Mathematics · Year 5

Active learning ideas

Improper Fractions and Mixed Numbers

Active learning helps students grasp improper fractions and mixed numbers because these concepts rely on spatial reasoning and real-world contexts. Moving between visual models and numerical forms builds lasting understanding that rote memorization cannot.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions

• 30–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 45 min · Pairs

Simulation Game: The High Street Sale

The classroom becomes a shop where items have price tags and 'discount' signs (10%, 25%, 50%). Students work in pairs to calculate the new prices and the total savings, using their knowledge of equivalent fractions.

Explain the difference between an improper fraction and a mixed number.

Facilitation Tip

During The High Street Sale, circulate with fraction cards to ask probing questions like, 'If this discount is 3/2, how many whole discounts do we have?' to keep students thinking in both forms.

What to look for

Provide students with three cards. Card 1 has an improper fraction (e.g., 11/4). Card 2 has a mixed number (e.g., 2 3/5). Card 3 has a blank space. Ask students to convert the improper fraction to a mixed number and write it on Card 3. Then, ask them to convert the mixed number to an improper fraction and write it on Card 3 below their first answer.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Inquiry Circle
• 40 min · Individual

Inquiry Circle: The 100-Square Mosaic

Students create a mosaic design on a 10-by-10 grid using different colours. They must then calculate the percentage, decimal, and fraction representation for each colour used in their design.

Construct a mixed number from an improper fraction like 7/3.

Facilitation Tip

In The 100-Square Mosaic, model how to shade 125 squares and then ask, 'How many whole squares and extra squares do you see?' to connect visuals to improper fractions.

What to look for

Display a set of fractions and mixed numbers on the board (e.g., 5/3, 1 1/2, 7/2, 2 1/4). Ask students to write each one in its alternative form on a mini-whiteboard. Observe student responses and address common misconceptions immediately.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Data Detectives

Display various 'stats' from newspapers or cereal boxes (e.g., '30% less sugar'). Students rotate to explain what that percentage means in terms of 'parts per hundred' and what the equivalent fraction would be.

Justify why converting to an improper fraction can simplify addition of mixed numbers.

Facilitation Tip

For the Gallery Walk, assign each pair a unique data set so you can target questioning to their specific conversions and misconceptions.

What to look for

Pose the question: 'Imagine you have 9/4 pizzas. How many whole pizzas and extra slices do you have? Explain your thinking using drawings or words.' Facilitate a class discussion where students share their methods for converting the improper fraction to a mixed number.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with concrete visuals like fraction tiles or paper folding to show how improper fractions and mixed numbers represent the same quantity. Avoid rushing to algorithms before students can explain why 5/4 is the same as 1 1/4. Research suggests linking this to real-world scenarios, such as measuring ingredients or dividing items, strengthens comprehension and retention.

Successful learning looks like students confidently switching between improper fractions and mixed numbers using both visual and numerical methods. They should explain their reasoning clearly and apply these skills to practical situations without prompting.

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Watch Out for These Misconceptions

• During The High Street Sale, watch for students who assume 100% is always the largest possible value.

  Use a bar model to show 200% growth on a plant poster, asking students to draw and label where 100% ends and where 200% begins to reinforce that percentages can exceed 100.

• During The 100-Square Mosaic, watch for students who divide by 100 instead of 10 when finding 10% of a number.

  Have students shade 10 squares on their 100-square grid and then write 10/100 = 1/10. Ask them to divide the grid into 10 equal parts to see that 10% is the same as 1 part out of 10.

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Gallery Walk