Algebra

Expressions equations and solving equations

Energiser

Which of these are true?

2 + 3 = 3 + 2

2 + 3 + 1 =1 + 3 + 2

3 - 2 = 2 - 3

2 x 3 = 3 x 2

2 x 3 x 4 = 3 x 2 x 4

2 x 3 + 3 x 3 = 5 x 3

2 x 5 + 3 x 5 = 5 x 5

true

true

false

true

true

true

true

2 x 3 3 x 3 5 x 3+

+

=

=

2 x 4 3 x 4 5 x 4+ =

+ =

2 x c 3 x c 5 x c+ =

+ =

Cost = c

Check by substituting values.

16 8 4 2 1Can you make 22 ?

16 + 4 + 2

16 + 8 - 2

3 x 8 - 2

5 x 4 + 2

2 x 16 - 8 - 2

Can you make 21?

a b c m n

16 8 4 2 1

a b c m n

What is 2b + c ?

2b + c = 20

Can you make 20 another way ?

aWhat does a represent?

aWhat does a represent?

The length of a fence

a a

a a a

a a a a a

a b

aa b

a a a b b

a a a b b

a ba b a

a ba b a

a a a b b

a ba b a

a ba b a3

3a + 2b + 3

aa a3

If this was the fencing arrangement at the front of my garden and my garden is 9m long, how long is each fence?

9

aa a 3

9

3a + 3 = 9

aa a

3a =

6

6

aa a

a =

2

2

2 2

aa a4

If this was the fencing arrangement at the front of my garden and my garden is 40m long, how long is each fence?

40

a

aa a 4

40

a

4a + 4expression

equation

4a + 4 = 40

aa a

36

a

4a = 36

aa a 4

40

a

4a + 4 = 40

aa a

a =

a

4a + 4 = 40

4a = 36

9 9 99

9

One person thinks of a length for a fence and gives it a letter.

The person then draws some of the fences with a length added on.

The rest of the group have to write an expression for the total length.

The person then tells the group the total length and the group have to write an equation.

The group then solve the equation and asks if the solution is right.

Another person starts back at the beginning.

Task 1

What about subtraction?

aa a

4a - 2

a

2

aa a

4a - 2

a

210

= 10

aa a

4a = 12

a

12

aa a

a = 3

a

12

3 3 3 3

One person thinks of a length for a fence and gives it a letter.

The person then draws some of the fences with a length subtracted.

The rest of the group have to write an expression for the length left.

The person then tells the group the length left and the group have to write an equation.

The group then solve the equation and asks if it is right.

Another person starts back at the beginning.

Task 2

b 3b b b b

b 7b b

3b + 7

5b + 3

3b + 7 = 5b + 3

b b b b b

b 7b b

3b + 7

5b

3b + 7 = 5b + 3

b b b b b

b b b

3b +4

5b

4

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

b b b b b

b b b

3b +4

5b

4

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

b b

4

2b

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

b b

4

2b

3b + 4 - 3b = 5b - 3b

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

b b

4 = 2b

4

2b

3b + 4 - 3b = 5b - 3b

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

4 = 2b

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

b b

4 = 2b

4

2b

3b + 7 = 5b + 3

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

4 = 2b

3b + 7 = 5b + 3

3b + 4 = 5b

3b + 7 - 3 = 5b + 3 - 3

3b + 7 = 5b + 3

2 = b