Fitness programme

Fitness programme

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about algebraic expressions to describe patterns.
illustration: woman doing exercise
Lia began a keep-fit exercise programme. In the first week, she exercised for 20 minutes daily.
Every week after that she added an extra 5 minutes of exercise time. In the second week she exercised for 25 minutes daily; for the third week for 30 minutes, and so on.

Question 2Change answer

a)  How many minutes exercise would she be doing in the 6th week?
 minutes per day

Question 2Change answer

b)  How many minutes will she be exercising daily in the 12th week?
 minutes per day

Question

c)  Which of these expressions describes how many minutes she would be exercising after x weeks?

    • 20x

    • 15 + x

    • 15 + 5x

    • 20 + 5x

    • 25x

Question 2Change answer

d)  Explain why this exercise programme would be impossible to do over a long time.
Task administration: 
This task is completed with pencil and paper or online with some auto-marking.
 
Copyright: 
illustration: woman doing exercise
Image: Public domain
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
number patterns, algebraic expressions, linear equations
Description of task: 
Students answer two questions about exercise times for an incrementing fitness programme. They identify an expression relating time exercised to the number of weeks on the programme, and explain why this pattern couldn't continue indefinitely.
Curriculum Links: 
Key competencies
This resource involves recognising and explaining that a particular number patterns for a real situation cannot continue indefinitely. This relates to the Key Competencies: Thinking and Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

   

Y8 (04/1997)

Y9 (04/1997)

a)

45

easy

easy

b)

75

difficult

difficult

c)

C [15 + 5x]

very difficult

very difficult

d)

The time spent exercising every day would become more than the hours in a day.

moderate

moderate

 

Diagnostic and formative information: 
 

Common error

Likely calculation

Likely misconception

a)

60 minutes

30 × 2

Doubles the exercise in week 3.

b)

90 minutes

45 × 2

Doubles the exercise in week 6.

c)

D [20 + 5x]

  

Can calculate the answer but can't recognise that at "week 0" there would have been 15 minutes of exercise.