Multiplicative Growth Rules

Overview

Lesson 4 of 8 in Growing Patterns, Powerful Rules. Students use equal groups and drawings to recognise patterns that grow by multiplying by a constant whole number, then describe and justify the rule using mathematical language.

Learning intentions

• WALT build and represent multiplicative patterns.
• WALT describe a pattern using “multiply by”.
• WALT distinguish multiplying from adding the same amount.
• WALT apply a doubling rule to a real-life problem.

Success criteria

• I can build and draw equal groups to show a pattern.
• I can identify whether a pattern is growing by addition or multiplication.
• I can describe a rule such as “multiply by 2” or “multiply by 3”.
• I can explain how I know my rule fits every term.

Curriculum links

• Number: use multiplication and equal groups to represent and solve problems.
• Algebra: recognise, continue and describe patterns using a rule.
• Mathematical practices: reason about relationships, represent ideas in different ways, and communicate mathematical thinking.
• Progression focus: move from repeated addition and skip-counting towards multiplicative thinking with whole numbers.

Lesson structure (45 minutes)

1. 0–5 min – Notice and wonder

Display a visual sequence of groups containing 3, 6, 12 and 24 objects using the opening pattern slides. Ask: “What is changing? What might the next group look like?” Accept all observations, but record both “add 3” and “multiply by 2” for later discussion.

2. 5–12 min – Build the meaning

In pairs, give students counters or linking cubes. Ask them to build 3, then make the next group by doubling it, and continue to 24 or 48. Model that doubling means making two equal groups of the previous amount: 3 × 2 = 6, 6 × 2 = 12. Emphasise that multiplying by 2 is not simply adding 2; the amount added changes each time.

3. 12–20 min – Compare two rules

Use the rule comparison slides to show:

• 3, 6, 9, 12
• 3, 6, 12, 24 Ask pairs to represent each pattern with counters or quick drawings. Discuss: “What stays the same?” “What changes?” Establish that the first pattern adds 3 each time, while the second multiplies by 2 each time. Invite students to explain how they can check a rule.

4. 20–32 min – Differentiated pair investigation

Distribute the multiplicative patterns worksheet. Students complete the section matched to their readiness:

• Enabling: build and draw ×2 patterns with concrete groups, such as 2, 4, 8, 16.
• Consolidating: continue and describe ×2 or ×3 patterns, such as 4, 8, 16, 32 or 3, 9, 27, 81.
• Extending: compare additive and multiplicative patterns and decide which rule fits different scenarios. Circulate, asking: “What is the number of groups?” “What is being multiplied?” “How could you prove your rule?”

5. 32–40 min – Bacteria problem

Present the problem from the bacteria investigation slides: “A bacteria population starts at 3. It doubles each hour. How many bacteria are there after 1, 2, 3 and 4 hours?” Students solve using cubes, a table, a drawing or equations. Share strategies and clarify that “doubles each hour” means multiply the previous population by 2, not add 2.

6. 40–45 min – Explain and reflect

Revisit the plenary slides. Students complete the final explanation on the worksheet: “A multiplicative pattern is different from a repeated-addition pattern because…” Invite two or three students to share. Check that students use “multiply by 2” or “multiply by 3” accurately and can identify the starting number.

Resources

• Counters, linking cubes or other equal-group materials; one set per pair.
• Whiteboard and markers.
• the complete lesson slide deck
• the multiplicative patterns worksheet
• Pencils and coloured pencils.
• Prepared bacteria problem displayed on the board or slides.

Assessment

• Observe pair work: Can students build equal groups and recognise whether the pattern is additive or multiplicative?
• Question students during the investigation: Can they state the multiplier and justify it with a model, table or equation?
• Review worksheet responses and the final explanation, noting who needs further support with equal groups, doubling or mathematical vocabulary.

Differentiation

• Support: begin with ×2 patterns using counters, keep the starting number small, and provide a table with the first term completed. Pair students strategically and rehearse the sentence frame: “The rule is multiply by ___ because ___.”
• EAL/SEN: use gestures and visual models for “same number of groups”, “double”, “add” and “multiply”; allow students to explain orally, draw or point before writing.
• Consolidation: offer ×2 and ×3 patterns with missing middle terms and ask students to check answers using multiplication.
• Extension: ask students to create two patterns with the same starting number—one additive and one multiplicative—then write a real-life situation that matches each rule.