Fitness plan

Fitness plan

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finishing a number pattern and writing a rule.
tina exercising
Petra and Sina are working together on their fitness plan. Each day they plan to jog for 5 minutes longer than the previous day.
Here is their plan.

Question 2Change answer

a)  Fill in the missing numbers in the table.
Day (d) 1 2 3 4 5 ... 10 25
Time spent jogging (t)
(minutes)
 4 9 14  

Question 2Change answer

b)  Complete this rule relating the time spent jogging (t) to the number of the day (d).
t =
 
c)  On what day would they jog for exactly 84 minutes?
 
d)  Why is it impossible for Petra and Sina to keep to this plan for a whole year?
Task administration: 
This task is completed with pencil and paper or online with some auto-marking.
Copyright: 
Image: 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 rule 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 (10/1999)
a)

19, 24
  
49
 
124

first two numbers –  very easy

third number – moderate

fourth number – difficult
b)

Any 1 of:

•   5d - 1
•   4 + 5(d - 1)
•   algebraically equivalent statement

 difficult
c) 17 moderate
d)

Because they would have to be jogging for more minutes than there are in a day.
or
Because they would be jogging continually.

 difficult
Diagnostic and formative information: 
   Common error Likely reason
a) 19, 24, 29, 34

Continues sequence for 6 and 7 days rather than 10 and 25.
b)

d + 5
+5

 Sees rule as "add on another 5 per day".