Sharing in Ratios

Overview

In this lesson, students share quantities into given ratios using counters, bar models and written calculations. They connect equal groups to the total number of ratio parts, then check that their shares preserve the original total.

Learning intentions

• WALT interpret a ratio as equal-sized parts.
• WALT share a quantity into a given ratio.
• WALT represent ratio sharing with materials, bar models and calculations.
• WALT check that our answers are reasonable and add to the original total.

Success criteria

• I can explain what the parts in a ratio represent.
• I can use a bar model to show a ratio share.
• I can calculate the value of one part and each share.
• I can check that my shares add to the original quantity.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenging tasks connected to relevant mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, explaining and justifying mathematical thinking.

Lesson structure (45 minutes)

1. 0–5 min · Hook and connect. Display the question from the opening ratio-sharing slide: “A team has 24 points to share in the ratio 1:3. Does each person get 12 points?” Students make a quick estimate, discuss with a partner and explain why they agree or disagree. Teacher revisits that a ratio compares parts, not necessarily the final amounts, and records students’ ideas without confirming the answer immediately.

2. 5–13 min · Model with materials. Teacher uses counters to model sharing 20 into the ratio 2:3, placing counters into two groups and three groups; then records the matching bar model on the worked-example slides. Students describe the number of equal parts, find the value of one part, and calculate both shares. Emphasise: total parts = 2 + 3 = 5; one part = 20 ÷ 5 = 4; shares are 2 × 4 = 8 and 3 × 4 = 12. Check 8 + 12 = 20.

3. 13–20 min · Guided examples. Teacher works through two examples with the class: share 18 in the ratio 1:2, then share 35 in the ratio 2:5. Use the prompts on the guided-practice slides: “How many parts altogether?”, “What is one part worth?” and “How can we check?” Students use mini-whiteboards to show the total parts, one-part calculation and final shares before answers are discussed.

4. 20–34 min · Paired problem solving. Distribute the ratio-sharing practice worksheet. Students solve the practical sharing problems in pairs, first using counters or drawn bars, then recording calculations. Include contexts such as fruit shared between two groups, points divided between teams and books allocated to classes. Teacher circulates, checking that students divide by the total number of ratio parts rather than by one ratio number. Pause midway at the problem-solving prompt slide for students to compare methods with another pair and identify how totals were checked.

5. 34–41 min · Reasoning challenge and discussion. Teacher presents: “Sam says that sharing 42 in the ratio 4:3 gives 16 and 26 because 42 ÷ 3 = 14 and 14 × 4 = 56. What has gone wrong?” Students identify the error, correct the method and explain their reasoning using a bar model or words. Invite several students to share different representations. Highlight that the ratio parts must be treated as one complete set and that the final shares must preserve the total.

6. 41–45 min · Plenary and exit check. Display the final question on the reflection and exit-question slide: “Share 32 in the ratio 3:5. Show one calculation and one check.” Students complete it independently on the bottom of the worksheet or in their books. Teacher collects responses to identify who can independently find total parts, calculate one part and verify the total.

Resources

• the ratio-sharing slide deck
• the ratio-sharing practice worksheet
• Linking counters, cubes or other small manipulatives
• Mini-whiteboards and pens
• Prepared ratio examples on the board
• Exercise books and pencils

Assessment

• Listen during modelling and guided examples for correct use of “parts”, “one part” and “share”.
• Use mini-whiteboard responses to identify whether students divide by the total number of ratio parts.
• Mark the independent exit question for the three essential steps: total parts, share calculation and total check.

Differentiation

• Support students with counters, a pre-drawn bar model and the sentence frame: “There are __ parts altogether, so one part is __ ÷ __ = __.”
• Begin with ratios whose totals divide evenly, such as 1:2, 2:3 and 2:5; provide multiplication facts or a calculator only when calculation, rather than reasoning, is the barrier.
• Pair students strategically and allow oral explanations, labelled diagrams and bilingual discussion where helpful for English language learners.
• Extend confident students with missing-total problems, such as “One ratio part is 6 and the ratio is 2:5. What is the total?” Ask them to create a sharing problem with more than one possible representation and justify that their answer is correct.