Equal Groups, Clever Counting

Overview

Two sequential 20-minute lessons for six Year 3 learners, based on assessment information showing a need to strengthen multiplication and division understanding. Students move from making and describing equal groups to representing the same situations with equations, using materials, drawings and efficient counting strategies.

Curriculum links

• Phase 1 Number teaching sequence: equal groups, multiplication and division, and developing flexible counting strategies.
• Mathematics and Statistics — Mathsteasers: higher-order questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge connected to current classroom mathematics.
• Mathematics and Statistics — Additional resources for advanced learners: open-ended challenge and reasoning.

Lesson 1: Make Equal Groups

Learning intentions

• WALT make equal groups using concrete materials.
• WALT describe equal groups using repeated addition.
• WALT explain how multiplication can show equal groups.

Success criteria

• I can make groups that are the same size.
• I can count equal groups efficiently.
• I can draw or write a repeated-addition number sentence.
• I can explain how I know my groups are equal.

Lesson structure (20 minutes)

1. 0–3 min · Hook and connect. Open the equal-groups introduction slides and show a visual of three baskets with three kūmara in each; ask, “How could we find the total without counting every kūmara one at a time?” Students think, talk with a partner and share strategies.

2. 3–6 min · Model. Teacher uses counters and hoops to model 3 groups of 3, saying “three groups of three”, then records 3 + 3 + 3 = 9 and 3 × 3 = 9. Students build the same example and rehearse the language “groups of” and “altogether”.

3. 6–13 min · Guided investigation. Give pairs counters, small hoops and a context card from the equal-groups investigation sheet. Teacher prompts: “How many groups?”, “How many in each group?”, and “What stays the same?” Students make equal groups for totals such as 6, 9, 12 and 15, then draw each arrangement and record repeated addition.

4. 13–17 min · Reasoning challenge. Display the question from the equal-groups challenge slide: “Can 10 counters be arranged into equal groups in more than one way?” Students test possibilities, explain why one arrangement may or may not work, and listen respectfully to different ideas.

5. 17–20 min · Plenary and assessment. Students complete the final prompt on the equal-groups investigation sheet: draw 4 groups of 2 and write the repeated-addition sentence. Each student explains their representation to the teacher or a peer.

Resources

• the equal-groups introduction slides
• the equal-groups investigation sheet
• Counters or bottle tops
• Six small hoops, paper circles or plates
• Mini-whiteboards and pens
• Pencils and crayons

Assessment

• Observe whether students create equal-sized groups without teacher correction.
• Listen for accurate use of “groups of”, “each” and “altogether”.
• Collect the final worksheet prompt to identify students needing further work with equal groups or counting.

Differentiation

• Support: begin with totals to 6, use a group mat, and provide the sentence frame “There are __ groups of __. Altogether there are __.”
• Support EAL learners with gestures, pictures and repeated oral rehearsal of “group”, “each”, “equal” and “altogether”.
• Extension: ask confident students to find two different equal-group arrangements for 12 or 18 and explain which is more efficient to count.
• Use paired talk and manipulatives before recording, ensuring every learner has a role as builder, counter or explainer. This promotes inclusion, cooperation and the belief that all learners are capable mathematicians.

Lesson 2: Connect Groups, Multiplication and Division

Learning intentions

• WALT connect equal groups with multiplication and sharing.
• WALT use a drawing, materials or an equation to solve a problem.
• WALT explain how multiplication and division are related.

Success criteria

• I can make equal groups or share equally.
• I can write a multiplication or division equation.
• I can check my answer by counting or using the related operation.
• I can explain my strategy clearly.

Lesson structure (20 minutes)

1. 0–3 min · Retrieval hook. Reopen the multiplication-and-division sequence deck and revisit the image from Lesson 1. Ask, “If 12 kūmara are put into 3 equal baskets, how many go in each basket?” Students solve mentally, with counters or by drawing.

2. 3–7 min · Explicit teaching. Teacher builds 3 groups of 4 and records 4 + 4 + 4 = 12 and 3 × 4 = 12. Then share 12 into 3 equal groups and record 12 ÷ 3 = 4. Emphasise that multiplication finds the total and division can find the number in each equal group.

3. 7–14 min · Guided problem solving. Distribute the equal-sharing problem sheet. Students solve short contexts involving 2s, 3s, 5s and 10s, using counters or drawings before choosing an equation. Teacher conferences with each learner and asks, “What do you know?”, “What are you finding?”, and “How can you check?”

4. 14–17 min · Independent mathematics activity. Students choose one problem from the choice-and-check challenge slide and solve it independently: “There are 15 fruit pieces. Show two ways to share them equally.” They record a drawing and equation, then explain their answer to a partner.

5. 17–20 min · Plenary and next steps. Finish with the multiplication facts exit ticket slips. Students answer the assigned question, show working if needed, select a self-assessment face and complete “One thing I can do now…” Teacher briefly groups students for the next session: concrete grouping, supported equation recording, or multiplication/division reasoning.

Resources

• the multiplication-and-division sequence deck
• the equal-sharing problem sheet
• the multiplication facts exit ticket slips
• Counters, hoops or paper plates
• Mini-whiteboards and pens
• Pencils and crayons

Assessment

• Check whether students distinguish between finding the total and finding the number in each group.
• Use questioning and worksheet representations to identify whether errors arise from counting, grouping or equation notation.
• Use the exit slip and self-assessment to plan next steps: revisit concrete groups, practise facts in 2s, 3s, 5s and 10s, or extend to missing-number problems.

Differentiation

• Support: provide pre-drawn circles, smaller numbers and the frame “__ shared into __ equal groups gives __ in each group”; allow counters throughout.
• For learners needing language support, use picture contexts, partner rehearsal and the repeated structure “I know __. I need to find __. My equation is __.”
• Extension: offer missing-number problems such as 3 × __ = 18 and __ ÷ 3 = 6, asking students to justify more than one strategy.
• Use familiar Māori and Pacific contexts respectfully, such as sharing kai among whānau, while inviting students to contribute contexts from their own lives. Cooperative problem solving, fairness, care and perseverance are made explicit as classroom values; teacher feedback affirms each learner as creative, relational and capable.