A table of values pairs each input with an output made by the same rule. Look at how much the outputs go up each time the input goes up by 1: that is the number to multiply by. Then check the first column to see if anything is added. Use the whole rule on any input, even one far along the table. To find an input from an output, undo the rule: take away, then divide.
Explore this idea with maths tools
Equal groups
3 × 4 = 12
12 ÷ 3 = 4
The same picture shows multiplication and division. Each group must have the same number.
Words to know
- input
- the number that goes into a rule
- output
- the number that comes out of a rule
- rule
- the steps that turn every input into its output
Worked examples
Inputs 1, 2, 3, 4, 5 give outputs 4, 8, 12, ?, 20. What is the missing output?
- 1.The outputs go up by 4, so the rule is × 4.
- 2.Check: 1 × 4 = 4. So 4 × 4 = 16.
= 16
Inputs 1, 2, 3, 4 give outputs 5, 8, 11, 14. What is the output for 10?
- 1.The outputs go up by 3, and 1 × 3 = 3, so add 2. The rule is × 3 then + 2.
- 2.10 × 3 + 2 = 32.
= 32
Inputs 1, 2, 3, 4 give outputs 5, 8, 11, 14. Which input gives 47?
- 1.The rule is × 3 then + 2.
- 2.Undo it: (47 − 2) ÷ 3 = 15.
= 15
For parents
Method: Find the rule, then use it
What to say: How much do the outputs go up by? Does your rule work for every column?
Common mistakes:
- Uses only the multiplying part of a two-step rule and forgets the adding part.
- Uses only the adding part of a two-step rule and forgets to multiply.
- Sees the outputs go up by m and uses 'add m to the input' as the rule.
- Thinks the output goes up by one because the input does.
- Scales up a known output (input 10 is 5 lots of input 2, so output is 5 lots of that output), which fails when the rule adds a number.
- Continues the table by one step instead of jumping to the input asked for.
- Applies the rule to the output when asked for the input, instead of undoing the rule.