KS3 Maths · Year 7 · Chapter 10: Algebra · Lesson 1

Algebraic notation

Year 7About 60 minutesNo calculator52 marks

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Quick questions to start.

A1
Needed today
Work out $3 \times 7 - 12 \div 4$ .
[1 mark]
Answer
A2
Needed today
Work out $\frac{18 + 6}{4}$ .
[1 mark]
Answer
A3
Last lesson
As the temperature goes up, sales of hot drinks go down. What type of correlation is this?
[1 mark]
Answer
A4
From chapter 8
Write $3.9 \times 1 0^{4}$ as an ordinary number.
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Write each expression as simply as possible.

(a) $5 + a \times b \times 3$

(b) $m \div 4 - 2$

Hint Leave out the

\times

sign and write the number first. Write a division as a fraction.

B1
Write each expression as simply as possible.
(a) $7 + p \times 2 \times q$
(b) $6 - k \div 3$
(c) $4 \times (n + 1) \div 7$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 2

Simplify each expression.

(a) $n \times n \times 5$

(b) $3 x \times 2 x$

Hint A letter multiplied by itself is a square:

n \times n = n^{2}

. Multiply the numbers, then the letters.

B2
Simplify each expression.
(a) $w \times 4 \times w$
(b) $5 y \times 3 y$
(c) $a \times a \times a \times 2$
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$

Example 3

Work out the value of each expression when $x = 8$ and $y = 2$ .

(a) $3 (x + y)$ (b) $\frac{x}{y} + 4$

Hint Put the numbers in place of the letters. Brackets first; a fraction line works like brackets round the top and the bottom.

B3
Work out the value of each expression when $a = 10$ and $b = 5$ .
(a) $2 (a - b)$ (b) $\frac{a}{b} + 7$
(c) $\frac{a + 5}{b}$ (d) $a b^{2}$
[4 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$ (d) $\dots$

Example 4

Which two of these expressions are equivalent?

$A \frac{n}{3} + 5 - y$

$B 5 + y - \frac{1}{3} n$

$C \frac{1}{3} n - y + 5$

$D y - 5 + \frac{n}{3}$

Hint Write each one in the same order: the

n

term, then the

y

term, then the number. Keep each sign with the term after it.

B4
Which two of these expressions are equivalent?
$A 3 k - \frac{m}{2} + 1$
$B 1 + \frac{1}{2} m - 3 k$
$C \frac{m}{2} + 3 k - 1$
$D 1 - \frac{1}{2} m + 3 k$
[2 marks]
Answer $\dots\dots$ and $\dots\dots$

Example 5

Zoe thinks of a number, $n$ . She subtracts $3$ , multiplies the answer by $5$ and then divides by $2$ .

(a) Write an expression for her answer.

(b) Work out her answer when $n = 11$ .

Hint Do the steps in order. The subtraction is done first, so it goes in a bracket.

B5
Raj thinks of a number, $x$ . He multiplies it by $4$ , adds $6$ and then divides the answer by $3$ .
(a) Write an expression for his answer.
(b) Work out his answer when $x = 9$ .
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Practice

Year 7

C1
Write $7 \times (a + 2) \div 3$ in two different ways.
[2 marks]
Answer $\dots\dots$ and $\dots\dots$
C2
Write $(k - 1) \div (k + 4)$ as simply as possible.
[1 mark]
Answer

C3
Work out the value of $r^{s} + s^{r}$ when $r = 2$ and $s = 5$ .
[2 marks]
Answer
C4
Simplify $0.4 d \times 15 d \div 2$ .
[2 marks]
Answer
C5
Ella thinks of a number, $y$ . She adds $5$ , multiplies by $4$ and then divides by $3$ . Which two of these expressions give her answer?
$A \frac{4 ( y + 5 )}{3}$ $B \frac{4 y + 5}{3}$
$C \frac{4}{3} (y + 5)$ $D 4 y + \frac{5}{3}$
[2 marks]
Answer $\dots\dots$ and $\dots\dots$
C6
A tin holds $b$ biscuits. Zak eats $3$ of them and shares the rest equally between $4$ friends. Write an expression for the number of biscuits each friend gets.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Sam says, " $4 n \times 3 n = 12 n$ ."
Sam is wrong. Explain why, and write down the correct simplified answer.
[2 marks]

D2
$a = 4$ and $b = - 3$ .
(a)
Work out the value of $5 a + 2 b$ .
[1 mark]
Answer
(b)
Work out the value of $a^{2} - 4 b$ .
[1 mark]
Answer
(c)
Work out the value of $\frac{a - b}{7}$ .
[1 mark]
Answer
Total for D2: 3 marks
D3
A taxi charges £3 plus £2 for each mile.
(a)
Write an expression for the cost, in pounds, of a journey of $m$ miles.
[1 mark]
Answer
(b)
Four friends share the cost of a journey of $m$ miles equally. Write an expression for the amount, in pounds, each friend pays.
[2 marks]
Answer
(c)
The journey is $9$ miles. Work out the amount each friend pays.
[2 marks]
Answer£ $\dots\dots$
Total for D3: 5 marks
D4
Here is a rectangle. All lengths are in centimetres.
Not drawn accurately
(a)
Write an expression for the area of the rectangle. Give your answer as simply as possible.
[2 marks]
Answer
(b)
Work out the area of the rectangle when $y = 3$ .
[2 marks]
Answer
(c)
A square has sides of length $3 y$ cm. Show that the area of the rectangle is $y^{2}$ cm² more than the area of the square.
[2 marks]
Total for D4: 6 marks
D5
Here are four expressions.
$3 n n^{2} 2 (n + 5) \frac{n ^{3}}{10}$
Write the expressions in order of size when $n = 6$ . Start with the smallest. You must show your working.
[3 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
$x$ and $y$ are whole numbers, and $x$ is smaller than $y$ .
$x + y = 7$ and $x + y = 5$
Work out the values of $x$ and $y$ .
[3 marks]
Hint 1 · What to try
$x + y = 5$ tells you what $x + y$ is. Then try square numbers for $x$ and $y$ .
Hint 2 · The first line
$x + y = 25$ . If $x = 3$ then $y$ must be $4$ .
Hint 3 · The full method
$x = 3$ and $y = 4$ give $3 + 4 = 7$ , and $x + y = 9 + 16 = 25$ , whose square root is $5$ . So $x = 9$ and $y = 16$ .
Answer $x = \dots\dots$ $y = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write an algebraic expression as simply as possible.
I can use square and cube notation, such as $n^{2}$ and $2 a^{3}$ .
I can work out the value of an expression by substituting numbers.
I can write an expression from a description in words.

Answers and mark scheme

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