Linear Sequences Mastery

Overview

This 48-minute lesson is designed for a small class of 5 Year 8 students, focusing specifically on recognising and continuing linear numerical sequences up to 100. It aligns precisely with the National Curriculum for England’s Programme of Study for Mathematics at Key Stage 3, where students are expected to "describe and continue sequences formed by linear rules" (DfE, 2013).

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National Curriculum Links

• Number - Algebra
  Pupils should be taught to:

  • Recognise and use sequences of numbers, including those generated by linear rules (NC Programme of Study for KS3 Mathematics, 3.2/3.4).

• Assessment Focus

  • Demonstrate fluency in extending linear sequences to 100
  • Apply reasoning to predict sequence terms
  • Use vocabulary: nth term, difference, term

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Learning Objectives

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

• Identify linear (arithmetic) sequences with positive and negative integer differences up to 100
• Continue linear sequences given the first few terms
• Use the term-to-term rule to explain sequences clearly
• Predict specific terms within a linear sequence confidently

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Success Criteria

Students can:

• Recognise sequences increasing and decreasing by a constant difference (integer steps)
• Continue sequences correctly to specified terms without error
• Express the term-to-term rule in words and simple algebraic form
• Explain reasoning behind their predictions verbally or in writing

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Resources

• Whiteboard and markers
• Printed sequence cards (with sequences up to 100)
• Mini whiteboards and pens (for each student)
• Number line (0 to 100) on display for visual aid
• Pre-prepared “mystery sequences” envelopes for group activity

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Lesson Outline

1. Introduction & Engagement (8 minutes)

• Starter questions: Show simple sequences such as 2, 4, 6, 8… and 100, 95, 90, 85… on the board.
• Ask: What do you notice about these sequences?
• Elicit responses about constant differences and identify these as linear sequences.
• Refer to the National Curriculum vocabulary: term-to-term rule, difference, sequence.

WOW factor: Use a rapid-fire “sequence detective” warm-up: students guess the next term of fast-projected sequences on screen to build excitement.

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2. Direct Teaching (10 minutes)

• Define a linear sequence: difference between terms is constant.
• Show examples on the board (e.g., +3, -2 steps).
• Introduce term-to-term rules in simple language, modelling aloud, e.g.
  “The difference is +4, so add 4 each time.”
• Demonstrate continuing sequences up to the 10th term, ensuring the largest term does not exceed 100.

WOW factor: Incorporate algebra briefly by writing nth term expressions for simple sequences (like 3n + 2) but keep it accessible.

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3. Guided Practice (10 minutes)

• Distribute mini whiteboards.
• Students work together on creating sequences with a constant difference, e.g., start at 5, add 7 each time.
• Challenge: Students identify errors in deliberately incorrect sequences created by the teacher.
• Use number line to help visualise jumps between terms.

WOW factor: Use “human number line” activity—place five sticky notes with sequence numbers around the room and have students physically arrange them in the correct order.

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4. Independent Activity — “Mystery Sequence” (15 minutes)

• Each student receives an envelope with partial sequences (including missing terms and term-to-term rules).

• Tasks:

  • Identify the difference
  • Continue the sequence
  • Write the next three terms
  • Predict the 10th term

• Teacher circulates, providing tailored support.

WOW factor: Include a “hidden code” challenge — when sequences are completed correctly, the first letters of each sequence answer reveal a maths-related word (e.g., “ANGLE”).

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5. Assessment and Recap (5 minutes)

• Quick verbal quiz: Teacher calls out sequence terms; students shout or write the next term.
• Discuss one or two example responses, emphasising use of vocabulary and clear reasoning linking to term-to-term rules.
• Summarise key points linking back to the National Curriculum.
• Set homework: create your own linear sequence and write the first 10 terms.

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Differentiation

• Support: Provide sequence cards with visual aids (number lines, repeated addition) for students needing extra help.
• Challenge: Introduce sequences with negative differences or non-integer steps for higher ability students and encourage general expressions for nth term.

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Assessment Opportunities

• Ongoing observation during discussions and activities.
• Review of mini whiteboard work and completed mystery sequences.
• Quick verbal quiz at lesson end to gauge understanding.
• Homework to extend and consolidate learning.

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Reflection & Follow-up

Teachers should review student work for misconceptions about difference and order. Follow-up lessons will extend to non-linear sequences and introduction to quadratic sequences (Year 9).

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Note to teachers: This compact, interactive approach balances concrete and abstract understanding, making linear sequences both accessible and engaging while precisely embedding National Curriculum expectations.