Mr Toimata's Books

Mr Toimata's Books

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This task is about finding percentages of whole numbers.  

Question

illustration: lots of book
 
Mr Toimata has 150 books on his bookshelves.   
 
a) 120 of his books have hard covers. What percentage of all his books have hard covers?

    • 12 %

    • 20 %

    • 60 %

    • 80 % 

    • 120 %

Question

b)  70% of his 150 books are non-fiction. How many non-fiction books does he have?

    • 70

    • 75

    • 80

    • 105

    • 120

Question

c)  Mr Toimata knows that 4% of his 150 books are about Māori history. 
     How many books about Māori history does he have?

    • 4

    • 6

    • 8

    • 40 

    • 60

Task administration: 
This task is completed with pencil and paper or online with auto-marking.
Copyright: 
illustration: lots of book
Image: Vicky Van de Kerckhoven, Public Domain Pictures 
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
percentages
Description of task: 
Students answer multiple choice questions about finding percentages of a whole number, and express a quantity as a percentage of another.
Curriculum Links: 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to obtain percentages of whole numbers.
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)

D (80%)

easy

b)

D (105)

moderate

c)

B (6)

difficult
Diagnostic and formative information: 
 

Common error

Likely calculation

Likely misconception

b)
c)

C (80)
C (8%)

70% is 70 out of 100, so it's a little more.
4% = 4 out of 100, so it's about ×2.

Uses 100 instead of 150 as a base for calculating the percentages and adjusts using an estimate.

a)
b)
c)

E (120%)
A (70)
A(4)

  

Confuses the number with the percentage