Marble fractions

Marble fractions

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding fractions of numbers and writing them in their simplest form.
 
 

 
a)

 
Maraea had 18 marbles and lost 3 of them in a game. What fraction of her marbles did she lose? 
Write your answer in its simplest form.
 
__________
 
b)
Tamatea had 18 marbles and lost 8 of them. How could you find what fraction of 18 marbles he still has? 
 

Show your working.

 

 

 

Answer (write the fraction in it's simplest form) : __________
 
c)
 
Leilani had 56 marbles and lost 7 of them. How could you find what fraction of 56 marbles she still has?
 

Show your working.

 

 

 

Answer (write the fraction in it's simplest form) : __________
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
fractions, equivalent fractions, part-whole fractions
Description of task: 
Students answer questions involving finding fractions in story problems about marbles and write their answer in its simplest form.
Curriculum Links: 
This resource can help to identify students' ability to apply multiplicative strategies to partition quantities into common fraction parts.
Key competencies:
This resource involves recording the strategies students use to express fractions of quantities. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

Y9 (03/2004)

a)

1/6 (solved and simplified)
3/18 or equivalent fraction (not simplified)

2 marks
or
1 mark

difficult
moderate

b)

5/9 (solved and simplified)
10/18 or equivalent fraction (not simplified)
Working that indicates subtraction, and constructs a fraction.
[NOTE: To attain a mark for working the answer does not have to be correct].

2 marks
or
1 mark
1 mark

difficult
difficult
moderate

c)

7/8 (solved and simplified)
49/56 or equivalent fraction (not simplified);
Working that indicates subtraction, and constructs a fraction.
[NOTE: To attain a mark for working the answer does not have to be correct].

2 marks
or
1 mark
1 mark

difficult
moderate
moderate

NOTE:  For full marks for b) and c) students are required to:

  • construct the fraction;
  • correctly simplify (either by a common factor or successive halving); and
  • show how they solved the problem.
Diagnostic and formative information: 
  Common error Likely misconception
b)
c)		 10
49		 Writes the count not the fraction.
b) 4/9 or 8/18 Solves for marbles "lost" not "still has".