Racing car combos

Racing car combos

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about finding all possible combinations.
Practical Task
At the start line of a race cars can be ordered in different ways.
For example: 2 cars could be ordered either:
 
or
1 2 2 1
------------------------------------   ------------------------------------
Cut out the pictures of the cars from the sheet and use them to help you solve the problems below.
 
a)
List all the different ways 3 cars could be ordered at the start line.
 
 
 
 
 
 
 
b)
List all the different ways 4 cars could be ordered at the start line.
 
 
 
 
 
 
 

Template sheet - cars

 

1
 
 

2
     
 

3
 

4
Task administration: 
This task is completed with pencil and paper, and other equipment.
 
[Equipment: A car template sheet for each student; scissors.]
  • This task assesses students' ability to work out and list all the different combinations for groups of cars.
  • This assessment activity can be carried out with one student at a time or a small group of students working independently.
  • The scoring guide may be copied onto an OHT to assist self/peer assessment.
Level:
3
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
combinations
Description of task: 
Students use the picture cards provided to explore and list all the possible combinations of race cars at a starting line.
Curriculum Links: 
This resource can be used to help to identify students' understanding of finding all possible outcomes.
 
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, sets 3-4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    

2 marks (for all correct)
or
1 mark (for 1-2 errors including repeats or non-valid combinations)

 a)

1, 2, 3   1, 3, 2
2, 1, 3   2, 3, 1
3, 1, 2   3, 2, 1

Accept in any order

4 marks (all correct and no repeats)
or
3 marks (for 20-23 correct)
or
2 marks (for 13-19 correct)
or
1 mark (for 6-12 correct)

 b)

1, 2, 3, 4   1, 2, 4, 3   1, 3, 2, 4
1, 3, 4, 2   1, 4, 2, 3   1, 4, 3, 2
2, 1, 3, 4   2, 1, 4, 3   2, 3, 1, 4
2, 3, 4, 1   2, 4, 1, 3   2, 4, 3, 1
3, 1, 2, 4   3, 1, 4, 2   3, 2, 1, 4
3, 2, 4, 1   3, 4, 1, 2   3, 4, 2, 1
4, 1, 2, 3   4, 1, 3, 2   4, 2, 1, 3
4, 2, 3, 1   4, 3, 1, 2   4, 3, 2, 1

Accept in any order