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Lesson plan

Patterns & Relationships: Finding and Generalising Rules

Teacher-facing plan: I do · We do · You do.

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Explicit teaching — I Do (~15 min)

The goal is to move students from describing the step of a pattern ("add 3") to a general rule that links any position directly to its term.

1. Building patterns WA6MNAP1

Make a growing pattern with matchsticks: 1 square uses 4 sticks, 2 squares use 7, 3 squares use 10. Record position against count in a table.

A growing matchstick-square pattern showing terms 1 to 3, a table of position against stick count, and the generalised rule 3n plus 1.
From a built pattern to a position-to-term table to a general rule.

2. Spotting the rule

3. Decreasing patterns

Guided practice — We Do (~20 min)

  1. Grow it together. Build a triangle-tile pattern as a class and fill the position/count table to 5 terms.
  2. Predict term 10. Use the rule to jump ahead without building, then verify by extending the pattern.
  3. Words to rule. Convert several verbal descriptions into a position rule, and rules back into words.
  4. Make a decreasing pattern. Pairs design one decreasing pattern, tabulate it, and write the rule in words.

Independent practice — You Do (~15 min)

Students complete the worksheet:

  • continue three given patterns (two increasing, one decreasing) for three more terms;
  • complete position/term tables;
  • write the rule for each in words;
  • use a rule to find the 10th and 20th terms without drawing.