Hands on a clock

Hands on a clock

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out distance and speed.
town-hall-md.png
 
The minute hand of the town hall clock is 3 metres long and the hour hand is 2 metres long.

Question 2Change answer

a)  A spider clings to the tip of the minute hand for exactly an hour.
     How far does the spider travel? (Use   = 3.14) metres 

Question 2Change answer

b)  Another spider clings to the tip of the hour hand for exactly an hour.
     How far does the spider travel? metres

Question 2Change answer

c)  The clock was put forward one hour for daylight saving.
     During this time the spider on the minute hand travelled 20 metres in 1 minute.
     What speed is this in kilometres per hour?  km/h
Task administration: 
This task can be completed with pen and paper or online (with NO auto marking).
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
circles, circumference, time, distances, speed
Description of task: 
Students calculate the distance travelled by the tips of the hands on a clock, and calculate the speed of one of the tips.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y11 (11/1999)

a)

18.84 [Accept 18.8 to 18.9]

difficult

b)

1.047 [Accept 1.04 to 1.05]

very difficult

c)

1.2

very difficult
Diagnostic and formative information: 

 

Common error

Likely calculation

Likely reason

a)

 

9.42

28.26

3 × 3.14

32 × 3.14

Uses radius (3) rather than diameter (6), i.e., πr rather than  πd.
Uses πr2 rather than πd, i.e., confuses circumference and area.

b)

 

12.56

6.28

4 × 3.14

2 × 3.14

Assumes hour hand travels as fast as minute hand (forgets to divide by 12).
Uses πr rather than πd and assumes hour hand travels at same speed as minute hand.

c)

.12, 12
1200


20 × 60

Wrong order of magnitude.
Speed in metres per hour rather than km/h.