Building a pattern from a rule

Mathematics · Multiplication & Division · ages 9-10

Name ______________________ Date ____________

A shape pattern goes circle, square, circle, square, circle. What comes next?
- circle
- square
- triangle
A pattern rule says 'start at 1, add 3.' What is the number right after 1?
- 3
- 4
- 5
The pattern 'start at 1, add 3' gives 1, 4, 7, 10, 13. True or false: these numbers alternate between odd and even.
Circle one: True False
Start at 2 and add 4 each time: 2, 6, 10, 14, 18. True or false: this pattern will always give even numbers, no matter how far you go.
Circle one: True False
A pattern goes circle, circle, square, circle, circle, square, circle, circle, and then a missing shape. What is missing?
- circle
- square
- triangle
Start at 1 and add 3 each time. What is the 5th number in the pattern?
Answer: ______________
A pattern starts at 5 and adds 3 each time: 5, 8, 11, 14, 17. What do you notice about odd and even numbers in this list?
- They alternate every number
- They are all odd
- They are all even
Priya says: 'If I start at 3 and add 4 each time, I'll only get even numbers, just like starting at 2 and adding 4.' Is she right?
- Yes, because the step is even
- No, because the start number is odd
- Yes, because 4 is even

Answer key

For grown-ups. Fold this page away before handing over the rest.

square · The rule is circle, then square, repeat. After circle comes square.
4 · Start at 1, then add 3: 1 + 3 = 4.
True · 1 is odd, 4 is even, 7 is odd, 10 is even, 13 is odd. It flips every time.
True · Adding an even number to an even number always gives another even number, so the pattern can never reach an odd one.
square · The rule repeats every three shapes: circle, circle, square. The ninth shape completes that group with square.
13 · Keep adding 3: 1, 4, 7, 10, 13. The fifth number is 13.
They alternate every number · 5 is odd, 8 is even, 11 is odd, and so on. Adding an odd step always flips odd to even and back, just like the 'start at 1, add 3' pattern.
No, because the start number is odd · Adding an even number never changes whether a number is odd or even. Since 3 is odd, every number in Priya's pattern stays odd.