Mathematics K–6 · Years 3–4
Times tables on a circle: an algorithm that draws patterns
Number and algebra
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The idea
Following a fixed sequence of steps (multiply, keep the last digit, join that point on a ten-point circle) turns each times table into a shape, and the shape depends on the factors the multiplier shares with 10.
What you need
- 10 copies per learner of a circle with 10 equally spaced points labelled 0 to 9
- coloured pencils and a ruler
- a multiplication chart to 10 × 10
How to do it
- Write the algorithm as steps: start at 0; multiply the chosen number by 1, 2, 3 and so on; keep only the last digit of each answer; draw a line from the previous point to that point; stop when the line returns to 0.
- Follow the algorithm for the 2 times table and name the shape.
- Follow it for the 3, 4, 5, 6, 7, 8 and 9 times tables, one circle each.
- Sort the drawings into groups that make the same shape and look for what the numbers in each group have in common.
- Predict the shape for the 12 times table, then follow the steps to check.
What you should see
The 2 times table ends in 2, 4, 6, 8, 0, so the drawing is a pentagon; the 8 times table gives 8, 6, 4, 2, 0, the same pentagon drawn the other way. The 4 and 6 times tables give a five-pointed star (4, 8, 2, 6, 0 and 6, 2, 8, 4, 0). The 3 and 7 times tables visit all 10 points and draw a ten-pointed star, the 1 and 9 times tables draw a ten-sided shape round the circle, the 5 times table draws a single line between 5 and 0, and the 10 times table stays at 0. The shapes group by what each number shares with 10: 1, 3, 7 and 9 share no factor with 10 and visit all 10 points, 2, 4, 6 and 8 share the factor 2 and visit 5 points, 5 visits 2 points and 10 visits only 0. The 12 times table ends in the same digits as the 2 times table and draws the pentagon.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Odd times tables always make stars and even times tables always make polygons.
- The 9 times table makes a different shape from the 1 times table.
Safety card
Hazards
- none beyond an ordinary classroom
Controls
- none needed
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.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
- vocabulary.curriculum.edu.au/MRAC/2024/04/LA/MAT/9c81a6d5-3683-4d03-abe7-f704b6084efc
- www.mathematicshub.edu.au/planning-tool/3/number/follow-and-create-algorithms
- www.mathematicshub.edu.au/planning-tool/4/number/follow-and-create-algorithms
- nrich.maths.org/problems/round-and-round-circle