Create and Communicate Patterns

Overview

Lesson 6 of 8 in Growing Patterns, Powerful Rules. Students design growing numerical and non-numerical patterns, represent them with materials, pictures and words, then exchange patterns with a partner to identify and continue the rule.

Learning intentions

• WALT identify how a pattern grows or changes.
• WALT create a pattern using a constant whole-number rule.
• WALT represent a pattern concretely, pictorially and linguistically.
• WALT communicate a rule clearly so someone else can solve the pattern.

Success criteria

• I can create a valid growing pattern.
• I can explain whether my rule adds, subtracts or multiplies by a constant whole number.
• I can show my pattern with objects, a drawing and words or number sentences.
• I can use a partner’s rule to find missing and future terms.

Curriculum links

• Recognise, describe and continue repeating and growing patterns using mathematical language.
• Represent mathematical ideas in concrete, pictorial and symbolic forms.
• Use addition, subtraction and multiplication to describe how quantities change.
• Communicate mathematical thinking, justify a rule and respond to another person’s strategy.

Lesson structure (45 minutes)

1. 0–5 minutes – Notice and wonder hook Open with the opening pattern challenge. Display a growing garden-bed pattern and ask: “What is changing? What might the next row look like? How could we explain the rule without showing the picture?” Accept different observations, but distinguish a pattern that grows regularly from one that changes unpredictably.

2. 5–12 minutes – Model clear communication Use counters or drawn squares to model a garden bed with 3 plants in the first row, then 6 and 9. Think aloud: “The rule is add 3 plants each row.” Record the first terms, a quick sketch and the sentence rule on the concrete-to-pictorial model. Briefly show that “add 3 each time” is different from “multiply by 3 each time”. Emphasise that the core task uses a constant whole number.

3. 12–16 minutes – Check understanding Students respond in pairs to two examples on the rule-check questions: 4, 8, 12, 16 and 20, 17, 14, 11. They identify the rule and predict the next term. Invite explanations using “I know because…”. Clarify that a growing pattern may increase or decrease, but the change must stay constant for this task.

4. 16–30 minutes – Design a pattern Put students in 15 mixed-ability pairs. Distribute the pattern designer worksheet. Each pair designs either a numerical pattern or a non-numerical pattern, including a garden-bed layout that adds a fixed number of plants in each row. They must show at least four terms, a concrete or drawn representation, and a written rule involving adding, subtracting or multiplying by a constant whole number. Circulate and ask: “How do you know it is growing regularly?” and “Could another person use your rule without asking you questions?”

5. 30–38 minutes – Partner solve and improve Pairs exchange their pattern with a nearby pair, keeping the rule hidden initially. The receiving pair continues the pattern, identifies the rule and finds one missing term. They then read the designer’s explanation and check their thinking. Return patterns to the designers, who revise any unclear drawing, language or number sentence.

6. 38–43 minutes – Share and compare Select two or three examples, including a numerical and a non-numerical pattern. Use the sharing and comparison prompts to discuss: “What stayed constant?” “Which representation helped most?” and “Could the same rule be shown in another way?” Reinforce precise language such as term, constant, add, subtract, multiply and rule.

7. 43–45 minutes – Exit reflection Students complete the final section of the pattern designer worksheet: draw or write a short pattern, state its rule and explain how they checked it. Collect worksheets for assessment and preview that the next lesson will investigate unknown terms and general rules.

Resources

• the growing patterns teaching deck
• the pattern designer worksheet
• Linking cubes, counters or square tiles
• Mini-whiteboards and pens
• Pencils, rulers and coloured pencils
• A3 paper or chart paper for pair designs
• Optional rule cards showing “add 2”, “add 5”, “subtract 3”, “multiply by 2” and “multiply by 3”

Assessment

• Observe pair talk and questioning during modelling and design: listen for a constant change and accurate use of mathematical vocabulary.
• Check each worksheet for four valid terms, a clear concrete or pictorial representation, and a correct written rule.
• Use the partner’s solution and exit reflection to assess whether students can communicate and apply a rule independently.

Differentiation

• Support: provide selected rule cards, counters and a partially completed four-term template. Begin with adding 2, adding 5 or subtracting 1, and rehearse the sentence frame: “The rule is ___ because ___ changes each time.”
• Support for EAL and students needing accessibility: use gestures, colour-code each term, display vocabulary with simple examples, allow oral recording or scribing, and pair students strategically.
• Consolidation: require a valid pattern with four terms, one missing term and an explanation proving the rule works.
• Extension: create a pattern with a hidden term, show the same rule in two different representations, or investigate a challenge pattern that changes by a decimal constant, explaining why this is beyond the core whole-number rule.