Car racing

Car racing

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about drawing equations on a line graph.
car       car      car

The Tamaiti brothers decided to race their remote control cars over a distance of 10 metres.

  • Malachi's car was given a 6 metre head start and it raced at 1/2 a metre per second.
  • Liam's car was given a 1 metre head start and it raced at 2 metres per second.
  • George's car was given no head start. His car raced at 1 metre per second for the first 3 seconds, then raced at 3 metres per second for the rest of the race.

Complete the graph below by drawing in lines to show the distance travelled over time (speed) for each car during the race.

 

The speed of the Tamaiti brothers' remote control cars

graph

Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
linear equations, intercepts, graph construction, distance-time graphs, speed
Description of task: 
Given their intercepts and slopes, students are required to graph three different linear equations that have been written in a practical context.
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: 

  

Y10 (11/2002)

See graph drawn below.

car-racing-graph-answers-ii.png

Malachi

  • Starting point (0,6).
  • Line drawn, slope = 1/2.

Liam

  • Starting point (0,1).
  • Line drawn, slope = 2.

George

  • Starting point (0,0).
  • Line drawn, slope = 1 for 0-3, and
  • slope = 3 when x > 3.

Clear labelling of different lines drawn/or correct key given

 
 
easy
easy
 
easy
easy
 
very easy
easy
easy
easy
Diagnostic and formative information: 
Student response Likely misconception
Malachi's starting point (1,6)
Liam's starting point (1,1)
George's starting point (1,0)		 Started plotting at time t = 1 second, instead of t = 0 seconds.
Malachi's slope = 1
Liam's slope = 1