Find and Give the Rule

Overview

Lesson 2 of 3 in Growing Patterns With Two Variables. Students identify the term number and quantity as two variables, describe constant growth, record a rule, and use it to predict a later term.

Learning intentions

• WALT find and give a rule for a sequential growing pattern with two variables.
• WALT use a table and words to show how a pattern grows.
• WALT use a number sentence to find a later term.
• WALT explain why a rule works.

Success criteria

• I can name both variables.
• I can find the amount added each time and continue the pattern.
• I can give the rule in words or a suitable number sentence.
• I can use the rule to predict a later term and explain my thinking.

Curriculum links

• Algebraic thinking: identify, continue, describe, and represent sequential growing patterns.
• Relationships between variables: connect term number with the quantity in each term.
• Mathematical communication: use tables, words, diagrams, and number sentences to explain a relationship.
• Mathematics practices and competencies: reason, notice structure, use representations, and justify a prediction.

Lesson structure (15 minutes)

1. 0–3 minutes – Revisit yesterday’s pattern

Open with the pattern hook and learning intention slides. Display the pattern:

Term number	1	2	3	4
Number of squares	5	8	11	14

Ask: “What are the two variables?” and “What changes each time? What stays the same?” Students briefly discuss with a partner, then state: “Start at 5 and add 3 for each new term.” Establish that the variables are term number and number of squares.

2. 3–7 minutes – Model two forms of the rule

Use the table and rule modelling slides to record the relationship in a table and in words: “Start at 5 and add 3 each time.” Explain that this describes how the sequence grows. Then model the general rule:

number of squares = 3 × term number + 2

Check it with Term 1: (3 × 1 + 2 = 5), and Term 3: (3 × 3 + 2 = 11). Ask students to test one calculation with a partner and explain why the rule works. Emphasise that a general rule can find any term, not only the next one.

3. 7–11 minutes – Guided partner pattern

Display the second pattern using the guided pattern task slides:

Term number	1	2	3	4	5	6
Number of dots	2	6	10	14

Students complete or copy the table, draw or describe Terms 5 and 6, and discuss the growth rule with a partner. Prompt: “How many dots are added each time?” and “How can you find Term 6 without drawing every term?”

Confirm: “Add 4 each time.” For students ready for Year 6, model or invite the general rule: dots = 4 × term number − 2. Check it using Term 1 and Term 3.

4. 11–14 minutes – Independent follow-up

Distribute the growing patterns rule worksheet. Students work independently on:

“A pattern has 7 matchsticks in Term 1 and grows by 5 matchsticks each term. Complete Terms 2, 3, and 4; give the rule in words; and find Term 7.”

Expected sequence: 7, 12, 17, 22. The rule in words is “Start at 7 and add 5 each time.” Term 7 is 37. Year 6 students should also record matchsticks = 5 × term number + 2 and check it by substitution.

5. 14–15 minutes – Check and collect

Use the final check slide to ask: “Would your rule still work for Term 10? How do you know?” Students give a quick spoken justification or write one sentence on their worksheet. Collect responses and note who can move from repeated addition to a general rule.

Resources

• the complete 6-slide teaching deck with the hook, learning intention, worked examples, guided task, prompts, and final check.
• the growing patterns rule worksheet with tables, the matchstick task, and a Year 6 challenge.
• Whiteboard and markers.
• Pencils and erasers.
• Optional counters, squares, dots, or matchsticks for students who benefit from concrete representation.

Assessment

• Listen to partner explanations for accurate identification of both variables and the constant growth.
• Check tables, continued terms, spoken rules, and whether predictions agree with the rule.
• On the worksheet, identify students who can use substitution to test a general rule and those who need further support with starting value and growth.

Differentiation

• Year 5 support: provide a partially completed table, concrete materials, and the sentence stem “Start at ___ and add ___ each time.” Ask students to predict a near term such as Term 5.
• Year 6 extension: require a rule that works for any term, such as matchsticks = 5 × term number + 2, and ask students to justify it using substitution, including Term 10.
• Provide large-print tables, highlighted columns, and read-aloud instructions for students with visual, literacy, or processing needs. Allow drawing, oral explanation, or practical materials before recording.
• EAL learners: explicitly teach and display term, variable, quantity, growth, rule, predict, with sentence frames: “The variables are ___ and ___.” and “The pattern grows by ___.”