Speed and distance

Speed and distance

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about speed and distance maths problems.

To get to River's house, Atawhai walked slowly for 30 minutes, then stopped for 10 minutes. 

Atawhai then continued at the same walking pace for 20 minutes to reach River's house.
 

illustration: Tana walking
a)
How long did it take Atawhai to get to River's house? ____________________
 
The equation below describes Atawhai's walk.
 

(30 × x) + (10 × 0) + (20 × x) = y

 
b)
What does y stand for? 
 
 
 
 
c)
What does x stand for? 
 
 
   
d)
What part of the trip does (10 × 0) represent?
 
 
 
e)
Atawhai's walking pace was a steady 50 metres per minute, how far was it to River's house?
 
____________________
Task administration: 
This task is completed with pencil and paper only.
 
Copyright: 
Image: iStock
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
linear equations, pronumerals
Description of task: 
Students explain the variables in a linear equation involving speed and distance. They then solve the equation by substitution.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   Y10 (09/1998)
a) 1 hour or 60 minutes very easy
b) Distance difficult
c) Speed [Do not accept "slowly walking"] difficult
d) Any 1 of:

•   The 10 minutes he spent resting.
•   When he travelled no distance at all.
•   When he stopped.

 very easy
e) 2500 metres or 2.5 km difficult
Diagnostic and formative information: 
  Common error Likely reason
b) "answer"
"time"		 Sees y as the answer to the equation.
Sees y as the time rather than distance.
e) 3000 m Ignores the 10 minute stop.