Swing ball competition

Swing ball competition

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about measuring full circles in a game of swing ball.

Tony and Hohepa were having a swing ball competition to see who could hit the ball and get the most full circles.


 

a) Tony won with his ball travelling 7 full circles.
 
How many metres did his ball actually travel? (Use = 3.14 approx.)
 
__________ metres

 

b) Hohepa's best hit made the ball travel 62.8 m.
How many circles did his ball go?
 
__________ circles
Level:
5
Description of task: 
Students answer questions about a ball travelling a number of full circles in a game of swing ball.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y9 (07/97) Y10 (07/97)
a) 87.92 (2 × 2 × × 7)
[Accept between 87.9 – 88.0]
difficult difficult
b) 5 (62.8 ÷ 4 ×)
[Accept between 4.9 – 5.0]
difficult difficult
Diagnostic and formative information: 
  Student response Likely calculation Likely misconception
a) 14
28
43.96
21.96
2 × 7
4 × 7
2 × 7 ×
7 ×
Wrong formula (radius × rotations)
Wrong formula (diameter × rotations)
Wrong formula (radius × rotations ×)
Wrong formula (rotations ×)
b) 31.4, 15.7, 10, 20, etc. 62.8 × 7 ÷ (answer to a)) Correctly apply a proportion argument to obtain a result consistent with part a)