Patterns and rules · Usually met around P4
Growing patterns
Write the counts down; see how many more each time.
How to do it
Method
Write the counts down; see how many more each time
4, 7, 10: pattern 10 = 4 + 9 × 3 = 31
Another way
Split the picture
1 stick + 10 lots of 3 = 31
In full
Count the matchsticks or dots in each pattern and write them in a row, say 4, 7, 10. See how many more each time: 3 more. Then find the new part in the picture: each new square adds only 3 sticks, because it shares one with the square before. To predict pattern 10, don't draw it: start with pattern 1's 4 sticks and add 3 sticks 9 times, 4 + 9 × 3 = 31. Or split the picture: 1 stick on the far left, then 3 more for each square, 1 + 10 × 3 = 31. When dots make a square, pattern n has n × n dots and the increase changes (3, 5, 7, …): look at how the increase itself grows.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
These dot patterns grow by a rule. How many dots does pattern 4 have?
Show the answer and working
Answer: 20
Write the counts in a row: 2, 6, 12. See how many more each time and how the picture is built: pattern 4 has 20.
Example 2
Matchstick patterns grow by a rule; patterns 1 to 3 are shown. How many matchsticks does pattern 15 need?
Show the answer and working
Answer: 46
Each pattern adds 3 sticks. Pattern 1 has 4; pattern 15 adds 3 another 14 times: 4 + 14 × 3 = 46.
Example 3
The matchstick patterns keep growing by the rule (patterns 1 to 3 shown), and pattern 9 needs 27 matchsticks.
True or false?
Show the answer and working
Answer: False
Each pattern adds 3 sticks. Counting on from pattern 1, pattern 9 needs 28.
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