Operations and Algebraic Thinking
Patterns and tiling
Continue number and shape patterns, work out a later term in a pattern, and tell which shapes tile without leaving gaps.
A pattern is a rule you can keep applying. Some patterns add the same amount every time — 3, 6, 9, 12 keeps adding three — and some do something else, like doubling. The first job with any pattern is never to guess the next number, but to work out what the rule is. Once you have the rule, you can carry on as far as you like.
Jumps, not terms
Getting from the first number in a pattern to the tenth takes nine jumps, not ten — the first number is already there before any jumping starts. Counting the jumps rather than counting the numbers is the difference between the right answer and one whole jump too far.
Worked example
A pattern goes 3, 6, 9, 12, ... What number comes next?
Find the jump: 6 − 3 = 3, and 9 − 6 = 3.
Checking two jumps rather than one is what tells you the rule is really the same every time.
Try it together
Now let us find the tenth number in the pattern 1, 4, 7, 10, ... together.
Carrying on one number at a time would work, but there is a quicker way once you know the jump.
1.What is the jump from each number to the next?
Have a go
Have a go on your own: a pattern goes 5, 9, 13, 17, ... What number comes next?
Hint: Find the jump between two numbers you can see first.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.