Tables and rules | Year 7 | Ascent Library

01 / LEARN

The idea, step by step

Match each input with its output

For $y = 3 n + 2$ , multiply n by 3 and then add 2. Use the same operations in the same order for every input.

A table organises results. Its rows do not prove what happens at every other input unless a rule or pattern assumption is supplied.

Rule y=3n+2
n	y
0	2
1	5
2	8
3	11

Find, test and reverse

If output rises by a fixed amount whenever input rises by 1, try multiplying by that amount, then add or subtract a fixed adjustment. Test every supplied row.

To reverse 3n+2=17, undo the last step first: subtract 2, then divide by 3. This gives n=5.

A common trap

Adding before multiplying in an expression such as 3n+2.

Instead: Substitute first, then multiply before adding.

02 / WORKED EXAMPLES

See the thinking

Example 1

Complete a table

Find outputs for $y = 3 n + 2$ when n=1,2,3,4.

Completed pairs
n	y
1	5
2	8
3	11
4	14

At n=1: 3×1+2=5.
Repeat at the other inputs.
The output increases by 3 each time.

5,8,11,14.

Example 2

Find and reverse a rule

Inputs 1,2,3,4 give outputs 4,9,14,19. Find a simple rule and the input giving output 34.

The change is 5, so try 5n.
At n=1 subtract 1 to obtain 4: y=5n-1.
5n-1=34 gives 5n=35 and n=7.

y = 5 n - 1

; input 7.

Check your understanding

For $y = 4 n - 3$ , find the output when n=5.

Show answer

17.

4×5−3=20−3=17.

03 / WORKSHEET

Your turn

6 questions · 15 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

For $y = 2 n + 5$ , find the outputs for n=0,1,2.
2 marks
For $y = 6 n$ , find the output at n=4.
2 marks
Complete the missing output using the constant-addition pattern.
2 marks
Input–output pairs
Input Output
0 2
1 6
2 10
3 ?
Give a simple rule for the supplied pairs and check it at n=2.
3 marks
Pairs
n y
0 2
1 6
2 10
3 14
For $y = 3 n + 1$ , find the input giving output 22.
3 marks
Does $y = 2 n + 4$ match every pair (1,6),(2,8),(3,11)? Explain.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

For $y = 2 n + 5$ , find the outputs for n=0,1,2.
2 marks
2×0+5=5; 2×1+5=7; 2×2+5=9.
5,7,9.
For $y = 6 n$ , find the output at n=4.
2 marks
6×4=24.
24.
Complete the missing output using the constant-addition pattern.
2 marks
Input–output pairs
Input Output
0 2
1 6
2 10
3 ?
Add 4 each time: 2,6,10,14.
14.
Give a simple rule for the supplied pairs and check it at n=2.
3 marks
Pairs
n y
0 2
1 6
2 10
3 14
Each input increase of 1 adds 4 to output.
At n=0 the output is 2.
$y = 4 n + 2$ ; at n=2 it gives 10.
For $y = 3 n + 1$ , find the input giving output 22.
3 marks
3n+1=22.
Subtract 1: 3n=21.
Divide by 3: n=7.
7.
Does $y = 2 n + 4$ match every pair (1,6),(2,8),(3,11)? Explain.
3 marks
2×3+4=10.
Testing only the first two rows would miss the mismatch.
No. At input 3 it gives 10, not 11.

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Curriculum reference & lesson scope

Australian Curriculum v9.0 / South Australian Curriculum

Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.

Official curriculum source ↗

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Input–output pairs
Input	Output
0	2
1	6
2	10
3	?

Input–output pairs
Input	Output
0	2
1	6
2	10
3	?