mathematics involving shape and space a algebra. the 9-dot problem
TRANSCRIPT
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!