sessions.
• Given a set of addition example and self-checking strategy, the student will find the sum for each example with 90% accuracy by the end of the second progress monitoring period.