Investigating Sharing Problems

Overview

This is lesson 1 of 5 in Solve, Share, Scale. Students investigate fair-sharing situations, using counters, drawings and equations to connect equal groups with division. The lesson is designed for 20 Year 5–6 students working in pairs.

Learning intentions

• WALT represent and solve real-life sharing problems.
• WALT identify the total and the number of equal groups.
• WALT connect materials and drawings to division equations.
• WALT explain what an answer means in context.

Success criteria

• I can identify the total amount and number of equal groups.
• I can model a sharing problem with equipment or a labelled diagram.
• I can write a matching division equation.
• I can explain what my answer means, including any remainder.

Curriculum links

• Number and Algebra: use multiplication and division strategies to solve problems involving equal groups and sharing.
• Number and Algebra: represent mathematical ideas with equipment, diagrams, words and equations.
• Mathematical communication: explain strategies, justify answers and interpret answers in context.
• Thinking and participating and contributing: choose strategies, listen to others and share mathematical reasoning.

Lesson structure (60 minutes)

1. 0–8 minutes – Launch: What is fair sharing? Open with the introduction and fair-sharing slides. Present: “Twenty-four apples are shared equally among six children. How many apples does each child get?” Ask students to think silently, then discuss with a partner. Invite several strategies and clarify that equal sharing means each group receives the same amount.

2. 8–15 minutes – Unpack the problem Model the problem with counters, drawing six circles for the children and distributing 24 counters one at a time. Ask: “What does 24 tell us? What does 6 tell us? What does the answer represent?” Record the language: total, equal groups, share equally, each group and division.

3. 15–32 minutes – Pair investigation Place students in pairs and distribute the sharing problems investigation sheet and counters. Pairs solve three problems, first using counters and then recording a drawing and equation. Suggested problems include 18 stickers shared among 3 children, 35 shells shared among 5 collectors, and 42 cards shared among 6 players. Encourage students to record equations such as 18 ÷ 3 = 6 and explain the meaning of each number.

4. 32–42 minutes – Teacher-guided strategy groups Pause the class and select two or three examples to discuss. Work with students who need support using counters and visual problem cards from the guided examples and vocabulary slides. Ask confident students to solve one problem using a related multiplication fact, then check it by sharing or repeated subtraction.

5. 42–52 minutes – Connect and compare representations Display one problem in three forms: counters, a labelled diagram and an equation. Ask pairs to explain how the representations match. Discuss the difference between the total, the number of groups and the amount in each group. Invite students to compare strategies and identify which method was most efficient for a particular problem.

6. 52–58 minutes – Extension and challenge Students attempt: “Twenty-nine grapes are shared equally among four people. How many does each person receive, and what happens to the leftovers?” Discuss the remainder in context. Students who finish early compare this sharing interpretation with a grouping question, such as “How many groups of four can be made from 29?”

7. 58–60 minutes – Plenary Return to the discussion and exit prompt slides. Students complete the sentence: “When I solve a sharing problem, I first look for…” Take two responses and collect the sharing problems investigation sheet for assessment.

Resources

• the sharing problems introduction deck
• the sharing problems investigation sheet
• Counters, bottle tops or linking cubes: one tub per pair
• Small whiteboards and pens
• Prepared visual problem cards
• Large paper or board space for class modelling
• Pencils, erasers and coloured pens
• Vocabulary displayed on the board: total, groups, equal, share, each, remainder

Assessment

• Observe whether students identify the total and number of groups before modelling.
• Check drawings and equations for a correct match, including the meaning of the answer.
• Use students’ explanations and completed worksheet responses to identify who needs further support with equal groups, notation or remainders.

Differentiation

• Support learners with counters, pre-drawn group circles, smaller totals and visual problem cards. Work with a teacher-guided group and model one step at a time.
• Provide vocabulary cards or sentence stems: “The total is…”, “There are… equal groups”, and “Each group gets…”.
• Accept oral explanations, acted-out sharing or labelled diagrams before expecting a written equation. Pair students thoughtfully and provide additional processing time.
• Extend capable students with larger totals, remainders and comparison of sharing and grouping interpretations. Ask them to prove an answer using multiplication.

Extension

For an additional challenge, students create their own sharing problem with a whole-number answer and another with a remainder. They swap problems with a partner, solve them using two representations, and explain whether the remainder can be shared, ignored or must be described in another way.