Download Activities 1

MEP: Demonstration Project
Y9B, Unit 11
UNIT 11 Algebraic Manipulation
Activities
11.1
Sums in Squares
11.2
Areas of Rectangles
11.3
Horseshoes
11.4
Flower Beds
Notes and Solutions (2 pages)
© The Gatsby Charitable Foundation
Activities
MEP: Demonstration Project
Y9B, Unit 11
ACTIVITY 11.1
1.
Draw a 2 × 2 square on
the number grid like the
one shown. Add up the
4 numbers in the square
and record your results
in a table as shown
below.
Repeat for several
other squares.
Smallest Number in
Square (x)
34
Sums in Squares
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
Total of the Four
Numbers (T)
Largest Number in
Square (y)
158
45
9 10
19 20
29 30
39 40
49 50
59 60
69 70
79 80
89 90
99 100
2.
Show that the formula T = 4 x + 22 is true for each of your starting numbers, x.
3.
Explain why the formula will always work.
4.
Determine a formula for T in terms of y.
Extension
Repeat for a 3 × 3 square and for a 4 × 4 square.
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Y9B, Unit 11
ACTIVITY 11.2
Areas of Rectangles
Calculate the area of each of the rectangles by calculating the area of each part:
A.
B.
2 cm
7 cm
5 cm
x cm
1 cm
3 cm
4 cm
C.
4 cm
D.
x
3x
x
2
y
3 cm
E.
F.
6
2x
6x
2
3x
x
y
G.
2x
8
3
x
© The Gatsby Charitable Foundation
5
MEP: Demonstration Project
Y9B, Unit 11
ACTIVITY 11.3
Horseshoes
Farriers can buy ready-made horseshoes, but many make their own so that the fit is better.
The horseshoe is made up from a straight strip of iron which is forged into the familiar
horseshoe shape.
The problem that the farrier has to solve is
to determine the length of iron (l) needed
to make the appropriate sized shoe.
Two formulae are commonly used:
A
l = 2w + 2
B
l = w + d + 1.5
where w is the width of the shoe, in inches,
and d is the diagonal measured in inches
from the toe to the heel, as shown.
Data for Horseshoes
3.
Horse
Width (w)
Diagonal (d)
Crystal
5.15
5.50
Honey
5.25
5.75
Frosty
5.50
5.80
William
5.75
6.00
Smudger
6.00
6.40
1.
Determine the length of iron required to
shoe each horse using
(a) formula A,
(b) formula B.
Comparing the lengths required by each
formula, what do you notice?
2.
What is the condition on d and w which
ensures that the two formula are the same?
The cost of the shoe is directly related to the length of iron, l, used. If Crystal has
a new set of horseshoes 8 times a year, what saving is made in iron using formula B
rather than formula A? What is the percentage saving?
Ready-made shoes often use 8 nail holes symmetrically placed so that they can be used on
either foot, but a handmade shoe is made specifically for the left or right foot, with 4 nails
on the outside half and 3 on the inside half.
4.
The nails for Honey's front left shoe
are shown opposite, with distances
between them as illustrated.
Determine the appropriate values
to take for x and y.
© The Gatsby Charitable Foundation
MEP: Demonstration Project
Y9B, Unit 11
ACTIVITY 11.4
Flower Beds
KEY
Flower bed
Paving slab
The council wish to create a long display made up of 100 flower beds each surrounded with
hexagonal paving slabs, according to the pattern shown above. (In this pattern 18 slabs
surround 4 flower beds.)
1.
How many slabs will be needed?
2.
Determine a formula that the council can use to decide the number of slabs needed for
any number of flower beds.
Extensions
There are many other ways of surrounding flower beds with hexagonal paving slabs.
1.
Find formulae for the number of slabs needed for configurations of each of the
layouts below, both of which have n hexagonal flower beds.
(a)
2.
(b)
Invent your own examples and find general formulae for the number of slabs needed
for any number of them.
© The Gatsby Charitable Foundation