Mathematics · Grade 6

Active learning ideas

Solving Percent Problems: Finding the Whole or Percent

Active learning helps students grasp percent problems because it moves them beyond abstract formulas into concrete, real-world contexts where they can test their understanding. When students manipulate real prices, recipe amounts, or survey data, they see how part-whole relationships work in practice, which builds lasting proportional reasoning skills.

• Ontario Curriculum Expectations
• 6.RP.A.3.C

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Pairs: Discount Detective

Pairs receive mock store flyers with sale prices and discount percents. They set up proportions to find original prices, then create their own problems for partners to solve. Pairs verify answers using calculators and discuss proportion setups.

Explain how to set up a proportion to find the whole when given a part and a percent.

Facilitation Tip

During Discount Detective, circulate and ask pairs to explain their proportion setup before they calculate, ensuring they connect the discount rate to the original price.

What to look for

Present students with a scenario: 'A store is having a 20% off sale. A jacket is now $60. What was the original price of the jacket?' Ask students to show their work using a proportion or equivalent method on a mini-whiteboard.

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

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Small Groups: Recipe Remix

Groups adjust recipes by finding the whole ingredient amount given a part and percent, using measuring cups with flour or water. They test mixtures, record proportions, and present adjustments to the class. Rotate roles for each problem.

Construct a real-world problem that requires finding the percent a part is of a whole.

Facilitation Tip

In Recipe Remix, assign each group a different recipe to scale, so they can compare strategies and challenge each other’s proportional adjustments.

What to look for

Give students two problems: 1. 'What percent is 15 of 25?' 2. '30 is 75% of what number?' Students write their answers and one sentence explaining how they solved one of the problems.

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

Activity 03

• Problem-Based Learning
• 25 min · Whole Class

Whole Class: Survey Percentages

Conduct a class poll on favorite activities. Tally votes, then solve as a group to find what percent each option represents of the total. Students justify steps on chart paper and vote on the most engaging survey question.

Analyze common errors made when solving for the whole or the percent.

Facilitation Tip

For Survey Percentages, provide a pre-made checklist of questions to guide students in collecting and analyzing data efficiently.

What to look for

Pose the question: 'Imagine a student wrote that if 10 is 50% of a number, the number must be 5. What mistake did they make, and how would you explain the correct way to solve it?' Facilitate a class discussion on common errors.

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

Activity 04

• Problem-Based Learning
• 20 min · Individual

Individual: Error Hunt Cards

Students receive cards with percent problems containing common errors. Individually, they identify mistakes, correct them with proportions, and explain fixes in writing. Share one with the class.

Explain how to set up a proportion to find the whole when given a part and a percent.

Facilitation Tip

With Error Hunt Cards, give students red pens to mark corrections directly on the cards, so they can see their own progress clearly.

What to look for

Present students with a scenario: 'A store is having a 20% off sale. A jacket is now $60. What was the original price of the jacket?' Ask students to show their work using a proportion or equivalent method on a mini-whiteboard.

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

A few notes on teaching this unit

Teach this topic by starting with visual models, like 10x10 grids, to reinforce the meaning of percents before introducing formal equations. Avoid rushing into abstract methods; instead, let students derive the proportion whole = part × (100/percent) from repeated concrete examples. Research shows that students who practice both visual and symbolic representations develop stronger proportional reasoning.

By the end of these activities, students should confidently set up and solve percent equations using proportions or equivalent methods, explaining their process with clear reasoning. They should also recognize common errors and correct peers' misunderstandings during collaborative tasks.

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Watch Out for These Misconceptions

• During Discount Detective, watch for students dividing the part by the percent without converting the percent to a decimal or fraction.

  Prompt pairs to test both methods by writing the proportion part/percent = whole/100 and then comparing it to their original calculation, noting which one matches the context of the problem.

• During Recipe Remix, watch for students treating percents as parts of 10 instead of 100.

  Have groups use 10x10 grids to represent the percent increase or decrease in their recipe, then challenge them to explain why a 20% increase means adding 20 tiles out of 100.

• During Survey Percentages, watch for students subtracting the part from the whole to find the percent instead of dividing.

  Ask students to calculate the percent live using (part/whole) × 100, then compare their result to their subtraction method, discussing which one accurately represents the rate per hundred.

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Methods used in this brief

• Problem-Based Learning