Combining fractions

Combining fractions

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

a) Chen, Malachi, and Rory ordered a giant pizza.

Chenate \(1 \over 3\), Malachi ate \(1 \over 4\), and Rory ate \(1 \over 5\) of the pizza.

Altogether, what fraction of the pizza did they eat? __________

 
b) In a relay, Toby ran 2\(1 \over 2\) laps, Celia ran 3\(1 \over 3\) laps, and Danica ran 4\(1 \over 4\) laps.
 

  
Altogether, how many laps, including part laps, did they run? __________

 

pets
c)

A pet shop has puppies with different-coloured coats.

\(1 \over 4\) are pure white, \(1 \over 5\) are pure black, and \(2 \over 5\) are both black and white.

The remaining puppies have no black or white colouring.

What fraction of the puppies ...
 
i)
 
ii)
 
iii)
are pure black or pure white in colouring? __________
 
have at least some white colouring? __________
 
have no black or white colouring? __________

 

Task administration: 
This task is completed with pencil and paper only.
 
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
fractions, addition, subtraction
Description of task: 
Students perform calculations using fractions with different denominators.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Additive thinking
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (10/1998)
a)     [Accept 0.783] moderate
b)   10  [Accept 10.08 or ] moderate
c) i)


ii)

iii)

   [Accept 0.45]

  [Accept 0.65]

  [Accept 0.15]

 moderate


difficult

difficult

NOTE: Accept any equivalent fractions.

 

Diagnostic and formative information: 
  Student response Likely reason
a) Calculates
c) 9, 13, 3 respectively Gives numerator of answers rather than whole fractions.
c) ii) 2/5 Sees "at least some white" to exclude "pure white"