Wrexham Maths Investigations
Year 8
Easter egg boxes
Teacher notes
The 3-dimentional activity requires a systematic approach to finding all possible boxes and then helps to develop the pupils’ concepts of surface area and edge length.
- Two designs are possible for 3 eggs.
Diagrams available on hard copy.
Eight designs are possible for 4 eggs.
Diagrams available on hard copy.
Year 8
Easter egg boxes
4-cube box / Surface area,sq . units / Edge length,
units / Cost, pence
A
B
C
D
E
F
G
H / 16
18
18
18
18
18
18
18 / 20
24
26
28
28
30
28
28 / 52
60
62
64
64
66
64
64
Box A is not only the cheapest to make but is also a conventional design which is easy to make.
The solids A to H give all possible shapes, but different orientations are possible. Pupils might decide that “overhanging” rooms are not allowed; for example
Except for these, other possibilities are drawn below.
Diagrams to follow. Available on hard copy.
Year 8
Easter egg boxes
Apartment / Cost of building£ / Cost of insulation
£ / Total cost
£
A1
A2
B1
B2
C1
C2
C3
D
E1
E2
F
G
H / 12 000
10 000
12 000
12 000
12 000
11 000
11 000
12 000
12 000
11 000
11 000
11 000
11 000 / 6 000
7 000
7 000
8 500
7 000
7 500
8 000
7 000
7 000
7 500
7 500
7 500
7 500 / 18 000
17 000
19 000
20 500
19 000
18 500
19 000
19 000
19 000
18 500
18 500
18 500
18 500
A2 is the likeliest choice for the builder; it is not only the cheapest design but is also traditional and so likely to attractive buyers.
Year 8
Easter egg boxes
Possible Extension :
An architect is asked to design some four roomed apartments in which each room has the shape of a cube. Construct all the different possibilities. One of them is shown here.
Which is the cost of building each of the possible apartments you have found?
If there is an additional cost of £500 to insulate each square of outside wall and each square of roof, what is the total cost now of each design? If you were the builder, which design would you choose?