Exploring Term-to-Term Rules

Lesson Overview

Unit: Mastering Sequences in Maths (Lesson 3 of 7) Duration: 60 minutes Class Size: 30 students Year Group: 7 Curriculum: National Curriculum for England (Mathematics) Reference Framework: White Rose Maths Year 7 v3

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National Curriculum Links

• Pupils should be taught to:
• Generate terms of a sequence from a term-to-term rule (National Curriculum Year 7 - Number - Number and Algebra)
• Express missing number problems algebraically
• Use simple formulae and generate sequences from them

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Learning Objectives (WALT)

We Are Learning To:

• Identify and explain term-to-term rules in different sequences.

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Success Criteria

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

• Explain the term-to-term rule for at least 3 different sequences using correct mathematical language.
• Demonstrate understanding by continuing sequences using term-to-term rules.
• Collaborate effectively in groups to discuss and articulate sequence patterns.

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Resources

• Whiteboards and markers (mini whiteboards for individual practice)
• Printed sequence cards (with sequences of varying complexity)
• Sentence starter handouts (to scaffold mathematical explanations)
• Interactive board or projector
• Worksheets for independent and group activities
• Challenge task sheets for advanced learners

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Lesson Structure

1. Starter Activity (10 minutes)

Objective: Engage students and recall prior knowledge on simple sequence identification.

• Begin with a whole-class interactive quiz using an interactive board or mini whiteboards.
• Display 2 simple sequences (e.g., 2, 4, 6, 8… and 5, 10, 20, 40…) and ask students to spot the pattern and the rule.
• Ask quick-fire questions: “What happens to the numbers each time?”
• Use this to lead into the idea of term-to-term rules: the operation needed to get from one term to the next.

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2. Introduction and Explanation (10 minutes)

Objective: Introduce term-to-term rules clearly using modelled examples aligned to the National Curriculum.

• Introduce the vocabulary: term, term-to-term rule, sequence
• Model how to identify the term-to-term rule using a variety of sequences, e.g.:
• Addition/subtraction (e.g., +3, –2)
• Multiplication/division (e.g., ×2, ÷3)
• Emphasise the difference between term-to-term rules and nth term rules, focusing solely on term-to-term here as per the unit sequence.
• Use visual aids and highlight how the rule “moves” along the sequence, reinforcing the procedural understanding recommended by White Rose resources.

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3. Guided Practice (15 minutes)

Objective: Students identify and explain rules for different sequences, using sentence starters for language support.

• Distribute sequence cards to mixed-ability groups of 4-5 students.
• Each group works collaboratively to:
• Continue their sequences by at least five terms.
• Write or orally explain the term-to-term rule using sentence starters such as:
• “To get from one term to the next, you... ”
• “The rule is to add/subtract/multiply/divide...”
• Circulate to provide support, prompting students who need help with sentence starters or simpler explanations.

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4. Independent Activity (15 minutes)

Objective: Develop individual skills in explaining and applying term-to-term rules.

• Hand out differentiated worksheets:

• Main tasks: Identify and explain the term-to-term rule for given sequences; continue sequences for 5 more terms.

• Support tasks: Use sentence starters to frame explanations; sequences with simpler operations (e.g., only addition or subtraction).

• Challenge tasks (Extension): Create own sequence with a unique term-to-term rule and explain it clearly.

• Encourage students to write clear explanations and check examples with peers.

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5. Plenary and Assessment (10 minutes)

Objective: Consolidate learning through sharing and formative assessment.

• Ask volunteers or groups to present their favourite sequence and explain their term-to-term rule to the class.
• Provide targeted questioning to assess understanding:
• “How do you know that is the rule?”
• “What would the next two terms be if we follow your rule?”
• Use mini whiteboards or quick exit tickets where students write a short explanation of a term-to-term rule from a new sequence shown by the teacher.

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Differentiation

• For learners needing more support:

• Provide sentence starters and structured writing frames.

• Use sequences with simpler operations (only + or –).

• Use paired or group work to scaffold language and concept understanding.

• For learners working at Expected Standard:

• Use varied sequences including multiplication and division term-to-term rules.

• Encourage explanations using appropriate mathematical vocabulary.

• For advanced learners:

• Challenge to create their own sequences with complex or mixed operations (e.g., alternate adding and multiplying).

• Explore sequences where the rule changes every few terms, explaining reasoning.

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Assessment Opportunities

• Observations during group discussions to assess verbal use of mathematical language and reasoning.
• Collection and marking of independent worksheets.
• Exit tickets assessing the ability to explain term-to-term rules in writing.
• Extension task submissions demonstrating creativity and deeper understanding.

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Reflection and Next Steps

• Identify students who struggled with articulating rules clearly and plan targeted interventions.
• Use insights from plenary and exit tickets to tailor the next lesson on connecting term-to-term rules and nth term expressions.
• Consider introducing simple algebraic notation for term-to-term rules in upcoming lessons, following progression plans.

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This highly interactive and scaffolded lesson plan blends White Rose Maths methodology with National Curriculum requirements, encourages mathematical language development, and nurtures collaborative as well as independent learning, ensuring comprehensive mastery of term-to-term rules for Year 7 students.