Check Growing Patterns

Overview

Lesson 3 of 3 in Growing Patterns With Two Variables. Students independently demonstrate that they can identify variables, continue a sequential growing pattern, describe its growth, and give a rule that can be checked.

Learning intentions

• WALT identify and use two variables in a growing pattern.
• WALT continue a sequential pattern accurately.
• WALT describe how a pattern grows and give a rule.
• WALT show our mathematical thinking using words, tables, drawings, or number sentences.

Success criteria

• I can identify the term number and the number of tiles.
• I can continue a pattern accurately.
• I can explain how the pattern grows.
• I can give a rule that matches and can be checked.

Curriculum links

• Algebraic thinking: identify, continue, represent, and describe sequential growing patterns.
• Relationships between two variables: connect term number with the quantity in each term.
• Mathematical practices: represent ideas in different ways, justify thinking, and check whether a rule works.
• Communication and reasoning: use mathematical language, tables, drawings, and number sentences to explain a pattern.

Lesson structure (15 minutes)

1. 0–2 min — Quiet check-in and instructions Open with the quiet check-in and task instructions. Explain that students will work independently and should show their thinking. Remind them to label both variables and that they may use words, a table, a drawing, or a number sentence.

Distribute the growing patterns check-in. Students write their name, read the task, and prepare to work quietly.

2. 2–8 min — Independent check-in task Students complete the following:

“A garden design has Term 1: 4 tiles, Term 2: 7 tiles, and Term 3: 10 tiles. (a) Name the two variables. (b) Continue the sequence to Terms 4 and 5. (c) Give the growth rule in words. (d) Find Term 8. (e) Create a different growing pattern with two variables, show its first four terms, and give its rule.”

Year 5 students may use a table and an add-on rule for part (e). Year 6 students should give a rule that works for any term where possible. Encourage students to check that their rule works for more than one term.

3. 8–11 min — Follow-up and self-check Display the answers using the answers and self-check prompt: the variables are term number and tile number; Terms 4 and 5 are 13 and 16; the rule is add 3 each time; Term 8 is 25.

Students check in a different colour, correct errors, and circle one part they need help with. Move around the room, supporting individuals or a small group. Accept equivalent representations and correct reasoning.

4. 11–14 min — Marking and reflection Mark students’ work using the following 10-mark guide while they complete the reflection on the self-check and reflection section:

• (a) Both variables named: 1 mark
• (b) Terms 4 and 5 correct: 2 marks
• (c) Correct growth rule: 1 mark
• (d) Term 8 correct: 2 marks
• (e) Valid different growing pattern with two variables: 2 marks
• (e) First four terms shown clearly: 1 mark
• (e) Rule matches the pattern: 1 mark

Award partial credit for a correct pattern with an unclear explanation. Students respond to: “My strongest skill was…” and “Next I need to practise…”. They may compare answers with a partner only after self-checking.

5. 14–15 min — Extension or close If time allows, display the final prediction question: “If the pattern starts at 4 and adds 3, which term has 40 tiles? Explain whether it is an exact term.”

Students explain that the rule is (3n+1), so (3n+1=40) gives (n=13). Therefore, Term 13 has 40 tiles. Students may also use the sequence to justify their answer. Select one clear response to share at the start of the next lesson.

Resources

• the growing patterns check-in deck
• the growing patterns check-in
• Coloured pens or pencils for self-checking
• Whiteboard or display screen
• Optional counters for students who need concrete support
• Class marking record or learning-progress notes

Assessment

• Use the 10-mark guide to assess students’ understanding of variables, continuation, growth rules, distant terms, and creating a pattern.
• Review students’ corrections and reflections to distinguish calculation errors from misunderstandings about variables or rules.
• Use results to group students for further support with tables and add-on rules, or extension with general rules and distant-term predictions.

Differentiation

• Year 5 students may use counters, a completed term-number/tile-number table frame, and the sentence stem “The pattern grows by…”.
• Year 6 students should justify a general rule where possible and explain how it predicts a distant term.
• Support EAL and students requiring additional assistance with labelled examples, oral rehearsal, clear vocabulary such as term, variable, and rule, and extra processing time where possible.
• For students ready for challenge, ask them to create a pattern with a different starting number and growth amount, then prove that their rule works for Terms 1, 2, 4, and 8.