Distance jogging

Distance jogging

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using an algebraic expression to work out answers.

 

Hine is a keen jogger. She jogged twice around the block on Monday, three times on Tuesday, but only once on Wednesday. The total distance she ran in the three days was 12 km.

a)

 

 Show how to work out the distance once around the block.

 

 

 

 Answer: __________ km
 
Here is an expression describing Hine's jogging each day for a week (from Monday to Sunday):

2x + 3x + x + 4x + 3x + 2x + 0x

b)

 

i)
 
ii)

Which day did she jog the greatest distance? ____________________
 
How far did she jog that day? __________ km
c)

 

i)
 
ii)
 
iii)

 

What does the 3 in the term 3x mean? __________________________________________
 
What does the 0 in the last term (0x) mean? _____________________________________
 
What does the x in this equation stand for? ______________________________________

 
d)

 

 Show how to find the total distance she jogged for the whole week.

 

 

 

 Answer: __________ km
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
algebraic expressions, linear equations
Description of task: 
Students solve mathematical problems involving distance, and identify parts of an algebraic expression.
Curriculum Links: 
This resource can help to identify students' ability to apply inverse operations to simple linear relationships.
 
Key Competencies
This resource involves showing how to solve simple linear equations. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y8 (11/2004)
a) 2
Shows a strategy that includes any 1 of:

  • Sums the coefficients (2 + 3 + 1), and 6 laps = 12 km;
  • 2x + 3x + x = 12, and 6x = 12;
  • x = 12 ÷ 6;
  • Other acceptable working.
 easy
easy
b) i) Thursday, or Day 4.
ii) 8 [Accept answer if consistent with answers in a) and b) i)]		 easy
moderate
c) i) 3 times/number of times around the block, and
ii) Any 1 of:

  • No laps/zero times around the block;
  • Hine did not jog on Sunday;
  • Other acceptable answer.

Distance around the block/laps/blocks/once around the block.

 moderate
difficult
d) 30 [Accept if answer is 15 × answer given in part a).]
Shows a strategy for the total distance that includes any 1 of:

  • Totals the coefficients and multiplies by 2;
  • 2x + 3x + x + 4x + 3x + 2x = 15x where x = 2;
  • Other acceptable working.

NOTE: Answer does not have to be correct to gain a mark for showing a correct strategy/working.

 difficult
moderate

Results are based on a trial set of 201 students.

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
b) ii)
d)		 4
15		 2+3+1+4+3+2 Correctly uses the coefficients of x (times around the block), but doesn't calculate the distance in km.
c) iii) times around the block   Confuses the meaning of the coefficients with the meaning of x.
d) 14
28		 2+3+4+3+2
(2+3+4+3+2) × 2		 Does not include the value of 1 for x.
Does not include the value of 1 for x, but goes on to correctly multiplies by 2 to get a total distance in km.
For similar ARB resources involving algebraic expressions at level 4 refer to: