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.

• Year 7
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Compare part-to-part and part-to-whole ratios using given quantities.
2. Explain the relationship between quantities represented by a given ratio.
3. Construct a real-world scenario that can be described using a ratio.
4. Identify and write ratios from descriptive statements and visual representations.

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Mixing Stations, present a scenario like 'A group has 8 cats and 12 dogs. Ask students to write the ratio of cats to dogs and the ratio of dogs to total animals, then trade with a partner to check notation and labels.

Exit Ticket

During Recipe Scale-Up, collect each group's scaled recipe sheet and listen to their justification of the scaling factor. Look for clear language like 'We multiplied by 3 because the original recipe serves 4 and we need 12.'

Discussion Prompt

After Bar Model Build, ask students to share their models and explain how the same ratio can look different when built with different unit sizes, reinforcing the idea of equivalent ratios.

Extensions & Scaffolding

• Challenge: Ask students to design their own recipe using a ratio of 4:1 and calculate three different scaled versions for different serving sizes.
• Scaffolding: Provide pre-sorted ratio cards with visuals for students who confuse part-to-part and part-to-whole, or offer a sentence stem like 'For every ____, there are ____.'
• Deeper exploration: Introduce a scenario with three quantities, such as a trail mix with nuts, seeds, and dried fruit, and ask students to write all possible ratios and explain which best describes the mix.

Key Vocabulary

Ratio	A comparison of two or more quantities, often expressed using a colon or as a fraction.
Part-to-Part Ratio	A ratio that compares two different parts within a whole group. For example, the ratio of red marbles to blue marbles in a bag.
Part-to-Whole Ratio	A ratio that compares one part of a group to the total number of items in the whole group. For example, the ratio of red marbles to the total number of marbles.
Quantity	An amount or number of something that can be measured or counted.