Connections
 |
| 6. |
There is only one way to arrange five identical cubes into
the shape of a rectangular prism. |
| |
a.
|
Sketch
the rectangular prism made from five identical cubes. |
| |
b. |
Give
some other numbers of cubes that can be arranged into a rectangular
prism in only one way. What kind of numbers are these?
|
| 7. |
a. |
Sketch
every rectangular prism that can be made from ten identical
cubes. |
| |
b. |
Find
the surface area of each prism you skethced in part a. |
| |
c. |
Give
the dimensions of the prism from part a that has the least
surface area. |
| |
d. |
Find
one other number of blocks that has this same number of rectangular
arrangements.
|
| 8. |
The
dimensions of the recreation center floor are 150 ft by 45
ft, and the walls are 10 ft high. A gallon of paint will cover
400 ft2. About how much paint is needed to paint
the walls of the recreation center?
|
| 9. |
a. |
If
a small can of paint will cover 1400 in2, about
how many cans are needed to paint the walls of the recreation
center described in question 8? |
| |
b. |
What
factors might affect how much paint is actually used?
|
| 10. |
a. |
Graph
the relationship between the area of the base and the height
for your rectangular arrangements in Problem 2.1. |
| |
b. |
Describe
the relationship between the height and the area of the base. |
| |
c. |
How
might your graph be useful to the packaging engineer at ABC
Toys? |
| 11. |
The
1994 World Cup soccer championships were held in the United
States. Some of the games were played in the Silverdome in
Pontiac, Michigan. The dimensions of the soccer field in the
Silverdome were 71 m by 115 m. |
|
a. |
How
many square meters of turf were needed to cover the field? |
|
b. |
What
were the dimensions of the field in feet? (1 in = 2.54 cm
and 1 m = 100cm)
|
|
Answers
Connections
(Note: To find the number of blocks in questions 1-3, some students
may count cubes; others may multiply measures. To find the surface
area, some students may try to count the faces of the cubes shown;
some may add the areas of the faces. What is important at this
stage is that they understand that the amount of wrapping is called
the surface area.)
| 6a. |
 |
| 6b. |
Other
numbers of cubes that can be arranged in only one way to make
a rectangular prism are 7, 11, and 13. These are all prime
numbers. |
| 7a. |
 |
| 7b. |
The
1 by 1 by 10 prism has a surface area of 42 square units;
the 1 by 2 by 5 prism has a surface area of 34 square units. |
| 7c. |
1
by 2 by 5 |
| 7d. |
Possible
answers:6, 14, 15 (Note: Any number that is the product of
two prime numbers has two possible rectangular arrangements.
ACE questions 7 and 8 connect to ideas in the grade 6 Prime
Time unit.) |
| 8. |
The
total area to be painted is 2(150 x 10) + 2(45 x 10) = 3900
ft2. About 3900 ÷ 400 = 9.75
or about 10 gallons of paint are needed. |
| 9a. |
There
are 144 in2 in 1 ft2, so the total area
to be painted is 3900 x 144 = 561,600
in2. A small can of paint covers 1400 in2,
so the job will require 561,600 ÷ 1400 » 401.1
or about 402 cans. |
| 9b. |
Possible
answer: the thickness of the coat of paint, the brush or roller
used, and whether more than one coat of paint is applied. |
| 10. |
See
previous page.
|
| 11a. |
71
x 115 = 8165 m2
|
| 11b. |
71
x 100 x 1/1.54 x 1/12
» 233 ft by 115 x 100 x 1/2.54
x 1/12 » 377 ft. |
|
|
