Mathematics · Year 7

Active learning ideas

Comparing and Ordering Fractions

Active learning helps students grasp fraction comparison because it turns abstract numbers into tangible comparisons they can see and touch. When students work with real-world materials like price tags or grid shading, they build lasting mental models of value and equivalence.

• ACARA Content Descriptions
• AC9M7N04

• 20–60 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 60 min · Small Groups

Simulation Game: The Pop-Up Shop

Students create a small 'store' with items and prices. They must calculate 10%, 20%, and 25% discounts for a 'sale' and then add 10% GST to the final price. Classmates 'shop' at different stores to check the accuracy of the calculations.

Justify the need for a common denominator when comparing fractions.

Facilitation Tip

During The Pop-Up Shop, circulate with a notepad to jot down common conversion shortcuts students invent, then share these strategies with the class at the end.

What to look for

Present students with two fractions, such as 2/3 and 3/4. Ask them to write down the steps they would take to determine which fraction is larger, requiring them to identify the need for a common denominator.

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

Activity 02

• Inquiry Circle
• 45 min · Small Groups

Inquiry Circle: Best Value Challenge

Groups are given flyers from different Australian supermarkets. They must compare the prices of similar items that are on sale (e.g., one is 20% off, another is 'buy one get one half price') to determine which is the best value per unit.

Analyze different strategies for ordering a set of fractions.

Facilitation Tip

For the Best Value Challenge, assign clear roles to each group member to ensure accountability during the investigation phase.

What to look for

Give students a set of three fractions (e.g., 1/2, 3/5, 2/3). Ask them to order these fractions from least to greatest and provide a brief written justification for their ordering, highlighting their method.

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

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: The Percentage Change Mystery

Students are asked: 'If a price increases by 50% and then decreases by 50%, do you get back to the original price?' They solve it individually, discuss their surprising results with a partner, and then explain the logic to the class.

Predict the relative size of two fractions without converting them to decimals.

Facilitation Tip

In The Percentage Change Mystery, give pairs exactly three minutes to discuss before sharing with the class to keep the think-pair-share focused and equitable.

What to look for

Pose the question: 'Imagine you have two recipes, one calling for 1/3 cup of butter and another for 2/5 cup of butter. How can you tell which recipe needs more butter without using a calculator?' Facilitate a class discussion comparing strategies.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teachers should start with concrete representations like 10x10 grids or play money before moving to symbolic notation. Avoid rushing to algorithms; instead, let students discover the need for common denominators or place value through guided discovery. Research shows that students who struggle benefit from visual-spatial representations before abstract symbols, while advanced students thrive when asked to justify their methods to peers.

Successful learning looks like students confidently converting between fractions, decimals, and percentages without prompting. They should explain their reasoning clearly, use multiple methods to verify answers, and apply these skills to unfamiliar problems like tax calculations or discount comparisons.

---

Watch Out for These Misconceptions

• During The Pop-Up Shop, watch for students who believe 0.5 is smaller than 0.15 because 5 is smaller than 15.

  Redirect them to the price tags. Have them compare $0.50 to $0.15 directly, then model writing the decimals with place value columns to make the comparison explicit.

• During the Best Value Challenge, watch for students who treat percentages as whole numbers rather than fractions of 100.

  Ask them to return to their 10x10 grid shading. Have them re-label each percentage as a fraction (e.g., 50% = 50/100) and simplify it to connect the ideas.

---

Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share