Patterns and rules · Usually met around P4
Repeating patterns
Find the repeating group, then the remainder.
How to do it
Method
Find the repeating group, then the remainder
5, 8, 6 repeating: 20 ÷ 3 = 6 r 2 → the 20th is 8
Another way
Count in groups
The 18th is 6, the 19th 5, the 20th 8
In full
First find the group that keeps repeating: start from the 1st and see after how many it begins again. The size of that group is how often the pattern repeats. To find the 20th, don't draw them all: divide 20 by the group's size and look at the remainder. Remainder 1 is the group's 1st, remainder 2 its 2nd… and no remainder means a whole number of groups, so it is the group's last. Or count group by group: with 3 in a group, the 3rd, 6th, 9th, … 18th are each a group's last, and 2 more reach the 20th.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Continue the pattern: 22, 3, 3, 22, 3, 3, 22, 3, □
Show the answer and working
Answer: 3
The numbers repeat in groups of 3, so the 9th is the same as the 3rd: 3.
Example 2
Following the pattern, what goes where the question mark is?
- A. 🐻
- B. 🖍️
- C. 🐰
- D. 🍌
Choose the right answer
Show the answer and working
Answer: D. 🍌
It repeats in groups of 4. After the 10th comes the 11th, which by the pattern is 🍌.
Example 3
The pattern in the picture keeps repeating. How many 📏 are there among the first 28?
Show the answer and working
Answer: 19
Groups of 3, each with 2 📏. 28 ÷ 3 = 9 r 1: 9 groups hold 18, and the 1 left over hold 1, so 19 in all.
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