Model car fractions

Model car fractions

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about fractions of numbers.
red-car.png blue-car.png black car.png
 
Jordan, Kelly, Ariana, Kimi and Iona have some model cars.

Question 1Change answer

a)  Kelly has 24 cars and \(1 \over 4\) of them are blue. 
     How many blue cars does she have?  

Question 1Change answer

b) \(1 \over 10\) of Jordan's 50 cars are red.
      How many red cars does he have? 

Question 1Change answer

c) \(3 \over 5\) of Ariana's 25 cars are Toyotas.
     How many Toyotas does she have?  

Question 1Change answer

d)  Kimi has 8 black cars. \(1 \over 4\) of all her cars are black.
     How many cars does Kimi have altogether? 

Question 1Change answer

e) \(2 \over 3\) of Iona's cars are Fords. She has 12 Fords.
     How many cars does Iona have altogether? 
Task administration: 
This task can be completed with pencil and paper or online (with auto-marking displayed to students).
Levels:
3, 4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
fractions, fractions as operators
Description of task: 
Students calculate fractions of a total number of cars. They also calculate the total number of cars, given an identified fraction of this total.
Curriculum Links: 
This resource can help to identify students' ability to apply simple multiplicative strategies to find fractions of sets, shapes, and quantities.
 
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 4-5
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y6 (11/2003)
a) 6 easy
b) 5 moderate
c) 15 easy
d) 32 moderate
e) 18 difficult

NOTE: d) and e) may be more difficult as they require working out the total number of cars from a number of cars that constitute a given fraction.

Diagnostic and formative information: 
 

Student response

Likely calculation

Likely misconception
d)
e)		 2
8		 1/4 of 8
2/3 of 12

Misinterprets the part for the whole
Misinterprets as 1/4 of 8 rather than 4 × 8.
Misinterprets 2/3 of 12.

a)
b)
c)
d)
e)

d)
e)

4
10
3
4
3

8
12

   
  

  
  

Other Misunderstandings with Fractions
Gives the denominator of the fraction

 

Gives the number of cars stated in the question.
e) 36 12 × 3

Using denominator only
Answers as if 1/3 of the 12 cars were Fords