Variables, constants and terms | Year 7

01 / LEARN

The idea, step by step

A letter represents a number

A variable is a symbol for a number that may change. In a notebook-cost rule, $n$ can represent how many notebooks are bought. The letter is not a notebook itself: it is a number, such as 2, 5 or 12. The same letter has the same value throughout one calculation.

A constant is a fixed numerical value. In $4 n + 3$ , the 4 multiplies the number of notebooks and the 3 is added once. Changing $n$ changes the whole expression, but not the written coefficient or constant.

Terms and coefficients

Addition and subtraction separate terms. In $5 x + 8$ , the terms are $5 x$ and 8. The coefficient of $x$ is 5: it counts five copies of $x$ . The constant term is 8. No value of $x$ is needed to describe this structure.

Keep a subtraction sign with the term after it. The terms of $7 a - 2 b + 9$ are $7 a$ , $- 2 b$ and 9. There are two variables, $a$ and $b$ . The negative coefficient tells us that copies of $b$ are being subtracted.

A common trap

Calling a letter an object instead of the number of objects.

Instead: Define the numerical quantity. For example, $b$ is the number of boxes, not a box.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read a cost rule

A booking costs $C = 6 t + 4$ dollars, where $t$ is the number of tickets. Name the coefficient of $t$ and the constant term.

The variable term $6 t$ means six times the number of tickets.
Its coefficient is 6. The added 4 does not depend on the number of tickets.

Coefficient: 6. Constant term: 4.

Example 2

Keep the subtraction sign

List the terms in $8 p - 3 q + 5$ and name its variables.

Separate the expression at addition and subtraction signs.
Keep the minus sign with $3 q$ : the terms are $8 p$ , $- 3 q$ and 5.
The quantities represented by letters are $p$ and $q$ .

8 p

- 3 q

, 5; variables

p

and

q

Check your understanding

What is the constant term in $9 k + 11$ ?

Show answer

The 11 has no variable and stays fixed when $k$ changes.

03 / WORKSHEET

Your turn

6 questions · 9 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Name the variable in $4 x + 7$ .
1 mark
What is the coefficient of $m$ in $9 m + 2$ ?
1 mark
What is the constant term in $3 a + 12$ ?
1 mark
List the terms in $6 p - 4 q + 10$ .
2 marks
A delivery costs $5 b + 8$ dollars, where $b$ is the number of boxes. What does 8 represent?
2 marks
How many terms are in $2 r + 3 s + 4$ ? Name its variables.
2 marks

Read the worked solutions

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

Name the variable in $4 x + 7$ .
1 mark
The letter $x$ represents a number that may change.
$x$
What is the coefficient of $m$ in $9 m + 2$ ?
1 mark
The term $9 m$ means nine copies of $m$ .
9
What is the constant term in $3 a + 12$ ?
1 mark
The added 12 is independent of $a$ .
12
List the terms in $6 p - 4 q + 10$ .
2 marks
Addition and subtraction separate terms.
The minus sign stays with $4 q$ .
$6 p$ , $- 4 q$ , 10
A delivery costs $5 b + 8$ dollars, where $b$ is the number of boxes. What does 8 represent?
2 marks
The $5 b$ part changes with the number of boxes.
The 8 is added once regardless of $b$ .
A fixed delivery charge of 8 dollars.
How many terms are in $2 r + 3 s + 4$ ? Name its variables.
2 marks
The terms are $2 r$ , $3 s$ and 4.
The letters are $r$ and $s$ .
Three terms; variables $r$ and $s$ .

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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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