ACARA v9 CONTENT DESCRIPTION “follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns”
This unit introduces an idea from computing into number work: the algorithm. An algorithm is simply a sequence of steps, sometimes with a decision built in, carried out in order to investigate numbers. Year 3 learns to follow an algorithm someone gives them, to create their own, and to describe any pattern that emerges as the steps run. Counting in fives, which a child already knows, is a tiny algorithm; this unit makes the idea explicit and shows how following clear steps turns into the patterns that run right through mathematics.
Follow the steps
An algorithm is a fixed sequence of steps carried out in order.
An algorithm is an ordered list of steps. This one starts at 2 and adds 3 each time. Run a step.
Following an ordered recipe
An algorithm is like a recipe: a list of steps done in a set order. The simplest kind for numbers is a rule applied again and again — start at 2, add 3, and keep adding 3 to get 2, 5, 8, 11 and onward. Following such a rule faithfully, step by step, is the first skill, and it produces a sequence that is completely determined by the starting number and the step. The order matters: doing the steps in a different order would give a different result, which is why an algorithm is always a precise sequence rather than a loose set of instructions.
A step with a decision
An algorithm can include a decision that changes what the next step does.
A step can include a decision. Here each step checks: is the number even or odd? Run it and watch the path.
When a step makes a decision
Algorithms become more powerful when a step includes a decision: a check that sends the next step one way or another. A rule like "if the number is even, halve it; if it is odd, add one" decides at each step based on the number it is looking at, so the path it takes depends on what happens along the way. Decisions are what let an algorithm respond rather than just repeat, and following one carefully means checking the condition at every step. This is exactly the sequence-of-steps-and-decisions the descriptor describes.
Stop when told
An algorithm often has an end condition that decides when to stop.
This algorithm has a stopping rule: double the number, but stop once it goes past 20. Run it to the end.
Knowing when to stop
Many algorithms also need an end condition — a rule for when to stop. "Double the number, but stop once it goes past 20" runs 3, 6, 12, 24 and then halts, because 24 is the first value past twenty. Without a stopping rule, a repeating algorithm would go on forever; the end condition is the decision that brings it to a close. Following an algorithm to its proper end, recognising when the stopping rule is met, is part of carrying out the steps correctly and a natural companion to the decisions inside them.
The pattern emerges
Running a number algorithm often makes a repeating pattern appear.
Following a counting algorithm can make a pattern appear. Count further in fives and watch the last digit.
Patterns that appear
The reason algorithms matter in number work is that following them makes patterns appear. Count in fives — 5, 10, 15, 20, 25 — and the last digit goes 5, 0, 5, 0, over and over. The pattern was not put there on purpose; it emerges from the simple rule of adding five. Noticing and describing such an emerging pattern, exactly as the descriptor asks, is what turns mechanical step-following into mathematical insight. Algorithms generate patterns, and spotting them is how a child begins to see the structure hidden in numbers.
Name the pattern
Describing a pattern means finding the rule that turns each number into the next.
What is the rule behind this sequence?
Describing the rule
Describing a pattern means naming the rule that produces it: what turns each number into the next. In 2, 5, 8, 11 the rule is adding three each time, a constant difference; in 3, 6, 12, 24 each number is doubled. Telling these apart — a steady add-on versus a doubling — is the heart of describing patterns, and it works backwards from the sequence to the algorithm that made it. Being able to look at numbers and state their rule is the investigative skill the unit is building toward, the mirror image of following a rule forwards.
Build your own rule
Creating an algorithm means choosing the start and the step, then following it.
Starting at 1 and adding 2 gives 1, 3, 5, 7, 9, 11. Creating your own algorithm and reading off its pattern is what the unit asks for.
Make your own
The final step is creating an algorithm rather than just following one: choose a starting number and a step, then run the rule and read off the pattern it makes. Starting at 4 and adding 5 gives 4, 9, 14, 19; starting at 10 and adding 10 gives the tens. Creating an algorithm and describing the pattern that comes out completes the cycle the descriptor sets — follow, create, and describe. With ordered steps, decisions, stopping rules, emerging patterns and the rules behind them all explored, a child can both follow and write simple number algorithms, finishing the Year 3 Number strand and the year's number work.
Quick self-check
1. An algorithm is...
2. Follow the rule "add 4" from 3: 3, 7, 11, ... What comes next?
3. Rule: "if even, halve; if odd, add 1." Starting at 5, the next number is...
4. Counting by fives (5, 10, 15, 20, ...), the last digit follows the pattern...
5. In 2, 4, 8, 16 each number is the one before it...