Continuing Number Sequences

Overview

This is lesson 2 of 7 in the unit "Mastering Sequences in Maths," designed for Year 7 students following the National Curriculum for England and White Rose Maths v3 scheme. The lesson focuses on continuing number sequences accurately, building on prior knowledge of sequence rules and notation. It integrates visual aids and peer collaboration to ensure accessibility while challenging advanced learners with more complex patterns.

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National Curriculum References

• Key Stage 3 Mathematics Programme of Study:
• Use and describe number sequences, including those involving negatives, decimals, and squares.
• Recognise and use terms of sequences; generate terms from position-to-term rules.
• Express the nth term of arithmetic sequences.
• White Rose Maths Alignment (Year 7, Block 1 - Sequences):
• Continue linear sequences using term-to-term rules.
• Identify and understand arithmetic sequences.

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Learning Objectives (WALT)

• We Are Learning To continue number sequences accurately by finding the missing terms using term-to-term rules.

Success Criteria

• Correctly identify the term-to-term rule for at least four different sequences.
• Accurately continue each sequence by writing additional terms.
• Explain the pattern or rule of a given sequence to a peer, using appropriate mathematical language and notation.

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Resources

• Sequence cards and worksheets with different sequence types (linear, quadratic, simple arithmetic)
• Pictorial aids (number lines, visual pattern blocks)
• Whiteboards and markers for 'show-me' activities
• Extension challenge sheets
• Paired seating arrangements for peer support

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Lesson Structure (60 minutes)

1. Starter (10 minutes)

• Activity: Quick Recap Game
• Display three short number sequences on the board (e.g., 2, 4, 6, __, __; 5, 10, 15, __, __; 1, 4, 7, __, __).
• Students individually write the next two terms on mini whiteboards.
• Teacher selects students randomly to explain the rule they used.
• Purpose: Activate prior knowledge and mentally prepare students to engage with sequence patterns.

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2. Main Teaching (20 minutes)

• Teacher Explanation:
• Introduce different types of number sequences focusing on term-to-term rules, including:
• Addition/subtraction patterns (e.g., add 3 each term)
• Multiplicative patterns (e.g., double each term)
• Mixed patterns or minor variations
• Write examples on the board and model how to find missing terms.
• Visual Support:
• Use number lines and coloured counters to represent sequences pictorially, showing how terms change step-by-step for struggling learners.
• Paired Work:
• Distribute a worksheet with four different sequences of increasing difficulty.
• Students work in pairs, discuss the rule and continue the sequences together. Teacher circulates offering scaffolded prompts for those who need extra help.
• Key Questions for Engagement:
• "What is happening between each term?"
• "How can you check your answer?"
• "Can you write the next two terms in your own words?"

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3. Differentiation Strategies

• For struggling learners:
• Use pictorial aids (number lines or blocks) to visualise the step increase/decrease.
• Provide sentence starters like "The rule adds..." or "Each time we multiply by..."
• Structured peer support within pairs.
• For advanced learners:
• Introduce quadratic sequences or geometric ones (e.g., 2, 6, 12, 20...)
• Challenge them to find the nth term for these more complex sequences on an extension sheet.
• Encourage explaining patterns algebraically or in written form to deepen understanding.

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4. Plenary (10 minutes)

• Class Discussion:
• Invite pairs to share one sequence they found particularly easy or challenging and explain the rule aloud.
• Address common misconceptions highlighted during paired work.
• Quiz with Whiteboards:
• Present three new sequences as a rapid-fire activity for students to write the next two terms.
• Use this as informal formative assessment.

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5. Assessment and Feedback

• Teacher observation during paired work to assess understanding and identify difficulties.
• Collect worksheets at the end to review sequence continuation accuracy.
• Provide verbal feedback during class discussions, highlighting correct use of terminology (e.g., term-to-term, nth term, addition, subtraction).
• Use plenary responses to judge readiness for next lesson’s introduction of algebraic expressions for sequences.

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Follow-up / Next Steps

• Next lesson will focus on understanding and generating the nth term for linear sequences.
• Prepare personalised tasks for learners based on assessment outcomes (e.g., more pictorial sequencing for those needing support, or more abstract nth term problems for higher achievers).

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This lesson plan ensures alignment with the National Curriculum for England and White Rose Maths scheme with clear progression, accessibility, and engagement strategies tailored for Year 7 learners.