MathPractice
Fractions · Grade 3

Equivalent fractions with models

Split the parts of a model without changing the amount selected. The fraction name changes, but its value stays the same.

Grade 38 questions per setNo account needed
Practice 8 questions Download worksheet

US Letter PDF · A4 version · Answer key

What we’re working onRecognize and make equivalent fractions by repartitioning the same whole.

First page of the Equivalent fraction models worksheet, with visible questions and room to work.Open worksheet PDF · 8 questions · US Letter
See how it works

Worked examples

Example 1

Split each third in two

A bar shows 2/3. Split each third into two equal parts. What fraction now names the shaded amount?

  1. The whole bar still has the same length.
  2. Three thirds become six equal parts, so the new parts are sixths.
  3. The two shaded thirds become four shaded sixths.

2/3 = 4/6

Example 2

Split each fourth in two

A bar shows 3/4. Divide every fourth into two equal parts without changing the shaded area.

  1. Four fourths become eight equal parts.
  2. Each shaded fourth becomes two shaded eighths.
  3. The three shaded fourths become six shaded eighths.

3/4 = 6/8

A question from this worksheet

Split each original part into 2 equal pieces. Keep the shaded amount the same.

See the explanation

Split each original part into 2 equal pieces: 10/8.

5/4 = (5 × 2)/(4 × 2) = 10/8. The whole and the shaded amount stay the same.

Choose how to practice

Pick the support you need.

Each set has eight questions. The online practice and prepared worksheet use the same questions.

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For the grown-up beside them

Help the thinking along.

A useful question

What changed about the parts? What stayed the same about the whole and the shaded amount?

What to look for

The learner explains that smaller parts require more pieces to represent the same value.

A common sticking point

Changing the denominator while leaving the numerator unchanged.

Help without giving the answer

Draw the new dividing lines through every part, including unshaded parts. Then recount the shaded parts.

Keep the words clear

Words in this skill.

equivalent fractions
Fractions that name the same number.
partition
Divide a whole or a part into smaller equal parts.
unit fraction
One equal part of a whole, such as 1/6.

What these sets cover.

  • Both generated denominators stay within 2, 3, 4, 6, and 8.
  • Begin with values up to 1; use values up to 2 only after seeing fractions beyond one.
  • A task that asks for a particular split also checks that structure, not just an equal value.

Common questions

Do equivalent fractions land at the same point?

Yes. On a number line with the same unit, equivalent fractions have exactly the same position.

Can I change just the denominator?

Usually that changes the value. When you split every part into two, both the total number of parts and the number selected double.

Try next

Compare familiar fractions

Next, compare fractions when either the part size or the number of parts is the same.

Explore this skill

Related standards: 3.NF.3. These materials focus on this skill, not every part of a grade-level curriculum. How we check materials.