Varying inputs in a digital formula table | Year 7

01 / LEARN

The idea, step by step

A table records repeated substitutions

A formula table records input values beside their matching outputs. For $C = 3 n + 5$ , substitute each selected $n$ and record the resulting cost. Each row is a fresh calculation using the same rule. Include units so a reader knows what the outputs mean.

When $n$ increases by 1, this cost increases by 3 dollars because there is one more item. The fixed charge of 5 dollars stays unchanged. Not every formula has a constant increase, so check the stated rule rather than assuming it.

Cost rule C = 3n + 5 dollars
Number n	1	2	3	4
Cost C (dollars)	8	11	14	17

A spreadsheet uses the same operations

If the input is in cell A2, =3*A2+5 calculates $3 n + 5$ . The equals sign starts the formula, * means multiplication, and A2 refers to the input cell. Copying down normally changes the relative reference to A3, A4 and so on.

Predict one output by hand before trusting the table. Check the cell reference and use brackets when a sum is multiplied. A finite table can suggest a pattern, but it does not establish a unique rule for every possible input. The supplied formula tells us which rule to use.

A common trap

Entering =3+A2+5 for the rule $3 n + 5$ .

Instead: Use * to multiply the coefficient and input. Check one known input by hand before copying the formula.

02 / WORKED EXAMPLES

See the thinking

Example 1

Three different inputs

Use $C = 4 n + 7$ dollars at $n = 0$ , 2 and 5.

$C (0) = 4 \times 0 + 7 = 7$ .
$C (2) = 4 \times 2 + 7 = 15$ .
$C (5) = 4 \times 5 + 7 = 27$ .

7 dollars, 15 dollars and 27 dollars.

Example 2

A changing increase

A rectangle is $w$ cm wide and $(w + 2)$ cm long. Find $A = w (w + 2)$ for $w = 1$ , 2 and 3. Are the increases equal?

Areas: $1 \times 3 = 3$ , $2 \times 4 = 8$ , $3 \times 5 = 15$ cm².
The increases are 5 and 7 cm².
Both dimensions change, so the increases need not be constant.

3, 8 and 15 cm²; the increases are unequal.

Check your understanding

Cell A2 contains 4. What does =2*A2+3 calculate?

Show answer

It gives $2 \times 4 + 3 = 11$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Use $y = 2 x + 1$ at $x = 0$ , 1, 2 and 3. List the outputs.
2 marks
Use $P = 4 s$ for square side lengths 2, 5 and 8 cm.
2 marks
Cell A2 holds $n$ . Write a spreadsheet formula for $5 n + 6$ .
1 mark
For $C = 3 n + 5$ , explain the cost change when $n$ rises from 4 to 5.
2 marks
Use $A = n^{2}$ at $n = 1$ , 2, 3 and 4. Are consecutive outputs equally spaced?
2 marks
A student uses =2*A2+4 for $2 (n + 4)$ . At input 3, find the student's answer and the correct answer, then correct the formula.
3 marks

Read the worked solutions

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

Use $y = 2 x + 1$ at $x = 0$ , 1, 2 and 3. List the outputs.
2 marks
Substitution gives $1$ , $3$ , $5$ and $7$ respectively.
1, 3, 5, 7
Use $P = 4 s$ for square side lengths 2, 5 and 8 cm.
2 marks
Multiply each side length by 4: $8$ , $20$ , $32$ .
8 cm, 20 cm, 32 cm
Cell A2 holds $n$ . Write a spreadsheet formula for $5 n + 6$ .
1 mark
Use * for multiplication and A2 for the input.
=5*A2+6
For $C = 3 n + 5$ , explain the cost change when $n$ rises from 4 to 5.
2 marks
$C (4) = 17$ and $C (5) = 20$ .
The $3 n$ term increases by 3; the fixed fee does not change.
An increase of 3 dollars.
Use $A = n^{2}$ at $n = 1$ , 2, 3 and 4. Are consecutive outputs equally spaced?
2 marks
The differences are 3, 5 and 7.
They are not constant.
1, 4, 9, 16; no.
A student uses =2*A2+4 for $2 (n + 4)$ . At input 3, find the student's answer and the correct answer, then correct the formula.
3 marks
The student's calculation is $2 \times 3 + 4 = 10$ .
The intended calculation is $2 (3 + 4) = 14$ .
Include brackets around the sum.
Student: 10. Correct: 14. Formula: =2*(A2+4).

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Curriculum reference & lesson scope

Australian Curriculum v9.0 / SA Curriculum Mathematics

Year 7 variables, expression notation, substitution, simple equivalence and formula tables. Digital methods are explained with supplied data; the topic test works by hand.

Official curriculum source ↗

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