1. What’s the same and what’s different?
x + 1 = 4
3 + 1 = 4
x + 3 3x
Can you sort them into groups?
Could you define what an equation is?

2. Glossary
Operation 
Term 
Expression 
Equation 
Identity 
Things used to solve problems, eg. +, -, x, ÷
Contains a number, a variable or a product (x) of both
Contains at least one term and operation
Mathematical statement containing an equals (=) sign
An equation that is always true (≡)
5x + 7
coefficient
constant
variable

3. Sort the following into the correct column of the table:
Operation
Term
Expression
Equation
Identity
5x + 6y 7a
y = mx + c
a/2 ≡ ½ a c² +
6(m – n)
sin²x + cos²x ≡ 1
7c – 9 = 54
3a + 4b - 2 - ½y

4. + + = 24 8 8 8 I have 3 bags of marbles. Altogether I have 24 marbles.
How many marbles are in each bag?
= 24

5. I have 3 bags of marbles. Altogether I have 24 marbles.
How many marbles are in each bag?
Using algebra:
3b = 24
÷3 ÷3
b = 8

6. Your turn!
4x = 20
x = 3
x = 16
x = 24
x = 5

7. Your turn!
3y = 18
y = 15
y = 7
y = 6
y = 54

8. Your turn!
c = 2 6
c = 12
c = 0.3
c = 3
c = 6

9. Your turn!
5a = -15
a = 3
a = -3
a = 5
a = -5

10. How many marbles were in the bag to begin with?
I have 1 bag of marbles. I put in 3 extra marbles. There are now 9 marbles in the bag.
How many marbles were in the bag to begin with?
+ 3 = 9 6

11. How many marbles were in the bag to begin with?
I have 1 bag of marbles. I put in 3 extra marbles. There are now 9 marbles in the bag.
How many marbles were in the bag to begin with?
Using algebra:
b + 3 = 9
b = 6

12. Your turn!
m + 5 = 8
m = 13
m = 5
m = 3
m = 12

13. Your turn!
p – 8 = 3
p = 11
p = -5
p = -11
p = 5

14. Your turn!
v + 5 = 2
v = 7
v = 3
v = -7
v = -3

15. I have 2 bags of marbles and 5 extras. Altogether I have 13 marbles.
How many marbles are in each bag?
= 13

16. I have 2 bags of marbles and 5 extras. Altogether I have 13 marbles.
How many marbles are in each bag?
Using algebra:
2b + 5 = 13
2b = 8
÷ ÷2
b = 4

17. Let’s try this one:
3x + 4 = 22
3x = 18
÷ ÷3
x = 6

18. One more:
6t – 8 = 46
6t = 54
÷ ÷6
t = 9

19. Your turn!
2k + 1 = 7
k = 3.5
k = 4
k = 3
k = 6

20. Your turn!
3g – 2 = 19
g = 6.5
g = 5.67
g = 6
g = 7

21. Your turn!
4n + 2 = 50
n = 13
n = 12.5
n = 12
n = 13.5

22. Answers
x = 3 y = -6
p = 12 q = 13
a = 4 b = 7
c = d = 2
e = f = -4

23. Which is the smallest variable in the following pairs?
When there is a variable on both sides of the equals sign, start by eliminating the smallest variable.
Which is the smallest variable in the following pairs?
2a and 4a
6m and m
4x and -2x
y and –3y

24. 2a + 5 = 4a - 1
-2a a
5 = 2a - 1 __
6 = 2a
÷2 ÷2____
3 = a

25. 6x + 4 = 2x + 6
-2x x
4x + 4 =
4x =
÷ ÷4
x = ½

26. Answers
x = 2 x = 3
x = 13 a = 8
b = 3 m = 12
z = h = 0.4 7
y = 2 f = -7 25

27. Can you right down an equation where x = 4?
Plenary
Can you right down an equation where x = 4?

28. Starter Solve the following equations: a + 4 = 2 6y = 72
8m – 9 = x – 3 = 2x + 9
-4 -4
÷6 ÷6
a = -2
y = 12
-2x x
8m = 64
3x – 3 = 9
÷8 ÷8
m = 8
3x = 12
÷3 ÷3
x = 4

29. Starter Solve the following equations: a + 4 = 2 6y = 72
8m – 9 = x – 3 = 2x + 9
-4 -4
÷6 ÷6
a = -2
y = 12
-2x x
8m = 64
3x – 3 = 9
÷8 ÷8
m = 8
3x = 12
÷3 ÷3
x = 4

30. Expand
4(t + 7)
4t + 21 A
11t B
4t + 28 C
4t + 7 D

31. Expand
7(x - 8)
7x - 8 A
7x - 56 B
15x C
7x + 56 D

32. Expand
9(2x + 5)
18x + 45 A
9x + 5 B
18x + 5 C
2x + 45 D

33. Expand
3(5 – 2x)
15 – 2x A
15 + 3x B
15 – 6x C
13x D

34. Expand
3y(y + 6)
9y² A
3y² + 18y B
3y + 18 C
3y + 6y D

35. Expand
6x(6x – 8)
36x² - 48x A
12x² - 48x B
36x² - 48 C
36x - 48 D

36. Solve the equation:
Your turn:
5 (4a + 2) = 70
4 (2x - 4) = 32
20a
+ 10
= 70 8x
- 16
= 32
- 10
- 10
+ 16
+ 16
20a = 60
8x = 48
÷20
÷20 ÷8 ÷8
a = 3
x = 6

37. Solve the equation:
Your turn:
5 (2x + 4) = 10 (6x – 8)
2 (5x + 2) = 4 (2x + 3)
10x
+ 20 =
60x
- 80
10x
+ 4 = 8x
+ 12
- 10x
- 10x
- 8x
- 8x
20 = 50x - 80
2x + 4 = 12
+ 80
+ 80
- 4
- 4
100 = 50x
2x = 8
÷ 50
÷ 50 ÷2 ÷2
2 = x
x = 4

38. Solve the equation:
4(3x + 2) + 3(2 – 3x) = 20
12x
+ 8
+ 6
- 9x
= 20
3x + 14 = 20
- 14
- 14
3x = 6
÷ 3
÷ 3
x = 2

39. Your turn:
7(x + 3) + 2(3 – 4x) = 27 7x
+ 21
+ 6
- 8x
= 27
-x + 27 = 27
- 27
- 27
-x = 0
x = 0

40. Answers Question 1 a. x = 5 b. d = 7 c. x = 4 d. x = 8
e. x = 5 f. b = 4
g. c = -2 h. y = 1
Question 2
a. x = 22 b. a = 1
c. y = 7 d. x = 0
e. x = f. n = -10
g. a = -1 h. x = 7
Question 3
a. x = 2 b. x = 3
c. x = 5 d. x = 3
e. x = 1 f. x = 0
g. x = 2 h. x = 4

41. What’s gone wrong? What should the answer be?
Plenary
What’s gone wrong? What should the answer be?
6 (4x + 5) = 2 (20x + 7)
24x + 30 = 40x + 14
30 = 16x + 14
44 = 16x
x = 2.75