Mathematics K–6 · Years 5–6
Matchstick patterns: finding the rule
Number and algebra
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The idea
A growing pattern built from matchsticks has a rule that links the position of a term to the number of sticks, and the rule predicts terms that are too big to build.
What you need
- 60 matchsticks (used, or craft sticks) per pair
- a recording table with columns term number, sticks, sticks added
- grid paper for a graph
How to do it
- Build a row of squares: one square, then two joined squares, then three. Count the sticks each time and record.
- Record how many sticks each new square adds. Predict the sticks for 5 squares and build to check.
- Write a rule in words for n squares, then check it for 10 squares without building.
- Repeat with a row of triangles joined along sides, and with a row of hexagons.
- Plot sticks against term number for each pattern and compare the lines.
What you should see
Squares in a row use 4, 7, 10 sticks, adding 3 each time, so 5 squares use 16 and n squares use 3n plus 1 (10 squares use 31). Triangles use 3, 5, 7, adding 2, so n triangles use 2n plus 1. Hexagons use 6, 11, 16, adding 5, so n hexagons use 5n plus 1. The graphs are straight lines whose steepness is the number of sticks added per term, and all three cross the vertical axis at 1.
What changes
- What you change
- the term number n
- What you measure
- the number of sticks
- What you keep the same
- the same shape joined the same way
- shapes sharing exactly one side with the previous shape
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Ten squares use ten times the sticks of one square.
- The rule is the number you add each time.
Safety card
Hazards
- matchstick splinters
Controls
- use spent matches or craft sticks
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.