Think Boards: Show and Explain

Overview

Students consolidate equal-sharing strategies by solving practical word problems and completing a full think board. They represent their thinking with concrete groups or drawings, an array, repeated subtraction and a matching sentence, then explain and compare solutions.

Learning intentions

Students will:

• use equal groups, arrays, drawings and repeated subtraction to solve sharing problems
• represent the same problem in more than one way
• explain what each number means in a sharing situation
• listen to and compare different mathematical strategies

Success criteria

• I can share a collection into equal groups.
• I can show my thinking with groups or a drawing, an array and repeated subtraction.
• I can write a sentence such as “12 shared between 3 is 4.”
• I can explain how I know my answer is correct.

Curriculum links

• Number — multiplication and division using equal grouping, arrays, repeated addition and partitioning.
• Number — recognising equal parts and sharing collections into two or more equal groups.
• Algebra — using doubling and halving to connect multiplication and related division facts.
• Number — modelling practical multiplicative problems, choosing a strategy and explaining the solution in context.

Lesson structure (50 minutes)

1. 0–5 min · Warm-up and learning intention. Open with the hook and WALT slides showing 12 counters shared between 3 children, and ask, “How could we prove that everyone gets the same amount?” State the WALT: We Are Learning To use groups, arrays, drawings and repeated subtraction to explain how an equal-sharing problem was solved. Students turn and talk, then share possible strategies.

2. 5–13 min · Model a think board. Use the worked example slides to model: “12 biscuits are shared equally between 3 plates. How many biscuits are on each plate?” Build three groups with counters, draw the groups, arrange an array of 3 rows of 4, and record repeated subtraction: 12 − 3 − 3 − 3 − 3 = 0. Write, “12 shared between 3 is 4,” and clarify that 12 is the total, 3 is the number of groups and 4 is the amount in each group. Students help identify what each representation shows and chorally rehearse the sentence.

3. 13–18 min · Guided example and check. Display a second problem from the guided practice slides: “15 apples are shared equally between 5 baskets.” Students solve it with a partner using counters, then suggest the array and repeated-subtraction recording. Check that the repeated subtraction subtracts 5 each time and that the final answer refers to apples in each basket, not the number of baskets.

4. 18–36 min · Independent or collaborative think boards. Distribute the four-part think-board worksheet and counters to pairs or individuals. Students choose, or are assigned, a word problem such as 10 stickers shared between 2 children, 16 blocks shared between 4 groups, 18 shells shared between 3 baskets or 20 pencils shared between 5 tables. They complete each section: concrete groups or a labelled drawing, an array, repeated subtraction and the sentence “___ shared between ___ is ___.” Read problems aloud, provide the structured template and conference with targeted students. Encourage students to check by counting every group and using the related multiplication fact where appropriate.

5. 36–46 min · Share, compare and critique. Revisit the examples and non-examples slides. Invite pairs to present one think board, explaining why each representation matches the problem. Show examples with an unequal group, a rotated or incorrectly labelled array, and repeated subtraction using the wrong number. Students use sentence starters: “I notice…”, “This matches because…” and “I would change…”. Compare two correct methods and discuss whether they always give the same result when the groups are equal.

6. 46–50 min · Plenary and exit check. Display the exit prompt slide: “8 frogs are shared equally between 2 ponds. How many frogs are in each pond?” Students draw two equal groups, write one subtraction sentence and complete: “8 shared between 2 is ___.” Collect responses and ask two students to explain how they checked their answer.

Resources

• the complete think-board teaching deck
• the four-part think-board worksheet
• Connecting cubes, counters or small classroom objects
• Pencils, erasers and coloured pencils
• Mini-whiteboards and markers
• Prepared word-problem cards or displayed problem list
• Classroom display or interactive whiteboard

Assessment

• Observe whether students make equal groups, identify the divisor as the number of groups and record repeated subtraction accurately.
• Conference with students using prompts: “What does this number mean?”, “How does your array show the story?” and “How can you check?”
• Use the exit response to assess representation, subtraction strategy, equal sharing and interpretation of the final sentence.

Differentiation

• Support students with counters, pre-drawn group circles, an array grid and a sentence frame: “___ shared between ___ is ___.” Work first with totals within 12 and use repeated subtraction with a visible number line.
• Read every word problem aloud, rehearse key language such as share equally, groups, each and total, and pair EAL learners with supportive peers. Use gestures, pictures and labelled examples rather than relying on lengthy written instructions.
• Provide the worksheet template with one section completed for students requiring additional structure. Accept oral explanations or scribed responses while maintaining the mathematical expectation.
• Extend confident students by assigning an array, such as 4 rows of 3, and asking them to write a matching word problem, solve it in two ways and explain whether both methods always produce the same result. They may also compare sharing into 3 groups with making groups of 3.