Mathematics · Year 8

Active learning ideas

Sharing in a Given Ratio

Active learning works for this topic because sharing in a ratio requires students to move beyond abstract numbers into tangible, proportional reasoning. Manipulatives and group tasks let students see how parts relate to totals, turning a potentially confusing process into a clear, visual process.

• National Curriculum Attainment Targets
• KS3: Mathematics - Ratio, Proportion and Rates of Change

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 35 min · Small Groups

Group Task: Sweet Sharing

Provide bags of 48 sweets to small groups. Give ratios like 3:5 and instruct students to use the unitary method: find total parts, value per part, then shares. Have groups verify by recombining sweets and discuss predictions if total changes to 60. Extend to drawing bar models.

Explain how the total number of parts in a ratio relates to the whole quantity being shared.

Facilitation Tip

During Sweet Sharing, circulate to ensure groups first model the ratio with counters before assigning any numerical values, reinforcing the link between physical and abstract steps.

What to look for

Provide students with the following problem: 'Share 45 sweets between two friends in the ratio 4:5. Show your working using the unitary method.' Collect these to check individual understanding of the calculation steps.

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

Activity 02

• Collaborative Problem-Solving
• 25 min · Small Groups

Relay Race: Ratio Divisions

Divide class into teams. Each student solves one step of a unitary method problem on a whiteboard (e.g., total parts for 3:4, then per part for 56 units), passes to next. First team to complete and explain correctly wins. Repeat with new ratios.

Compare the unitary method with other strategies for sharing quantities proportionally.

Facilitation Tip

For Relay Race: Ratio Divisions, place ratio cards face down so students must first interpret the ratio before moving, preventing rushed and incorrect calculations.

What to look for

Ask students to work in pairs. Give one pair a total quantity and ratio (e.g., £60 shared in 1:2). Give another pair a different total and ratio (e.g., 50kg shared in 3:7). Ask them to calculate the shares. Then, pose the question: 'What would happen to your shares if the total quantity was doubled?'

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

Activity 03

• Collaborative Problem-Solving
• 30 min · Pairs

Pairs Practice: Changing Ratios

Pairs get cards with quantities and ratios. One calculates shares using unitary method; partner predicts new shares if ratio changes to 3:4 or total doubles. Switch roles, then share whole-class solutions and compare methods.

Predict the impact on individual shares if the total quantity or ratio changes.

Facilitation Tip

In Pairs Practice: Changing Ratios, provide ratio strips so students can physically fold and compare lengths, making proportional changes visible and immediate.

What to look for

Present this scenario: 'Two teams, A and B, are sharing a prize of £100 in the ratio 1:3. Team C and D share a prize of £200 in the ratio 1:3.' Ask students: 'Who gets more money, Team B or Team D? Explain your reasoning, comparing the value of one part in each scenario.'

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

Activity 04

• Collaborative Problem-Solving
• 20 min · Whole Class

Whole Class: Real-World Scales

Project scenarios like dividing £100 in 2:3 for two shops. Students individually note unitary steps on mini-whiteboards, then vote on predictions for ratio 3:5. Discuss as class, modeling adjustments.

Explain how the total number of parts in a ratio relates to the whole quantity being shared.

What to look for

Provide students with the following problem: 'Share 45 sweets between two friends in the ratio 4:5. Show your working using the unitary method.' Collect these to check individual understanding of the calculation steps.

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

A few notes on teaching this unit

Experienced teachers begin with concrete examples, using manipulatives like counters or strips to anchor the concept of ratio parts. Avoid rushing to numerical steps; instead, scaffold from hands-on to symbolic by asking students to record their models as fractions or equations. Research shows that students who visualize ratios as scaled lengths or areas develop stronger proportional reasoning than those who only work numerically.

Successful learning looks like students confidently breaking ratios into unit parts, scaling quantities accurately, and explaining why totals matter. They should justify their answers by showing steps and verifying their work by adding parts back to the original total.

---

Watch Out for These Misconceptions

• During Sweet Sharing, watch for students who distribute sweets as fixed amounts (2 and 3) without considering the total quantity.

  Have these groups recount their sweets after dividing, asking them to add the parts and compare the total to the original number. Ask, 'Why does 2:3 of 10 not equal 5 sweets?' to prompt reflection on scaling.

• During Relay Race: Ratio Divisions, watch for students who add the ratio parts (2+3=5) but then divide the total incorrectly, such as dividing by 2 or 3 instead of 5.

  Place ratio cards and blank strips on the table. Ask students to lay out five equal sections on the strip, then label each with the ratio parts. This visual gap between 5 parts and the ratio numbers helps them see the error.

• During Pairs Practice: Changing Ratios, watch for students who treat ratios additively, such as adding 2+3 to the total quantity instead of scaling the parts proportionally.

  Provide measuring tapes and ask students to mark the total length first, then fold the tape into 5 equal parts for the ratio 2:3. Observing the physical fold helps them see that each part is a multiplier of the unit value, not an addition.

---

Methods used in this brief

• Collaborative Problem-Solving