Equivalent fractions

Equivalent fractions

Pencil and paper
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Using this Resource
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Marking Student Responses
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This task is about working with equivalent fractions.
a)   i)   Which fraction is not equivalent to \(1 \over 4\)?
             (A)   \(4 \over 16\)
             (B)   \(8 \over 32\)
             (C)   \(12 \over 64\)
             (D)   \(32 \over 128\)
 
       ii)   Which fraction is not equivalent to \(15 \over 45\)?
             (A)   \(6 \over 18\)
             (B)   \(8 \over 27\)
             (C)   \(12 \over 36\)
             (D)   \(18 \over 54\)

b)   Write these fractions in their simplest form.
 
  i) \(3 \over 15\)  = ​ ​
  ii) \(18 \over 24\)  = ​ ​
  iii) \(15 \over 21\)  =
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
equivalent fractions, simplest form
Description of task: 
Students identify equivalent fractions, and write fractions in their simplest forms.
Curriculum Links: 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to whole numbers, ratios and equivalent fractions (including decimals and percentages).
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 (03/1999)
a) i)
ii)		 C
B		 moderate
moderate
b)
i)
ii)
iii)
1/5
3/4
5/7
difficult
difficult
difficult
Diagnostic and formative information: 
  Common error Likely calculation Likely reason
 
b) i)

    ii)

    iii)
 
, ,
  Cannot simplify to simplest form.
 
b) i)

    ii)

    iii)
 

  
5

1.6

1.6
 

 = 5
= 1 r 6
= 1 r 6		 Inverts and divides (giving answer as whole number plus remainder).
 
b) i)

    ii)
 
 
1 ÷ (15 ÷ 5)

(15 ÷ 5) ÷ 7
 

 Uses wrong common factor (i.e., 5 instead of 3).