Thinking Skills: Critical Thinking and Problem Solving

328 Answers to assignments

Number of revolutions =^610

() 6464 +++

=

30, with 10 m remaining

One revolution = 2^6

4

4

6

 +  = 4

1

3

mins

Total time = 30 43

2

 ×  + 3

2

+^2

3

=

132 mins

If you failed to find the shortest possible

time, you may award yourself:

•    three marks for a correctly calculated

time under 300 minutes (using

possible dimensions)

•    two marks for a correctly calculated

time over 300 minutes (using

possible dimensions)

•    one mark if you showed you knew to

multiply the speed of a full revolution

by the number of revolutions needed,

but made an error in your calculation.

e   There are two ways to achieve a time

under 500 minutes:

Blocks sized 20 + 20 + 21 will take

(139 mins 24 secs) + 5 mins

+ (139 mins 24 secs) + 5 mins

+ (168 mins 29 secs)

= 457 mins 17 secs.

Blocks sized 21 + 24 + 16 will take

(168 mins 29 secs) + 5 mins

+ (132 mins 10 secs) + 5 mins

+ (153 mins)

= 463 mins 39 secs.

Award yourself full marks for the above

solutions (rounding is acceptable).

Award yourself three marks for correctly

calculated answers that add up to 61

m^3 , or one mark for choosing block sizes

adding up to 61 m^3 and another for

calculating the time taken to move any

block 610 m.

f    Answering this question involves

developing a new use of the model to

investigate moving a large amount of stone.

•    Along the 1 × 6 face:

distance = 1 + 6 + 1 + 6 = 14 m

•    Along the 6 × 4 face:

distance = 6 + 4 + 6 + 4 = 20 m

If you give more distances than this, do

not award yourself any marks.

c   The principles for using the model

having been developed in the first two

questions, this question now asks for a

real application of its use.

To minimise the number of turns

required, we need to find the face of a

24 m^3 block that would have the largest

possible perimeter.

Assuming the lengths are integers, this

would be a 24 m × 1 m face, giving us a

perimeter of 50 m.

610 ÷ 50 = 12 revolutions (48 turns of

90°) with 10 m remaining. We are able

to choose whether the block is standing

upright or lying down at the beginning,

which allows us to choose which way it

is standing at the end. If it starts each full

revolution upright then it can pass the

610 m mark with one more 90° turn, so it

would take 49 turns in total.

If you did not give 49 as your answer,

you might still claim two marks if you

gave the number of complete revolutions

or half revolutions for a 24 × 1 face, or

if you gave the number of 90° turns

for a set of measurements which could

reasonably be encountered for a 24 m^3

block (12 × 2, 8 × 3, 6 × 4, 6 × 2, 4 × 3, 3 ×

2, 2 × 2, 1 × 1). Award yourself one mark

if you calculated using one of the sets of

measurements in brackets, but gave the

number of 180° or 360° turns.

d   Here, the model is used to find the

optimum dimensions of a 24 m^3 block in

order to move it quickly.

The optimum dimensions are 4 m × 6 m.

To calculate the time taken to complete

610 m: