Lengths of the pool

Lengths of the pool

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This resource is about solving maths problems around swimming training.

Susan swam 25 lengths of a swimming pool at a steady rate, had a 10 minute rest, then swam 15 more lengths at the same speed. In total, this took exactly half an hour.
 

a) How many lengths did Susan swim? __________
 
b) How long was she swimming for? __________
 
c) How long did Susan take to swim 1 length? __________
 
d) How long did Susan take to swim the first 25 lengths of the pool? __________
 
e)
If Susan swam at the same steady speed, how long would 100 lengths of the pool take her? 
 
__________
 
f)
How many lengths of the pool would Susan cover in 10 minutes if she swam 5 lengths every 2 minutes? 
 
__________
Task administration: 
This task is completed with pencil and paper only.
 
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
time, distances, speed, multiplication, rates
Description of task: 
This task requires students to calculate multiplication and rate problems.
Curriculum Links: 
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers and rates  to solve problems.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y8 (10/1997)
a) 40 lengths very easy
b) 20 minutes (or 1200 seconds) easy
c) 30 seconds (or 1/2 minute)
[accept if answer = b) ÷ a)]		 easy
d) 12.5 minutes or 12 minutes 30 seconds or 750 seconds
[accept if = answer to c) × 25]		 moderate
e) 50 minutes or 3000 seconds
[accept if = answer to c) × 100]		 moderate
f) 25 lengths easy

 

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
b) 30

 

 Ignores rest time.
c) 7 min. 30 sec. 30 × 25 sec. Treats 750 sec. as 7.5 min.