Representing Rules Clearly

Overview

Lesson 5 of 8 in Growing Patterns, Powerful Rules. Students move from concrete and pictorial patterns to recording term position, value and constant change in tables, arrow diagrams and complete sentences.

Learning intentions

• WALT identify the term position, term value and constant change in a growing pattern.
• WALT record a pattern using a table, arrows and a complete sentence.
• WALT explain how a rule describes what happens each time.
• WALT apply a pattern rule to a familiar word problem.

Success criteria

• I can complete a table showing term position and value.
• I can show the constant change with arrows.
• I can describe the rule in a complete sentence.
• I can use a rule to solve a problem and explain my thinking.

Curriculum links

• Number: recognise, describe and continue additive patterns.
• Algebraic thinking: connect term position, term value and a rule.
• Mathematical representations: use tables, diagrams, symbols and words to communicate ideas.
• Mathematical and statistical investigations: notice relationships, explain reasoning and check whether a rule works.

Lesson structure (45 minutes)

1. 0–5 minutes – Notice the pattern

Open with the hook and pattern image. Display a visual pattern growing by the same amount each time, such as groups of counters. Ask: “What changes? What stays the same? How could we tell someone else exactly what is happening?” Students think-pair-share, then several pairs explain their observations.

2. 5–12 minutes – Build the language

Use the teaching slides on term position, value and change to model a simple pattern, such as 5, 8, 11, 14. Create a table with headings Term position, Term value and Change. Model arrows between values and say: “The value increases by 3 each time.” Clarify that the term position tells us which term we are describing, while the value tells us how many.

3. 12–18 minutes – Connect three representations

Continue with the table, arrow and sentence examples. Model how the same rule can be shown in three ways:

• Table: 1 → 3, 2 → 4.5, 3 → 6, 4 → 7.5
• Arrows: +1.5 between each value
• Sentence: “The pattern starts at 3 and increases by 1.5 each term.”

Ask students to identify the term position, value and constant change. Emphasise that a constant change is the same amount added each time.

4. 18–30 minutes – Guided and independent practice

Distribute the pattern rules recording worksheet. Complete the first example together. Students then complete tables, draw arrows and write rules in sentences. Include whole-number examples for students needing support and the Year 5 decimal pattern 3, 4.5, 6, 7.5 for consolidation and challenge. Circulate, asking: “How do you know the change is constant?” and “Where can you see the term position?”

5. 30–37 minutes – Apply the rule

Show the skipping challenge on the word problem and discussion prompt: “A skipping challenge increases by 1.5 skips each round. In round 1, the target is 3 skips. What are the targets for rounds 2, 3 and 4? How could you show the rule in a table, with arrows and in a sentence?” Students work in pairs, then compare representations. Discuss why the rule remains constant even though the values include decimals.

6. 37–42 minutes – Explain and check

Students use the explain-your-rule questions to choose one completed pattern and explain it to a partner. Partners check that the table, arrows and sentence all show the same change. Invite two students to present different examples, including one using decimals.

7. 42–45 minutes – Plenary

Return to the final reflection slide. Students respond orally or on mini whiteboards:

• What does the term position tell us?
• What does constant change mean?
• How can we show a rule clearly?

Collect a quick response: “The rule for my pattern is… because…”

Resources

• the complete pattern rules slide deck
• the pattern rules recording worksheet
• Counters, cubes or connecting blocks
• Mini whiteboards and pens
• Board or chart paper
• Pencils and rulers
• Prepared examples with whole-number and decimal changes

Assessment

• Listen during pair talk for accurate use of term position, term value and constant change.
• Check worksheet tables, arrows and sentences for consistency.
• Use the skipping challenge and plenary response to assess whether students can apply and explain a rule, not just continue a pattern.

Differentiation

• Support: provide tables with the first two terms filled in, use counters or cubes, and begin with whole-number changes such as +2 or +5.
• Support: offer sentence frames: “The pattern starts at __ and increases by __ each time”; allow students to explain orally before writing.
• Extension: ask students to create a decimal pattern, predict a later term and explain why the additive rule remains constant.
• EAL/SEN: use colour coding for position, value and change; display the vocabulary with symbols and rehearse explanations with a partner before independent work.