ACARA v9 CONTENT DESCRIPTION “recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects, formed by skip counting, initially by twos, fives and tens”
Algebra in Year 1? There is not a letter in sight — and there does not need to be. Algebra begins the moment a child notices that numbers can follow a rule. Say five, ten, fifteen, twenty, and you are not just counting: you are running a pattern in which every number is exactly five more than the one before. This unit takes the skip counting children met in Number and looks at it through a new lens. Here the sequence itself is the object of interest: can you recognise the rule that drives it, continue it past where it stops, and create a brand-new pattern of your own? Those three verbs — recognise, continue, create — come straight from the curriculum, and they are the heart of pattern thinking.
What is the jump?
Four numbers from a skip-counting pattern. Work out the rule that drives them.
Look at the gaps. What is the jump: +2, +5 or +10?
The rule hides in the gaps
A pattern’s rule does not live in any single number; it lives between them. To find it, look at the gap from one number to the next. From 3 to 5 is a jump of two; from 5 to 7, two again. Once the same jump shows up every time, you have caught the rule. Children sometimes guess from the first number alone — seeing 3 and calling it a pattern of threes — so the habit worth building is to check at least two gaps before deciding.
The pattern machine
Feed each answer back into the machine. One rule grows the whole sequence.
Press Next number; the machine adds +2 every time.
A rule is a little machine
Once you hold the rule, the pattern will run for as long as you like. Feed a number into a plus-five machine and out comes the number five more; feed that answer back in and the sequence grows another step. There is nothing new to memorise — the machine does the same move every time. This is a first quiet meeting with one of the biggest ideas in mathematics: a rule that turns each value into the next, applied over and over again.
Tower steps
Each tower grows by the same jump. The block counts chant the pattern.
Each tower is 2 more than the last. How tall is the next one?
The same pattern wears different clothes
Patterns are not made of digits only. Build towers of blocks where each tower is two blocks taller than the last, and the heights read 2, 4, 6, 8 — the very sequence you would chant by twos. Numbers, shapes and objects can all carry one rule, and recognising the rule beneath the surface is the real skill. The curriculum names all of them — numbers, symbols, shapes, objects — because the pattern lives in the relationship, not in the material.
Highways on the fifty chart
Shade the numbers you would say, and watch the rule become a picture.
Press Shade next and watch the pattern appear.
Patterns you can see
Shade the skip-counted numbers on a fifty chart and the rule turns into a picture. Counting by twos stripes every second square. Counting by fives lights up just two tidy columns, the fives and the tens. Counting by tens stacks into a single straight highway down the right-hand edge — a first glimpse of how our place-value system is built on tens. When a pattern is visible, children can check and extend it with their eyes as well as their voices.
Make your own pattern
Choose the jump, then build the sequence yourself — and say it as it grows.
Choose a jump, then build your own pattern.
Now make your own
Creating a pattern needs only two choices: where to start and how big to jump. Pick fives and lay out five-cent coins one at a time, saying the total as it grows — 5, 10, 15. Pick twos and count thongs by the pool in pairs. The pattern is yours, which is exactly the point: a child who can build a sequence, not just echo one, truly owns the rule.
Quick self-check
1. A pattern goes 3, 5, 7, 9 ... What is the jump?
2. 10, 20, 30, 40 ... What comes next?
3. 4, 6, 8 ... What are the next two numbers?
4. Block towers grow 5, 10, 15. How many blocks in the next tower?
5. You create a pattern that starts at 0 with jumps of 2. Which one is yours?