Solve Pattern Problems

Overview

Lesson 7 of 8 in Growing Patterns, Powerful Rules. Students apply additive and multiplicative pattern knowledge to multi-step problems, using tables, number lines, diagrams and verbal reasoning before selecting an efficient strategy.

Learning intentions

• WALT identify the rule in a growing pattern.
• WALT use a pattern to find missing and later terms.
• WALT solve pattern problems involving addition, multiplication and more than one step.
• WALT explain and check our mathematical reasoning.

Success criteria

• I can organise information in a table, diagram or number line.
• I can describe whether a pattern grows by adding or multiplying.
• I can find an unknown term or rule and show how I know.
• I can check my answer and explain it clearly.

Curriculum links

• Number and algebra: recognise, describe and continue additive and multiplicative patterns.
• Number and algebra: use tables, diagrams, equations and words to represent relationships.
• Mathematical practices: solve problems, choose efficient strategies, communicate reasoning and check solutions.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (45 minutes)

1. 0–5 minutes – Notice and wonder

Open with the pattern hook slide. Display a seating arrangement that grows from one row of 4 seats to two rows of 4, then three rows of 4. Ask: “How many seats would there be in 8 rows? How do you know?” Students think quietly, discuss with a partner, then share different representations. Emphasise that a pattern can be shown with a picture, table, number line or words.

2. 5–12 minutes – Model a problem-solving process

Use the strategy and worked-example slides to model: “A club has 6 seats in the first row. Each new row has 4 more seats than the previous row. How many seats are in row 7?” Think aloud: identify key information, represent the pattern in a table, find the rule, calculate and check. Then model a multiplicative example: “One plant has 3 leaves. The number doubles each week. How many leaves after 4 weeks?” Compare adding 3 with doubling, and clarify that these are different rules.

3. 12–15 minutes – Strategy rehearsal

Display the three representations on the representation choice slide. Pairs choose one mini-pattern and show the next two terms using a table, number line or diagram. Invite two pairs to explain why their representation is useful. Remind students that the representation should make the rule easier to see.

4. 15–30 minutes – Pair problem solving

Distribute the pattern problem-solving worksheet to pairs. Students solve three problems, recording a representation and an explanation for each:

• Seating: 5 seats in the first row, with 3 more seats in every new row. Find the number of seats in row 8.
• Saving: save $7 in week 1 and increase the amount saved by $4 each week. Find the amount saved in week 6 and describe the rule.
• Doubling: a collection starts with 3 counters and doubles each day. Find the number on day 5 and explain the pattern.

Circulate, asking: “What changes each time?” “What stays the same?” “How can you check?” Students may use counters or draw diagrams if needed.

5. 30–38 minutes – Compare and justify

Use the compare-and-critique slides to show two possible solutions to the saving problem, including one error that adds 7 each week instead of adding 4. Groups decide which solution is correct, identify the error and improve the explanation. Select students to share additive and multiplicative strategies. Reinforce that a correct answer needs a clear justification.

6. 38–43 minutes – Independent application

Students complete the final challenge on the pattern problem-solving worksheet independently: “A game starts with 2 points in round 1 and doubles the points each round. How many points are scored in round 6? Show it in two ways.” Students who finish write a related problem involving an additive pattern and solve it.

7. 43–45 minutes – Exit reflection

Return to the plenary slide. Students complete the sentence: “I know a pattern rule is working because…” Invite two quick responses. Collect worksheets or scan the final challenge to identify who is ready for the final lesson and who needs further support.

Resources

• the pattern problem-solving slide deck
• the pattern problem-solving worksheet
• Whiteboards or scrap paper
• Pencils and coloured pens
• Counters or connecting cubes
• Rulers for number lines
• Board space for shared representations

Assessment

• Observe pair talk and representations during guided and independent work. Note whether students identify the constant change, distinguish addition from multiplication and select a suitable strategy.
• Check worksheet solutions for accurate terms, rules, representations and explanations.
• Use the final challenge and exit reflection to group students for Lesson 8: support with concrete models, consolidate additive and multiplicative rules, or extend through creating and critiquing problems.

Differentiation

• Enabling: highlight key information on the worksheet, read problems aloud, use smaller numbers and provide partially completed tables, number lines or visual models. Work with a teacher-led group using counters.
• Consolidating: require students to solve and justify both an additive and a multiplicative problem, using at least one representation and a written explanation.
• Extending: ask students to write a related problem, solve it in two ways and critique a possible error, explaining why the incorrect strategy fails.
• EAL/SEN: pre-teach and display term, rule, increase, double, row, week; pair students strategically, allow drawing and oral explanation, and provide sentence frames such as “The pattern changes by…” and “I checked by…”.