25
Junior high school
Reshaping Cuboids
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
Students may benefit from the use of actual blocks that can be stacked to form the different cubic
combinations. An OHP calculator could also be used to collect solutions from the entire class.
• • • • • • • • • • • • • • • Points for students to discuss • • • • • • • • • • • • • •
The number of divisors for a number expressed as p
a
x q
b
x r
c
(where p, q, and r are all prime) is
(a +
1
) (b +
1
) (c +
1
). For example, 360 = 2
3
x 3
2
x 5
1
. Here, a = 3, b = 2, and c =
1
, so the number
of divisors is given by the expression (3 +
1
) (2 +
1
) (1 +
1
) = 24. Therefore, 360 has 24 divisors.
Further Ideas
• Use trial and improvement to find the side of a cube having a volume of
1
80 cm
3
.
• Move into “four (or more) dimensions” as a means of finding the factors of a number.
For example, 6006 = 77 x 78 = (7 x
11
) x (6 x
1
3) = 2 x 3 x 7 x
11
x
1
3. All stages can
be displayed using the replay function.
1
x
1
x
1
2 =
1
2
1
x 2 x 6 =
1
2
2 x 2 x 3 =
1
2
1
x 3 x 4 =
1
2
Find the five calculations that represent
cuboids that each have a volume of 30 cm
3
.
e.g.
1
1
30
etc.
In a similar way, find the twelve calculations for
cuboids each having a volume of 96 cm
3
.
How many similar calculations must there be
for
1
80 cm
3
?
Which of these cuboids is nearest to looking
like a cube?
For volumes between
1
50 cm
3
and 200 cm
3
,
which particular ones can be represented by at
least
1
6 cuboids each? Which volumes have
the smallest number of cuboids each?
Summary of Contents for EL-531RH
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