Mathematics · Year 5

Active learning ideas

Mixed Numbers to Improper Fractions

Active learning works for mixed numbers to improper fractions because students need to see how whole numbers and parts combine as a single quantity. Hands-on work with tiles or shading makes the abstract rule concrete, reducing errors about where to multiply or add.

• ACARA Content Descriptions
• AC9M5N04

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

Activity 01

• Collaborative Problem-Solving
• 35 min · Small Groups

Manipulative Build: Fraction Tiles Conversion

Give each small group fraction tiles for halves, thirds, and quarters. Students build a mixed number like 2 3/4, then regroup tiles to form an improper fraction, recording the equivalent. Pairs verify by rebuilding the improper fraction as a mixed number.

Analyze how to visualize three and a half using only quarters.

Facilitation Tip

During Fraction Tiles Conversion, circulate and ask each group to verbally explain their steps before writing anything down.

What to look for

Present students with 3-4 mixed numbers (e.g., 2 1/3, 5 1/2, 1 7/8). Ask them to write the equivalent improper fraction for each on a mini-whiteboard or paper. Observe their process and accuracy.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 25 min · Pairs

Visual Shading Relay: Mixed to Improper

In pairs, one student draws and shades a mixed number circle, such as 1 2/3. The partner counts total shaded parts to write the improper fraction, then switches roles for three rounds. Groups share one example on the board.

Predict the improper fraction equivalent of any given mixed number.

Facilitation Tip

For Visual Shading Relay, limit each round to two minutes so students practice quick recognition and conversion under time pressure.

What to look for

Provide students with a word problem that requires converting a mixed number to an improper fraction to solve (e.g., 'Sarah has 2 1/4 pizzas left. How many quarter slices does she have in total?'). Ask students to show their conversion step and the final answer.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 40 min · Small Groups

Problem-Solving Chain: Design and Solve

Individually, students design a word problem needing mixed-to-improper conversion, like dividing 5 1/4 meters of ribbon. In small groups, they solve each other's problems, converting first, then checking with drawings. Discuss solutions whole class.

Design a word problem where converting a mixed number to an improper fraction is a necessary step.

Facilitation Tip

In Problem-Solving Chain, require students to swap problems with another pair and solve using the converted improper fractions before sharing answers aloud.

What to look for

Ask students: 'Explain in your own words why multiplying the whole number by the denominator and adding the numerator helps us find the improper fraction. Use an example like 3 1/2 to support your explanation.'

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 30 min · Whole Class

Number Line March: Equivalent Fractions

Whole class uses floor number lines marked in fractions. Students physically move to represent mixed numbers, then adjust to improper fraction positions. Record and compare multiples like 4 1/2 to 9/2.

Analyze how to visualize three and a half using only quarters.

Facilitation Tip

On Number Line March, have students mark both the mixed number and its equivalent improper fraction to reinforce visual equivalence.

What to look for

Present students with 3-4 mixed numbers (e.g., 2 1/3, 5 1/2, 1 7/8). Ask them to write the equivalent improper fraction for each on a mini-whiteboard or paper. Observe their process and accuracy.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach this topic by starting with manipulatives to establish the denominator as the unit size, then connect visual models to the symbolic rule. Avoid rushing to the algorithm; let students discover why the denominator stays the same through repeated exposure to tiles or grids. Research shows that students who build and draw their own representations retain the concept longer than those who only follow steps.

Students will confidently convert mixed numbers to improper fractions by multiplying the whole number by the denominator, adding the numerator, and keeping the denominator unchanged. They will explain their steps using visuals and peer feedback to confirm accuracy.

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Watch Out for These Misconceptions

• During Fraction Tiles Conversion, watch for students who multiply the whole number by the numerator instead of the denominator.

  Redirect them by asking them to count out tiles: ‘Show me three whole tiles made of halves. How many tiles are there total before adding the extra half?’

• During Visual Shading Relay, watch for students who assume improper fractions are always larger values.

  Have them shade both the mixed number and its improper fraction on the same grid side by side, then ask, ‘Do both pictures show the same amount?’

• During Number Line March, watch for students who change the denominator during conversion.

  Ask them to measure the same distance on the number line using the mixed number and the improper fraction, confirming the denominator remains the same.

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Methods used in this brief

• Collaborative Problem-Solving