Follow & create algorithms to investigate numbers
Theory
An algorithm is a clear set of steps you follow in order to investigate numbers. This Year 3 maths page explains how to follow a number machine and its rule, read a flowchart with a yes/no decision, find the rule from an in and out table, and create your own steps. Curriculum: VC2M3N09 / AC9M3N07.
An algorithm is a clear list of steps you follow in order, one after another, to work something out. It is like a recipe: do each step at a time, and you get the same answer every time.
A number machine has a rule, such as add 6 or double it. A number goes in, the rule changes it, and a new number comes out. To find the rule, check how each In turns into its Out, then test the same idea on every row.
A flowchart draws the steps as boxes joined by arrows. A diamond asks a yes/no question and splits the path in two. Following an algorithm means doing the steps; creating one means writing the steps yourself so anyone can follow them to investigate numbers.
Algorithms do not need formulas, but these facts help you follow and check them.
How to follow an algorithm
- Read all the steps first. See how many steps there are and what order they come in.
- Start with the given number. Write it down so you can see what goes in.
- Do one step at a time. Apply each rule in order, and write the new number after every step.
- Answer a diamond before you move on. In a flowchart, work out the yes/no question, then take the matching path.
- Check the result. The last number you write is the answer. Try another number to test that your steps work every time.
| \(7 + 6\) | \(=\) | \(13\) |
Follow the rule once. The number \(13\) comes out.
| \(6 \times 2\) | \(=\) | \(12\) |
| \(12 - 2\) | \(=\) | \(10\) |
Do the steps in order. You finish with \(10\).
| In | Out |
|---|---|
| 2 | 10 |
| 3 | 15 |
| 5 | 25 |
| \(2 \times 5\) | \(=\) | \(10\) |
| \(3 \times 5\) | \(=\) | \(15\) |
| \(6 \times 5\) | \(=\) | \(30\) |
The rule works for every row, so it is multiply by 5. Then \(6\) gives \(30\).
| \(7\) | \(\to\) | \(\text{odd, take No path}\) |
| \(7 + 3\) | \(=\) | \(10\) |
\(7\) is odd, so add \(3\). The answer is \(10\).
| \(3,\ 8,\ 13,\ 18,\ 23,\ 28,\ 33\) | ||
| \(33 - 3\) | \(=\) | \(30\) |
| \(30 \div 5\) | \(=\) | \(6\) |
Count the jumps, not the numbers: there are \(7\) numbers but only \(6\) jumps, so you add \(5\) six times.
| \(15 - 4\) | \(=\) | \(11\) |
| \(\text{check: } 11 + 4\) | \(=\) | \(15\) |
Undo the rule: the opposite of add \(4\) is take away \(4\). The number \(11\) went in.
Common pitfalls
Frequently asked questions
What is an algorithm in maths?
An algorithm is a clear list of steps you follow in order to work something out. In maths it is like a recipe: you do each step one at a time, in the order it is written, and you get the same answer every time.
What is a number machine?
A number machine follows one rule, such as add \(6\) or double it. A number goes in, the rule changes it, and a new number comes out. If the rule is add \(6\) and \(7\) goes in, then \(13\) comes out.
How do you follow a flowchart?
Start at the top and follow the arrows down. When you reach a diamond, answer its yes or no question, then take the matching path. Keep going until you reach the answer box.
How do you find the rule of a number machine?
Look at how each In changes into its Out, then test the same idea on every row. The rule is right only if it works for all the rows. If \(2\) gives \(10\), \(3\) gives \(15\) and \(5\) gives \(25\), the rule is multiply by \(5\).
What does it mean to investigate numbers?
To investigate numbers means to explore them using clear steps, such as building a pattern, testing whether a number is even or odd, or growing a sequence by the same rule each time.
How do you create your own algorithm?
Decide what you want to do, then write short steps in the right order so anyone can follow them. Check your steps by trying them on a number to make sure they give the answer you expect.