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Common Core Math3rd GradeFractions

3.NF.2: Place Fractions on a Number Line

Also written as 3.NF.A.2 and CCSS.MATH.CONTENT.3.NF.A.2 · Cluster: Develop understanding of fractions as numbers.

Make a 3.NF.2 Number LineAll 25 3rd Grade Math Standards

The Official Wording

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Common Core State Standards, Grade 3, Number & Operations: Fractions · Read it at the source · Checked October 14, 2026

What 3.NF.2 Means in Plain English

Third graders treat a fraction as a point on the number line, not just a shaded shape. To show 3/4, they mark 0 and 1, cut that length into 4 equal jumps, and count three jumps from 0. The end of the third jump is 3/4.

Part a places one unit fraction such as 1/4 by splitting the 0 to 1 interval. Part b stacks copies of it to reach 3/4 or 5/4. The number line is where equivalence and comparison happen next (3.NF.3), and where 4th graders add fractions and place decimals (4.NF.6).

3.NF.2 I Can Statements

  • I can split the space from 0 to 1 into equal parts.
  • I can find 1/4 on a number line and explain why it belongs there.
  • I can mark 3/4 by counting three fourths from 0.

3.NF.2 Worked Example

Three fourths, built on a number line the way part a and part b describe it: first the unit fraction, then three copies of it.

Problem

Draw a number line from 0 to 1 and mark the point 3/4.

Placing 3/4 on a number line
  1. Draw the line and mark 0 and 1. The distance between them is the whole, and every fraction is measured against it.0 and 1 marked, the whole is the space between
  2. The denominator is 4, so cut the whole into 4 equal pieces. Three tick marks do it, and each piece is the same length.4 equal parts, 3 ticks between 0 and 1
  3. The first tick is one fourth of the way from 0, so it is the number 1/4. That is part a.first tick = 1/4
  4. Now 3/4. Start at 0 and jump three fourths: one fourth, two fourths, three fourths. Where the third jump lands is 3/4. That is part b.three jumps of 1/4 land at 3/4
  5. Label every tick, not just the answer, so the line reads like a ruler.0, 1/4, 2/4, 3/4, 1
Answer3/4 is the third tick mark after 0 on a line cut into four equal parts, one tick before 1.

Check it: One more jump of 1/4 should land exactly on 1, since 4/4 is the whole. If it overshoots or falls short, the parts were not equal.

Common Mistakes with 3.NF.2

Counting tick marks instead of spaces

Four tick marks drawn between 0 and 1 for fourths, so the line is really in fifths

Try this: Have students count the jumps, not the marks. Fourths means four spaces, which takes three tick marks between 0 and 1.

Unequal parts

0 to 1 cut into 4 pieces of visibly different lengths, with 1/4 at the first tick

Try this: Fold a paper strip the same length as the whole into fourths and lay it under the line to place the ticks.

The whole is the whole line

On a line from 0 to 2, 1/2 marked at 1 because 1 is halfway across the paper

Try this: Circle the 0 and the 1 first. The whole is always the distance from 0 to 1, no matter how long the line is.

Where 3.NF.2 Fits

Comes Before2.MD.6Show whole numbers as points on a number line and add on it.3.NF.1Know 1/4 as one of four equal parts and 3/4 as three of them.
Alongside3.NF.3Find equivalent fractions as the same point on the number line.3.MD.4Read a ruler marked in halves and quarters of an inch.
Comes Next4.NF.2Compare fractions with different numerators and denominators.4.NF.6Place decimals like 0.62 on a number line as 62/100.

Practice 3.NF.2

Number Line GeneratorFree ToolBlank lines from 0 to 1 or 0 to 2 with the ticks for fourths, sixths or eighths, or no ticks at all so students draw the equal parts themselves.0 to 1FourthsBlank ticks
Make Number Lines

Quick Check

  1. A number line from 0 to 1 is cut into 6 equal parts. What fraction is at the second tick after 0?
  2. How many tick marks go between 0 and 1 to show eighths?
  3. On a number line from 0 to 2 marked in fourths, where is 5/4?

3.NF.2: Other Names

3.NF.23.NF.A.2CCSS.MATH.CONTENT.3.NF.A.2

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.