Mathematics · Year 7

Active learning ideas

Introduction to Ratios

Active learning works for ratios because students need to see, touch, and manipulate quantities to grasp proportional relationships. When students measure, mix, and build with concrete materials, they move beyond abstract symbols to meaningful understanding of how quantities relate to each other.

• ACARA Content Descriptions
• AC9M7N08

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

Activity 01

• Carousel Brainstorm
• 35 min · Pairs

Mixing Stations: Colour Ratios

Set up stations with paint or coloured water in cups. Pairs mix solutions in given ratios like 1:2 or 2:3, observe shades, then swap to predict and create new mixtures. Groups record results and explain differences in a class share.

Differentiate between a ratio that compares parts to parts and one that compares parts to wholes.

Facilitation Tip

During Mixing Stations, circulate with measuring cups to ensure students record ratios before adjusting colors, reinforcing the idea that ratios describe fixed relationships.

What to look for

Present students with a scenario, such as 'In a class of 10 students, 6 are girls.' Ask them to write down: 1. The part-to-part ratio of girls to boys. 2. The part-to-whole ratio of girls to the total class.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Carousel Brainstorm
• 25 min · Small Groups

Sorting Cards: Ratio Categories

Provide cards with scenarios and diagrams. Small groups sort into part-to-part or part-to-whole piles, justify choices, then create counterexamples. Debrief as whole class to resolve debates.

Explain how ratios are used to describe relationships between quantities.

Facilitation Tip

For Sorting Cards, provide a mix of ratio types and quantities so students must justify their categorization choices aloud before placing each card.

What to look for

Provide students with a picture of a fruit bowl containing 3 apples and 4 bananas. Ask them to write two different ratios represented by the image, labeling each as either 'part-to-part' or 'part-to-whole'.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Carousel Brainstorm
• 30 min · Pairs

Bar Model Build: Visual Ratios

Students use linking cubes or strips to build bar models for ratios like 4:6. In pairs, they scale models up or down, compare equivalents, and apply to word problems. Share models on class display.

Construct a real-world example of a ratio.

Facilitation Tip

When building Bar Models, insist students label each segment clearly and write the ratio both numerically and in words to connect visuals to language.

What to look for

Pose the question: 'Imagine you are making lemonade with a recipe that uses 1 part lemon juice to 3 parts water. What does this ratio tell you about the ingredients? How would you describe this ratio in words?'

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 40 min · Small Groups

Recipe Scale-Up: Group Challenge

Give recipes with ratios for ingredients. Small groups double or halve quantities, measure and mix samples, then taste and discuss proportional changes. Present findings to class.

Differentiate between a ratio that compares parts to parts and one that compares parts to wholes.

Facilitation Tip

In the Recipe Scale-Up challenge, require groups to present both their scaled recipe and the reasoning behind their multiplication factor.

What to look for

Present students with a scenario, such as 'In a class of 10 students, 6 are girls.' Ask them to write down: 1. The part-to-part ratio of girls to boys. 2. The part-to-whole ratio of girls to the total class.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Experienced teachers know ratios are best taught through real contexts that demand proportional reasoning, not isolated drills. Avoid starting with symbols—let students verbalize ratios in words first, then connect to notation. Research shows students grasp ratios more deeply when they create their own equivalent forms rather than simplifying given ones. Always pair concrete tasks with explicit language frames to bridge informal and formal math talk.

Successful learning looks like students confidently identifying and writing ratios in part-to-part and part-to-whole forms, using correct terminology and justifying their choices with concrete examples. They should also recognize equivalent ratios and explain their meaning in context without defaulting to fractions or percentages.

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Watch Out for These Misconceptions

• During Mixing Stations, watch for students who treat the colored mixture as a fraction of the total liquid rather than comparing the amounts of each color.

  Prompt students to record the ratio of colors before mixing and ask, 'Does the order matter? What if you switched the colors?' to highlight that ratios compare quantities, not parts of a whole.

• During Sorting Cards, watch for students who confuse part-to-whole ratios with fractions by automatically converting ratios like 3:5 to 3/5.

  Ask students to physically group the items for the ratio 3:5 and label the parts before writing any numbers. Then have them write both the ratio and fraction side by side and discuss the differences in meaning.

• During Bar Model Build, watch for students who simplify ratios like 2:4 to 1:2 without understanding why equivalence matters in context.

  Have students build both 2:4 and 1:2 models using the same unit bar, then ask them to scale one model to match the other and explain what happens to the quantities.

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Methods used in this brief

• Carousel Brainstorm