### Rational Numbers

Fractions are the first rational numbers to which students with disabilities are exposed. It's good to be sure that we have all of the prior foundational skills in place before we start with fractions. We need to be sure students know their whole numbers, one to one correspondence, and at least addition and subtraction as operations.

Still, rational numbers will be essential to understanding data, statistics and the many ways in which decimals are used, from evaluation to prescribing medication.

I recommend that fractions are introduced, at least as parts of a whole, before they appear in the Common Core State Standards, in third grade. Recognizing how fractional parts are depicted in models will begin to build understanding for higher level understanding, including using fractions in operations.

### Introducing IEP Goals for Fractions

When your students reach fourth grade, you will be evaluating whether they have met third grade standards. If they are unable to identify fractions from models, to compare fractions with the same numerator but different denominators, or are unable to add fractions with like denominators, you need to address fractions in IEP goals. These are aligned to the Common Core State Standards:

### IEP Goals Aligned to the CCSS

### Understanding fractions: CCSS Math Content Standard 3.NF.A.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.

- When presented with models of one half, one fourth, one third, one sixth and one eighth in a classroom setting, JOHN STUDENT will correctly name the fractional parts in 8 out of 10 probes as observed by a teacher in three out of four trials.
- When presented with fractional models of halves, fourths, thirds, sixths and eighths in with mixed numerators, JOHN STUDENT will correctly name the fractional parts in 8 out of 10 probes as observed by a teacher in three out of four trials.

### Identifying Equivalent Fractions: CCCSS Math Content 3NF.A.3.b:

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.

- When given concrete models of fractional parts (halves, fourths, eighths, thirds, sixths) in a classroom setting, Joanie Student will match and name equivalent fractions in 4 out of 5 probes, as observed by the special education teacher in two of three consecutive trials.
- When presented in a classroom setting with visual models of equivalent fractions, the student will match and label those models, achieving 4 out of 5 matches, as observed by a special education teacher in two of three consecutive trials.

I have created free printables of halves, quarters, etc. that you can reproduce on card stock and use to teach and measure your students' understanding of equivalents.

### Operations: Adding and subtracting--CCSS.Math.Content.4.NF.B.3.c

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.

- When presented concete models of mixed numbers, Joe Pupil will create irregular fractions and add or subtract like denominator fractions, correctly adding and subtracting four of five probes as administered by a teacher in two of three consecutive probes.

- When presented with ten mixed problems (addition and subtraction) with mixed numbers, Joe Pupil will change the mixed numbers to an improper fractions, correctly adding or subtracting a fraction with the same denominator.

### Operations: Multiplying and Dividing--CCSS.Math.Content.4.NF.B.4.a

Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)

When presented with ten problems multiplying a fraction with a whole number, Jane Pupil will correctly multiple 8 of ten fractions and express the product as an improper fraction and a mixed number, as administered by a teacher in three of four consecutive trials.

### Measuring Success

The choices you make about appropriate goals will depend on how well your students understand the relationship between models and the numeric representation of fractions.

Obviously, you need to be sure they can match the concrete models to numbers, and then visual models (drawings, charts) to the numeric representation of fractions before moving to completely numeric expressions of fractions and rational numbers.