Mathematics

Involving Shape and Space a Algebra

The

9-Dot

Problem

Objectives

Solve geometrical problems

Identify the properties of 2-d shapes

Have a go at Triangles

Draw as many different triangles by joining three of

the nine dots

Have a go at Quadrilaterals

Draw as many different quadrilaterals by joining four

of the nine dots

Algebra Walls

Constructing and solving equations

using Algebra Walls

Algebra wallsAlgebra walls

5

= 27

n7

?12 ?n + 7

?n + 19

n + 19 = 27n + 19 = 27

n = 27 - 19n = 27 - 19

n = 8n = 8

Algebra wallsAlgebra walls

5

= 27

n7

?12 ?15

?27

n = 8n = 8

Back substitute to Back substitute to checkcheck

88

Algebra wallsAlgebra walls

2n

= 35

n + 3

7

?2n + 7 ?n + 10

?3n + 17

3n + 17 = 3n + 17 = 3535 3n = 35 - 173n = 35 - 17

3n = 183n = 18

n = 6n = 6

Algebra wallsAlgebra walls

= 35

?19 ?16

?35

n = 6n = 6

Back substitute to Back substitute to checkcheck

99

2n n + 3

7 1212

Algebra wallsAlgebra walls

5

= 42

n

= 27

12

n + 5

n 26

162n n + 26

= 73 = 32

n -16n + 14

n + 26

24 - n

3n + 4 4n + 6

= 88

4 - 2n

2n + 8 6n + 7

= 33

Solv

e f

or

n a

nd

back

su

bst

itu

te t

o

check

n = 5

n = 2

n = 5

n = 6

n = 6

n = 2.5

Constructing and solving equations

using the perimeter of shapes

Perimeter and algebra

n + 23n

6n

The perimeter of this shape is 22cm. Find the length of each side

Total perimeter =

?

3n + n + 2 + 6n =

10n + 2

10n + 2 = 2210n = 20 n = 2

?

?6

124

Check: 6 + 4 + 12 = 22 so n = 2 is correct

The length of each side is 6, 4 and 12

Substitute n = 2 into the expressions for each Substitute n = 2 into the expressions for each lengthlength

Perimeter and algebra

12 - n3n - 4

4n

The perimeter of this shape is 38cm. Find the length of each side

Total perimeter =

?

3n - 4 + 12 - n + n + 2 + 4n =

7n + 10

7n + 10 = 387n = 28 n = 4

?

?

8

16

8

Check: 8 + 8 + 6 + 16 = 38 so n = 2 is correct

The length of each side is 8, 8, 6 and 16

Substitute n = 4 into the expressions for each Substitute n = 4 into the expressions for each lengthlength

n + 2?

6

Perimeter and algebra

3n - 5

2n - 4

n +

6

The perimeter of each shape is inside the shape. Find the length of each side

n + 241cm

a)n +5

n + 6

n +

3050cm

b)

15 - n

2n + 8

2n +

6 n +

2

63cm

c)

2n +

8

15 - n

8n - 8

n + 6

24 –

2n

115cm

d)

n + 8

n +

6

Solv

e f

or

n a

nd

back

su

bst

itu

te

to c

heck

n = 3

n = 6

n = 4 n = 8

THE END!