Mathematics · Year 3

Active learning ideas

Representing Unit Fractions

Active learning with concrete materials lets students feel and see why equal parts matter when representing unit fractions. When students fold paper or share counters themselves, they internalize the meaning of denominators and numerators rather than memorizing rules.

• ACARA Content Descriptions
• AC9M3N02

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Paper Folding: Unit Fraction Models

Provide square papers for students to fold into halves, quarters, eighths, thirds, or fifths. Shade one unit fraction per fold, label it, and compare sizes across denominators. Pairs discuss why parts must be equal even if folds differ.

Justify why the parts of a fraction must be equal in size even if they are different shapes.

Facilitation Tip

During Paper Folding, remind students to make sharp creases and align edges to ensure equal parts before cutting or folding further.

What to look for

Give students a paper circle divided into 4 unequal parts and a paper square divided into 4 equal parts. Ask them to label the equal parts of the square with '1/4' and explain in one sentence why the parts of the circle cannot be labeled as fourths.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 35 min · Small Groups

Counter Sharing: Collections Fractions

Give small groups 12 counters to divide equally into 2, 3, 4, 5, 6, or 8 groups. Students record the unit fraction for one group and explain how group count affects piece size. Share findings whole class.

Analyze how the size of a unit fraction changes as the denominator gets larger.

Facilitation Tip

During Counter Sharing, ask students to count aloud as they distribute counters one by one to reinforce the idea of equal groups.

What to look for

Present students with a collection of 12 counters. Ask them to show you 1/3 of the collection using the counters and explain how they know they have shown one-third.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 40 min · Small Groups

Pattern Blocks: Shape Partitioning

Use pattern blocks to cover hexagon wholes with unit fraction pieces like half-hexagons or thirds. Students build models for each fraction, justify equal coverage, and trade blocks to compare denominators. Record sketches.

Explain the relationship between a half and a quarter of the same whole.

Facilitation Tip

During Pattern Blocks, ask students to name each piece’s fraction relative to the whole hexagon to connect shapes to symbolic notation.

What to look for

Show students two identical chocolate bars. Break one in half and the other into quarters. Ask: 'Which is bigger, one half of the chocolate bar or one quarter of the chocolate bar? How do you know?' Facilitate a discussion about the denominator's role in fraction size.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 30 min · Pairs

Fraction Strips: Size Comparison

Distribute pre-cut fraction strips. Students align unit fractions from the same whole, order by size, and predict patterns as denominators increase. Discuss relationships like half to quarter.

Justify why the parts of a fraction must be equal in size even if they are different shapes.

Facilitation Tip

During Fraction Strips, encourage students to stack strips vertically to compare sizes side-by-side before labeling fractions.

What to look for

Give students a paper circle divided into 4 unequal parts and a paper square divided into 4 equal parts. Ask them to label the equal parts of the square with '1/4' and explain in one sentence why the parts of the circle cannot be labeled as fourths.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with halves and quarters because students already have informal experience with these. Move to less familiar thirds and fifths only after they can justify equal partitions consistently. Avoid rushing to symbols—instead, link spoken and written fraction names directly to the physical models. Research shows that delaying symbolic notation until students can explain fractions with materials strengthens long-term understanding.

Students will confidently partition shapes and collections into equal parts, label unit fractions correctly, and explain why unequal parts do not represent the same unit fraction. They will also compare fractions using visual and physical models to understand size relationships.

---

Watch Out for These Misconceptions

• During Paper Folding, watch for students accepting unequal folds as valid unit fractions.

  Have students lay their folded shape over an unfolded copy to check if parts match exactly before labeling. Ask them to refold if edges do not align.

• During Counter Sharing, watch for students believing a larger denominator means more counters.

  Ask students to hold up their groups of counters and count how many are in each group. Guide them to see that more groups mean fewer counters in each group.

• During Fraction Strips, watch for students thinking one-half is always larger than one-quarter regardless of the whole.

  Provide two identical paper strips. Fold one in half and the other in quarters, then place halves side-by-side to compare. Ask students to measure the strips to confirm the size relationship depends on the whole.

---

Methods used in this brief

• Stations Rotation