What each grade covers
| Grade | Main fraction work | Limits in the standards |
|---|---|---|
| 3rd | A fraction 1/b is one of b equal parts; fractions on a number line; simple equivalent fractions (1/2 = 2/4, 4/6 = 2/3); comparing fractions with the same numerator or denominator (3.NF) | Denominators 2, 3, 4, 6 and 8 |
| 4th | Why a/b equals (n × a)/(n × b); comparing any two fractions, for example against 1/2; adding and subtracting with like denominators, including mixed numbers; multiplying a fraction by a whole number; tenths and hundredths as decimals (4.NF) | Denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100; unlike denominators in general not required, except tenths plus hundredths |
| 5th | Adding and subtracting with unlike denominators; a fraction as division (a/b = a ÷ b); multiplying fractions; dividing unit fractions by whole numbers and whole numbers by unit fractions (5.NF) | Dividing a fraction by a fraction not required |
Where the trouble usually is
The standards' own wording points at the ideas children have to hold onto:
- The same whole. "Comparisons are valid only when the two fractions refer to the same whole" (3.NF.A.3.d and 4.NF.A.2). Half of a small pizza isn't the same amount as half of a large one.
- Bigger denominator, smaller pieces. Comparing fractions "by reasoning about their size" (3.NF.A.3.d) means seeing that 1/8 is smaller than 1/4 even though 8 is bigger than 4.
- Equal value, different pieces. Equivalent fractions call for "attention to how the number and size of the parts differ even though the two fractions themselves are the same size" (4.NF.A.1).
- New pieces before adding. Adding unlike denominators means "replacing given fractions with equivalent fractions" first, as in 2/3 + 5/4 = 8/12 + 15/12 = 23/12 (5.NF.A.1).
- A fraction is also division. Fifth graders learn that 3/4 is the result of dividing 3 by 4 (5.NF.B.3).
What the research recommends
The federal What Works Clearinghouse practice guide on fractions, released in September 2010, makes five recommendations (practice guide):
| Recommendation | Level of evidence |
|---|---|
| Build on children's informal understanding of sharing and proportionality | Minimal |
| Help students see that fractions are numbers that extend the number system beyond whole numbers | Moderate |
| Help students understand why the procedures for computing with fractions make sense | Moderate |
| Build understanding of ratio, rate and proportion strategies before teaching cross-multiplication | Minimal |
| Make teachers' understanding of fractions a priority in professional development | Minimal |
The two with moderate evidence, fractions as numbers and procedures that make sense, are the ones parents can support most directly.
Ways to help at home
- Share things equally. Cutting a sandwich, a pan of brownies or a length of ribbon into equal parts builds on the sharing idea in the first recommendation. Ask: if four people share it, what does each get?
- Draw a number line from 0 to 1. Mark halves, then fourths, then eighths, and ask which is bigger, 3/8 or 1/2. This is the number line work of 3.NF.A.2.
- Measure. Measuring cups make the 5th-grade examples real: "How many 1/3-cup servings are in 2 cups of raisins?" comes straight from standard 5.NF.B.7.c.
- Compare to one half. Before finding common denominators, ask whether each fraction is more or less than 1/2, the benchmark named in 4.NF.A.2.
- Ask why before how. When your child uses a rule, such as multiplying the top and bottom by the same number, ask why the value doesn't change.
Fractions are also the base for the ratios, percents and equations of middle school, which the Algebra 1 readiness guide lists. For the methods your child uses with whole numbers, see why math homework looks different.
Questions parents ask
What fractions should a 3rd grader know?
Unit fractions such as 1/4, fractions on a number line, simple equivalent fractions such as 1/2 = 2/4 and 4/6 = 2/3, and comparing fractions with the same numerator or the same denominator. Third grade uses denominators 2, 3, 4, 6 and 8.
When do kids add fractions with different denominators?
In 5th grade (standard 5.NF.A.1). Fourth graders add and subtract fractions with like denominators; the one exception is adding tenths and hundredths, such as 3/10 + 4/100 = 34/100 (4.NF.C.5).
Do 5th graders divide fractions?
Only in two cases: a unit fraction divided by a whole number, such as 1/3 ÷ 4, and a whole number divided by a unit fraction, such as 4 ÷ 1/5. Dividing a fraction by a fraction isn't required in 5th grade.
Why does my child's homework put fractions on a number line?
Third-grade standard 3.NF.A.2 asks students to understand a fraction as a number on the number line, and the federal fractions practice guide recommends helping students see fractions as numbers, with moderate evidence.
Sources
- Grade 3 Number and Operations: Fractions, standards text. Opened October 13, 2026.
- Grade 4 Number and Operations: Fractions, standards text. Opened October 13, 2026.
- Grade 5 Number and Operations: Fractions, standards text. Opened October 13, 2026.
- What Works Clearinghouse practice guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, released September 2010. Opened October 13, 2026.