Percentages and Fractions Review

Active learning works well for this topic because percentage change and profit calculations can feel abstract until students see the real-world impact of markups and discounts. When students manipulate prices, calculate profits, and debate pricing strategies, they move beyond rote formulas to genuine understanding.

• Year 9
• Mathematics
• 3 activities
• 20 min–60 min

Learning Objectives

1. Convert between percentages, fractions, and decimals with 90% accuracy.
2. Calculate the percentage of a given whole number or decimal amount.
3. Explain the multiplicative relationship between percentages, fractions, and decimals.
4. Identify the percentage that one number represents of another number.
5. Construct a word problem requiring conversion between percentages, fractions, and decimals to solve.

Simulation Game

⏱ 60 min·Small Groups

Simulation Game: The Classroom Market Stall

Students are given 'wholesale' prices for items and must decide on a percentage markup to cover 'rent' and make a profit. They then have to react to a 'flash sale' (percentage discount) and calculate if they are still making a profit. This makes the maths of business tangible.

Prepare & details

Explain the relationship between percentages, fractions, and decimals.

Facilitation Tip: During The Classroom Market Stall, circulate and ask each group to explain one pricing decision using the terms 'cost price,' 'selling price,' and 'profit,' to ensure they connect vocabulary with action.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: The 10% Trap

Ask students: 'If a $100 item increases by 10% and then decreases by 10%, is it back to $100?' Pairs calculate the answer and then explain the result to the class. This is a powerful way to surface the misconception that percentage changes are always additive.

Prepare & details

Differentiate between finding a percentage of an amount and finding an amount as a percentage of another.

Facilitation Tip: During The 10% Trap, pause the pair discussion after two minutes and call on one pair to present their $100 example on the board to disrupt the common misconception early.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Inquiry Circle

⏱ 35 min·Small Groups

Inquiry Circle: The GST Detective

Students are given receipts where the GST has been 'smudged'. They must use their knowledge of reverse percentages (dividing by 1.1) to find the original pre-tax price. They then compare their methods and check each other's work. This applies maths to a standard Australian tax scenario.

Prepare & details

Construct a real-world scenario where converting between these forms is essential.

Facilitation Tip: During The GST Detective, provide a partially completed table so students focus on interpreting clues rather than setting up the entire calculation from scratch.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

Teaching This Topic

Teach reverse percentages by starting with concrete examples before moving to abstract methods. Use dual coding: pair numerical examples with visual bar models to show how a final price relates to the original. Avoid teaching shortcuts like 'divide by 0.9' until students grasp why those shortcuts work. Research shows that students who construct their own methods first retain knowledge longer than those who follow rigid procedures.

What to Expect

Successful learning looks like students confidently calculating reverse percentages, distinguishing between profit and revenue, and explaining their methods using precise language. They should also recognize why a 10% increase followed by a 10% decrease does not return to the original amount, and articulate the difference between GST-inclusive and GST-exclusive prices.

Watch Out for These Misconceptions

Common Misconception

During The Classroom Market Stall, watch for students assuming that a 10% increase followed by a 10% decrease returns them to the original price.

What to Teach Instead

Prompt students to calculate both steps using a $100 item during their stall pricing discussion, and ask them to present the final balance to the class. Have peers identify where the 'missing dollar' went, reinforcing that percentages are applied to changing base amounts.

Common Misconception

During The Classroom Market Stall, watch for students confusing the total money taken in with profit.

What to Teach Instead

Hand each group a 'money bucket' where they must first 'pay back' the cost of goods before counting profit. Ask them to explain why the leftover amount is profit, not the total collected, linking the bucket analogy directly to their pricing decisions.

Assessment Ideas

Quick Check

After The Classroom Market Stall, present three cards: one with 3/4, one with 0.75, and one with 75%. Ask students to hold up the cards that represent the same value, then call on one student to explain the conversion process for one pair on the board.

Exit Ticket

After The 10% Trap, ask students to complete a slip with: 1. Convert 4/5 to a decimal and a percentage. 2. Calculate 15% of $80. 3. Write one sentence explaining why knowing these conversions is useful for shopping.

Discussion Prompt

During The GST Detective, pose the scenario: 'A store is offering a 30% discount on all items. You want to buy a game that originally costs $50. What is the sale price?' Ask students to share their methods, then have them compare approaches in pairs before revealing the answer.

Extensions & Scaffolding

• Challenge: Ask students to design a pricing error that a competitor might make and explain how to exploit it using percentage calculations.
• Scaffolding: Provide a scaffolded worksheet for The GST Detective with pre-labeled rows for 'GST amount' and 'final price' to reduce cognitive load.
• Deeper exploration: Have students research a real business’s pricing strategy and calculate the actual markup percentage on a featured item.

Key Vocabulary

Percentage	A ratio or fraction out of 100, represented by the symbol '%'. It signifies a part of a whole.
Fraction	A number that represents a part of a whole. It is written as one number over another, separated by a line.
Decimal	A number expressed in the scale of tens. It uses a decimal point to separate whole numbers from fractional parts.
Percentage of an amount	Calculating a specific portion of a total value, expressed as a percentage. For example, finding 25% of $200.
Amount as a percentage	Determining what percentage one value is of another. For example, finding what percentage $50 is of $200.