Grouping and Multiplication

Overview

Lesson 2 of 5 in the unit Solve, Share, Scale. Students distinguish sharing and grouping division problems, represent them with arrays and equal groups, connect multiplication and division equations, and explain why their strategies work.

Learning intentions

• WALT use multiplication and division to solve grouping problems.
• WALT distinguish between sharing and grouping situations.
• WALT show a problem using arrays, equal groups or skip-counting.
• WALT explain the inverse relationship between multiplication and division.

Success criteria

• I can tell whether a problem involves sharing or grouping.
• I can use an array, equal groups or skip-counting to solve it.
• I can write a related multiplication and division fact family.
• I can justify my strategy using mathematical language.

Curriculum links

• Number and Algebra: use multiplication and division facts and strategies to solve problems involving equal groups and quantities.
• Number and Algebra: understand the inverse relationship between multiplication and division and use related facts.
• Mathematical communication: represent, explain and compare mathematical ideas using diagrams, equations and spoken or written reasoning.
• Key competencies: thinking; using language, symbols and texts; participating and contributing.

Lesson structure (60 minutes)

1. 0–8 min – Hook and sort contextual problems Open with the hook and learning intentions. Present two situations, such as “24 apples are shared equally among 6 children” and “24 apples are packed into bags of 6”. Ask: “What is unknown in each problem?” In groups of four, students sort problem cards or teacher-read examples into sharing or grouping. Establish that sharing asks how many in each group, while grouping asks how many groups can be made.

2. 8–18 min – Teacher modelling Use counters or linking cubes to model 18 shared among 3 and 18 grouped in threes. Draw both representations and connect them to the equations 18 ÷ 3 = 6, 18 ÷ 6 = 3 and 3 × 6 = 18. Think aloud using the repeated structure: “I know the total is __. The group size/number of groups is __. I need to find __.” Refer to the sharing and grouping model and check understanding with a quick thumbs-up choice.

3. 18–30 min – Build and represent Give each pair counters and a set of teacher-prepared contexts. Students build an array or equal groups for each context, then record the total, known number and unknown number. Pairs explain their model to another pair before changing it into an array where possible. Encourage skip-counting for students who do not yet recall the fact. Provide the grouping and multiplication recording sheet for diagrams and equations.

4. 30–42 min – Fact families Students choose three contexts from the worksheet and write a related fact family for each, for example: 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4. Partners use the sentence stem, “The multiplication fact shows __ groups of __. The division fact shows __ divided into groups of __.” Circulate and ask, “Which number is the total? How does your model prove the equation?” Use the fact-family examples and talk prompts.

5. 42–53 min – Compare efficient strategies Groups select one problem and compare two methods, such as counters, an array, skip-counting or a known multiplication fact. Record findings in the table on the strategy comparison table: method, representation, equation, answer and why it works. Invite two groups to share different approaches. Discuss that an efficient strategy may depend on the numbers and what facts a student knows.

6. 53–60 min – Plenary and assessment Display the final prompt in the plenary challenge: “There are 30 stickers. They are put into groups of 5. How many groups? Write the fact family and explain your answer.” Students complete it independently on the worksheet, then share with a partner. Collect responses to identify who can distinguish grouping, represent accurately and justify the inverse relationship.

Resources

• the complete lesson slide deck
• the grouping and multiplication recording sheet
• Counters, linking cubes or bottle tops, one set per pair
• Small cards or teacher-prepared slips showing contextual problems
• Mini-whiteboards and pens
• Large paper or whiteboard for class modelling
• Pencils, rulers and coloured pens

Assessment

• Listen during sorting and partner explanations for correct use of “sharing”, “grouping”, “total”, “group size” and “number of groups”.
• Check models and fact families for matching quantities and inverse equations.
• Use the independent plenary challenge to identify students needing further modelling in the next lesson.

Differentiation

• Support learners with smaller totals, array templates, counters, multiplication charts and explicit teacher modelling. Begin with totals within 20 before moving to 30 or 40.
• Pair students strategically and provide repeated language structures: “The total is __; each group has __; there are __ groups.”
• For EAL and SEN learners, use visual examples, gestures and colour-coding for the total, group size and number of groups. Allow oral explanations, pointing and recorded responses.
• Extend confident learners by asking them to find multiple equations for one context, identify factor pairs, and investigate how changing one number changes the answer.