Scaling and Bar Models

National Curriculum Links

• Year 3 Maths - Number: Multiplication and Division
  • Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables (3.1)
  • Solve problems, including missing number problems, involving multiplication and division, including integer scaling problems (3.2)

Learning Objectives (WALT)

• WALT: Solve integer scaling problems using concrete resources and bar modelling.
• WALT: Understand and represent multiplication as repeated addition or scaling.
• WALT: Use bar models to visualise and solve word problems involving multiplication and division.

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Success Criteria

• I can arrange counters/cubes to represent multiplication problems.
• I can draw a bar model to match the concrete resource model.
• I can explain how to solve scaling problems.
• I can find unknown values by reasoning about equal parts in bar models.

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Resources Needed

• Counters or cubes (at least 30 per pupil)
• Whiteboards and pens
• Large paper for class bar model drawing
• Dyslexia-friendly printed problem cards (clear font, coloured paper options)
• Visual aids/posters of bar models and scaling

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Lesson Breakdown (45 Minutes)

1. Introduction and Recap (5 minutes)

• Briefly review multiplication as ‘groups of’ and repeated addition to fill gaps in prior knowledge.
• Use a simple familiar example: “If I have 3 packs of pencils and each pack has 4 pencils, how many pencils?” Use counters to demonstrate.

2. Concrete Resources Modelling (15 minutes)

• Present the first problem: Holly is making pizzas with 5 slices of tomato on each pizza. She is making 4 pizzas. How many slices of tomato will she need?
• Give each pupil 20 counters or cubes.
• Ask pupils to build 4 groups of 5 cubes. Walk around supporting and asking guiding questions:
  • "How many slices in one pizza?"
  • "How many pizzas are there?"
  • "What does putting groups together tell us?"
• Emphasise counting all the cubes to get the total.
• Quick plenary: “How many slices did you count in total?”

3. Bar Model Introduction (10 minutes)

• Draw a bar on the board or large paper segmented into 4 equal parts. Label each part “5 slices.”
• Align the bar model directly with what the pupils created with cubes: each segment represents one pizza.
• Model how the total length of the bar represents the total number of slices (5 + 5 + 5 + 5 = 20).
• Encourage a pupil to explain what the bar model shows.

4. Challenge Problem: Scaling Backwards (10 minutes)

• Present the next problem: A spring is stretched to three times the length that it was before. The stretched spring is 18cm. What was the length before it was stretched?
• Ask pupils to model 18 cubes in a long line.
• Guide them to split this line into 3 equal parts (each part representing the original length).
• Label each group.
• Relate this to the bar model by drawing a bar separated into three equal parts, total length 18cm.
• Use questioning to uncover the answer: “What is each part worth?”
• Reinforce the understanding of division as sharing into equal parts (link back to the multiplication).

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Differentiation Strategies

• For low prior attainment / Year 3 learners:
  • Use counters with larger print labels.
  • Provide extra time with concrete materials before drawing bars.
  • One-to-one or small group support to reinforce basic multiplication facts for 2s, 5s.
• For students with dyslexia:
  • Provide problem statements in a dyslexia-friendly font (e.g., Arial, Comic Sans), on yellow or blue paper to reduce visual stress.
  • Use colour-coded bar segments (e.g., red for one group, green for another) to aid visual memory.
• For more able learners:
  • Extend by asking: “If Holly made 7 pizzas, how many slices would she need?”
  • Pose a problem involving missing values in scaling (e.g., “If the spring was stretched to 21cm and that’s 3 times its original length, what was the original length?”).
  • Encourage them to create their own integer scaling problems and solve them.

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Assessment and Review (5 minutes)

• Give a quick oral quiz: “If I have 6 boxes with 8 apples each, how many apples in total?” Use counters or quick drawing.
• Ask individual pupils to draw a bar model to represent the multiplication fact.
• Summarise learning: “Today we learnt how to use counters and bar models to solve problems about lots of groups and scaling.”

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Homework/Extension (Optional)

• Create your own bar model problem at home with your family, using objects like fruit or toys in groups. Draw your bar model and write an explanation of the answer.
• Try some simple online games/activities on multiplication scaling suitable for Year 3 (teacher to select an appropriate site matching curriculum).

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Reflection Notes for Teacher

• Monitor pupils who struggle with equal grouping and emphasise the concept of equal parts in scaling.
• Use peer discussion to reinforce reasoning and vocabulary such as “times as many,” “groups of,” and “equal parts.”
• Celebrate correct use of bar models and encourage verbal reasoning alongside visual representation.

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This plan ensures alignment with the English National Curriculum for Year 3, supports diverse learners, and provides engaging, hands-on experiences to build foundational mathematical reasoning around integer scaling through concrete and visual models.