Drawing Equal Groups

Overview

In this third lesson of the unit Share, Group, Array, students use concrete materials to represent equal sharing and grouping. They move from making groups to drawing them and recording repeated subtraction, such as (12 - 3 - 3 - 3 - 3 = 0), beginning a think board to show their reasoning.

Learning intentions

• WALT represent equal groups and sharing situations with drawings.
• WALT use repeated subtraction to solve grouping problems.
• WALT explain what each number means in a number sentence.
• WALT record our thinking on a think board.

Success criteria

• I can make equal groups using counters.
• I can draw groups or an array to match a problem.
• I can record repeated subtraction until I reach zero.
• I can explain how my drawing and number sentence match.

Curriculum links

• Number — multiplication and division using equal grouping, arrays, repeated addition and partitioning.
• Number — mathematical modelling of practical additive and multiplicative problems.
• Algebra — using addition and subtraction facts to support calculation strategies.
• Algebra — developing related multiplication and division facts through doubling and halving.

Lesson structure (50 minutes)

1. 0–5 min · Hook and connect. Open with the hook and learning intention slides and show 12 counters with the question, “How could we put these into equal groups of 3?” Students turn and talk, then briefly share strategies from the previous lesson.

2. 5–13 min · Model with materials. Teacher models the problem, “There are 12 shells. How many groups of 3 can we make?” using counters, physically removing one group at a time. Record (12 - 3 = 9), (9 - 3 = 6), (6 - 3 = 3), (3 - 3 = 0), then combine the steps as (12 - 3 - 3 - 3 - 3 = 0). Students help identify that the answer is 4 groups and explain what each 3 represents.

3. 13–20 min · Draw and discuss. Teacher demonstrates two representations on the worked-example slides: four colour-coded groups of 3 and a 4-by-3 array. Model how to label the drawing and connect it to the repeated subtraction sentence. Students build and draw (15) grouped into (3)s with a partner, then explain their representation using the sentence frame: “I made __ groups of __. I subtracted __ each time, so there are __ groups.”

4. 20–35 min · Guided think board task. Distribute the equal-groups think board to pairs and provide counters. Display the first worded problem: “18 apples are packed into bags of 3. How many bags are needed?” Students use counters, draw equal groups or an array, complete the repeated subtraction sentence, and write the answer in context. Teacher circulates, checking that students subtract the group size rather than the number of groups. Pairs then solve a second problem independently or with support.

5. 35–43 min · Share and compare. Open the discussion and comparison slides and select two or three student examples. Students compare drawings and explain how they know the groups are equal. Discuss the difference between the total, the group size and the number of groups; clarify that in (18 - 3 - 3 - 3 - 3 - 3 - 3 = 0), six groups of 3 were made.

6. 43–48 min · Extension and reasoning. Students who finish connect one repeated-subtraction problem to a related multiplication or division fact, such as (18 \div 3 = 6) and (6 \times 3 = 18), and complete: “I know these facts are connected because …” Other students practise a teacher-selected problem with counters and a number line.

7. 48–50 min · Exit check. Display the exit-ticket slide. Students solve: “Share 12 biscuits into groups of 2. Draw the groups and complete (12 - 2 - __ - __ - __ - __ - __ = 0). How many groups are there?” Collect responses as students leave or begin the next routine.

Resources

• the equal-groups teaching deck
• the equal-groups think board
• Counters, linking cubes or shells; one tub per pair
• Mini whiteboards and markers
• Pencils and coloured pencils
• Open number lines, including 0–20
• Large teacher modelling mat or magnetic counters
• Word-problem cards prepared by the teacher

Assessment

• Observe whether students create equal groups, identify the group size and remove one equal group at a time.
• Question students during pair work: “What does this number mean?”, “How does your drawing show the subtraction?” and “How do you know no counters are left?”
• Use the exit check to identify students who can connect a drawing, repeated subtraction and the number of groups.

Differentiation

• Support students with colour-coded counters, partially completed drawings, pre-drawn circles or arrays, an open number line and smaller totals such as 8, 10 or 12.
• Provide sentence frames: “I started with __,” “I took away __ each time,” and “There are __ equal groups.”
• Explicitly teach and display total, equal group, group size, array, subtract and repeated subtraction, using gestures and real objects for EAL learners.
• Pair students purposefully and allow students to explain orally, point to a model or draw before writing; provide adult scribing or enlarged templates where needed.
• Extend advanced learners by asking them to solve the same total with a different group size, compare two arrays, and justify the related multiplication and division facts.

Extension

• Find two different ways to group 12 counters equally and record both repeated-subtraction sentences.
• Explain why (12 - 3 - 3 - 3 - 3 = 0) connects to (4 \times 3 = 12) and (12 \div 3 = 4).
• Create a short equal-grouping problem for a partner to solve.