Exercise programme

Exercise programme

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finishing a pattern and writing a rule.
tina exercising
Kahu decided to begin an exercise programme to get fit. On the first day they exercised for 14 minutes and they increased this by a set amount each day.

The following table records the time they spent exercising:
 
Day number (n)
1
2
3
4 
5
6
Time spent in minutes (m)
14
16
18
 
 
 
 
a)
 
Complete the table above by filling in the three missing values Day number 4,5 and 6.
 
b)
How many minutes will they exercise for on day 12? __________
 
c)
Complete this equation that relates the day number (n) with the number of minutes (m) they exercise.
 
m = ____________________
 
d)
On which day will they exercise for 60 minutes? __________
Task administration: 
This task is completed with pencil and paper only.
Copyright: 
tina exercising
http://www.publicdomainfiles.com (USG | Public domain)
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number patterns, functional rules, linear equations
Description of task: 
Students complete a table to show a fitness plan pattern, finish a equation to describe the relationship, and answer questions to demonstrate their understanding of the pattern.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

   

Y10 (11/1999)

a)

20, 22, 24

very easy

b)

36

moderate

c)

2n + 12 or 14 + 2(n – 1)
or other algebraically equivalent expressions.

difficult

d)

24 [Accept if consistent with equation given in c.)]

moderate
 

NOTE: Accept expressions such as 2 x n as being equivalent to 2n.

Diagnostic and formative information: 

 

Common error

Likely calculation

Likely reason

b)

48

24 x 2

Doubles the time spent on day 6.

c)

2
+ 2

 

Gives the amount of extra exercise each additional day.

d) 

18
23

60 = 30 x 2

Doubles the time spent on day 9 (30 minutes).
Solves by continuing sequence rather than by formula, and misses a day.