Dividing by Eight

Overview

Duration: 60 minutes
Class size: 30 pupils
Topic focus: Problem solving and reasoning with division by 8
Year group: 3 (Age 7–8)
Curriculum reference:

• Maths Programmes of Study – Number – Multiplication and Division (Year 3)
• National Curriculum for England (DfE, 2013)
• Key objectives:
  • Recall and use multiplication and division facts for the 8 multiplication table
  • Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

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Learning Objectives

By the end of this lesson, pupils will be able to:

1. Recall multiplication facts for the 8 times-table and use these facts to divide numbers by 8.
2. Solve a variety of division problems involving dividing by 8 with increasing reasoning and problem-solving skills.
3. Use visual representations and practical resources to support understanding of division by 8.

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Success Criteria

Pupils will:

• Confidently say and write division facts for 8 (e.g. 64 ÷ 8 = 8).
• Demonstrate how to divide numbers by 8 using arrays, grouping, or sharing methods.
• Solve at least 3 word problems involving division by 8 with step-by-step reasoning shown.
• Explain their thinking either verbally or in writing when solving division problems by 8.

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National Curriculum Links

Year 3 Multiplication and Division:

• Pupils should be taught to:
  • Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables.
  • Write and calculate mathematical statements for multiplication and division using the multiplication tables they know, including for two-digit numbers times one-digit numbers, using mental methods and progressing to formal written methods.
  • Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

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Resources Needed

• Whiteboard and pens
• Number cards (multiples of 8, with answers on reverse)
• Counters or small objects for grouping/shared activities
• Worksheets with division problems by 8 (varied difficulty)
• Visual aids: arrays and grouping diagrams
• Interactive smartboard or tablet for group activities
• Mini whiteboards and pens for pupil work

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Lesson Outline

Starter (10 minutes)

Activity: Quick Recall Warm-Up

• Begin with a fun chant or song focusing on the 8 times-table (e.g., "8, 16, 24…").
• Use “flash cards” on the board: call out multiplication facts for 8, pupils respond with the answer or corresponding division fact (e.g., “64 ÷ 8?”).
• Challenge pupils to write down the division fact for a given multiplication (8 × 7 = 56, then 56 ÷ 8 = ?).
• Use mini whiteboards for quick short written answers.

Success criteria checked: Can pupils recall division facts corresponding to the 8 times table?

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Main Teaching (30 minutes)

Step 1: Understanding Division by 8 (10 mins)

• Model division by 8 using counters/picutures: e.g., sharing 24 counters into 8 equal groups (how many counters in each group?).
• Show arrays (e.g., 8 rows of 3, 8 × 3 = 24), link to division as the inverse.
• Discuss the language: "divide", "equal groups", "how many in each group", "quotient".

Differentiation:

• Support lower-attaining pupils with physical counters and visual grouping.
• Provide verbal sentence stems for reasoning: “If I have 24 counters and put them in 8 groups, then each group has ___ counters.”

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Step 2: Problem Solving with Division by 8 (20 mins)

Activity 1: Tiered Problem Cards

• Pupils work in pairs or small groups with problem-solving cards, sorted by difficulty:
  • Level 1: Simple division (e.g., 48 ÷ 8) using practical objects or drawings.
  • Level 2: Word problems requiring one-step division by 8 (e.g., “There are 64 apples shared equally into 8 baskets. How many apples in each basket?”).
  • Level 3 (challenge): Two-step problems or missing number problems (e.g., “___ ÷ 8 = 7. What is the missing number?” or “If 8 boxes hold 6 apples each, how many apples total?”).

Success criteria checked: Can pupils solve division problems by 8 and explain their answers?

Extension:

• Advanced learners create their own division-by-8 problems for peers to solve or explore division facts for multiples of 8 beyond 96, e.g., 104 ÷ 8 = ? using mental strategies.
• Investigate patterns in division by 8 – what happens when you divide even vs odd multiples of 8?

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Plenary (10 minutes)

• Invite pupils to share a problem they solved and explain how they found the answer (emphasising reasoning and verbalising method).
• Quick-fire mental division quiz by 8 on the board for the whole class.
• Self-assessment: Pupils tick or colour the success criteria they feel confident with.

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Differentiation Strategies

Ability Level	Supports / Strategies	Examples
Lower Attainers	Use counters, grouping arranged by teacher, sentence stems, peer buddies	Grouping 24 counters into sets of 8 physically
Middle Attainers	Use arrays and pictorial representations, guided problem solving	Solve standard word problems supported by visuals
Higher Attainers	Independent multi-step problems, create own problems, explore division patterns	Missing number problems, explain division rules orally

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Assessment Opportunities

• Teacher observations during paired work: Are pupils using correct methods and vocabulary?
• Marking of written problem-solving cards for accuracy and reasoning explanation.
• Plenary quiz responses and self-assessment for confidence levels.
• Oral explanations to check conceptual understanding.

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Extension Activities for Advanced Learners

• Investigate division by multiples of 8, e.g., 16 ÷ 8, 24 ÷ 8, and predict answers mentally.
• Use inverse operations to check answers (multiplying quotient by 8).
• Explore correspondence problems involving division by 8 (e.g., ‘If 8 toys are placed in 3 boxes each, how many toys are there in total?’).
• Begin simple formal written division method for division by 8 with larger numbers (e.g., 96 ÷ 8).

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Reflection Notes for Teacher

• Monitor if pupils understand division as sharing into equal groups, not just repeated subtraction.
• Focus on encouraging verbal reasoning to improve articulation of maths understanding.
• Adjust pacing if pupils need more concrete experience before moving on to abstract problems.
• Use formative assessment to group pupils effectively for next division sessions.

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This plan is designed to build solid conceptual foundations for division by 8 while embedding reasoning and problem-solving in line with the National Curriculum for England at Year 3. It incorporates practical activities combined with challenging thinking to inspire all learners.