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?

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

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

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

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

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

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

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

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

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

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 -3 -3 b = 6

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

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

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

I have 2 bags of marbles and 5 extras. Altogether I have 13 marbles. How many marbles are in each bag? + + = 13 4 4

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 -5 -5 2b = 8 ÷2 ÷2 b = 4

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

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

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

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

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

Answers x = 3 y = -6 p = 12 q = 13 a = 4 b = 7 c = 2.5 d = 2 e = -1.5 f = -4

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

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

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

Answers x = 2 x = 3 x = 13 a = 8 b = 3 m = 12 z = -27 h = 0.4 7 y = 2 f = -7 25

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

Starter Solve the following equations: a + 4 = 2 6y = 72 8m – 9 = 55 5x – 3 = 2x + 9 -4 -4 ÷6 ÷6 a = -2 y = 12 +9 +9 -2x -2x 8m = 64 3x – 3 = 9 ÷8 ÷8 +3 +3 m = 8 3x = 12 ÷3 ÷3 x = 4

Starter Solve the following equations: a + 4 = 2 6y = 72 8m – 9 = 55 5x – 3 = 2x + 9 -4 -4 ÷6 ÷6 a = -2 y = 12 +9 +9 -2x -2x 8m = 64 3x – 3 = 9 ÷8 ÷8 +3 +3 m = 8 3x = 12 ÷3 ÷3 x = 4

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

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

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

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

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

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

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

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

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

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

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 = 2.5 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

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