KS3 Maths · Year 7 · Chapter 10: Algebra · Lesson 4

Using algebraic expressions

Year 7About 70 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Last lesson
Expand $4 (3 x - 5)$ .
[1 mark]
Answer
A2
Needed today
Work out $\frac{7 + 9}{2} \times 5$ .
[1 mark]
Answer
A3
Needed today
Write down the highest common factor of $14$ and $35$ .
[1 mark]
Answer
A4
From chapter 6
A cuboid is $2$ cm by $3$ cm by $6$ cm. Work out its volume.
[1 mark]
Answer $\dots\dots cm^{3}$

Example, then your turn

Year 7

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

Example 1

The area of a trapezium can be written as $A = \frac{( a + b ) h}{2}$ or as $A = \frac{h}{2} (a + b)$ . Work out the area of this trapezium both ways.

Not drawn accurately

Hint

a

and

b

are the parallel sides;

h

is the height. Both forms must give the same answer.

B1
The perimeter of a rectangle can be written as $P = 2 (l + w)$ or as $P = 2 l + 2 w$ . Work out $P$ both ways when $l = 7.5$ and $w = 3.5$ . Then expand $2 (l + w)$ to show that the two forms always agree.
[3 marks]

Example 2

Write an expression for the perimeter of this rectangle in the form $2 (\dots\dots)$ .

Not drawn accurately

Hint Add all four sides. Then ask: what times

2

gives each term?

B2
Write an expression for the perimeter of this rectangle in the form $2 (\dots\dots)$ .
[2 marks]
Not drawn accurately
Answer $2 (\dots\dots)$ cm

Example 3

This shape is split into two rectangles in two different ways. Lengths are in cm.

(a) Use each diagram to write an expression for the area.

(b) Show that the two expressions are equivalent.

Hint Left: a

9

4

rectangle and a

5

x

one. Right: a

5

(x + 4)

rectangle and a

4

4

one.

B3
This shape is split into two rectangles in two different ways. Lengths are in cm.
(a) Use each diagram to write an expression for the area.
(b) Show that the two expressions are equivalent.
[3 marks]

Example 4

For this cuboid, write an expression for (a) its volume, (b) its total surface area in the form $4 (\dots\dots)$ .

Not drawn accurately

Hint A cuboid has three pairs of equal faces: front and back, top and bottom, the two ends.

B4
For this cuboid, write an expression for (a) its volume, (b) its total surface area in the form $2 (\dots\dots)$ .
[3 marks]
Not drawn accurately
Answer(a) $\dots\dots$ (b) $2 (\dots\dots)$

Practice

Year 7

C1
Each brick is the sum of the two below it. Write the top brick in the form $4 (\dots\dots)$ .
[2 marks]
Answer $4 (\dots\dots)$
C2
Which two of these are equivalent to $12 y - 18$ ?
$A 6 (2 y - 3)$ $B 12 (y - 18)$
$C 3 (4 y - 6)$ $D 2 (6 y - 18)$
[2 marks]
Answer $\dots\dots$ and $\dots\dots$

C3
(a) Write $15 n + 20$ in the form $5 (\dots\dots)$ .
(b) Write $12 n - 8$ in the form $4 (\dots\dots)$ .
[2 marks]
Answer(a) $5 (\dots)$ (b) $4 (\dots)$
C4
A $2$ cm by $2$ cm square is cut out of a rectangle. Write an expression for the shaded area in the form $4 (\dots\dots)$ .
[2 marks]
Not drawn accurately
Answer $4 (\dots\dots)$ cm²

Exam-style questions

GCSE Foundation

D1
Jo says, " $4 x + 12$ written with a bracket is $4 (x + 12)$ ."
Jo is wrong. Explain why, and write $4 x + 12$ correctly with a bracket.
[3 marks]

D2
Here is a shape. All the lengths are in centimetres.
Not drawn accurately
(a)
Show that the perimeter of the shape is $8 (x + 2)$ cm.
[3 marks]
(b)
The perimeter is $56$ cm. Work out the value of $x$ .
[2 marks]
Answer $x = \dots\dots$
Total for D2: 5 marks
D3
Rectangle $P$ is $3$ cm by $(2 y + 5)$ cm. Rectangle $Q$ is $6$ cm by $(y + 1)$ cm.
Show that the area of $P$ is always $9$ cm² more than the area of $Q$ .
[4 marks]
Not drawn accurately
D4
Three friends share a taxi. The fare for a journey of $n$ miles is $£ (6 n + 15)$ . They share the fare equally.
(a)
Write $6 n + 15$ in the form $3 (\dots\dots)$ .
[1 mark]
Answer $3 (\dots\dots)$
(b)
Write an expression for the amount each friend pays.
[1 mark]
Answer $£ \dots\dots$
(c)
Each friend pays $£13$ . Work out how many miles the journey was.
[3 marks]
Answer $\dots\dots$ miles
Total for D4: 5 marks

Extension

Stretch

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

E1
$12 x + 18$ can be written as $k (\dots\dots)$ , where $k$ is a whole number greater than $1$ and the bracket has whole numbers in it.
Find every way of doing this.
[5 marks]
Hint 1 · What to try
$k$ must divide into both $12$ and $18$ .
Hint 2 · The first line
The numbers greater than $1$ that divide both $12$ and $18$ are $2$ , $3$ and $6$ .
Hint 3 · The full method
$12 x + 18 = 2 (6 x + 9) = 3 (4 x + 6) = 6 (2 x + 3)$ .

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can show that two forms of a formula give the same answer.
I can write a perimeter or area in the form $k (\dots\dots)$ .
I can split a shape two ways and show the areas are equivalent.
I can write expressions for the volume and surface area of a cuboid.

Answers and mark scheme

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