Movie ratios

Movie ratios

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

A multiplex cinema was showing several different movies.
 
a)
At the first movie the ratio of boys to girls was 3 : 5. There were 45 girls.
 
How many boys were there?  __________
 
b)
The ratio of children to adults at the second movie was 15 : 6. There were 35 children.
 
How many adults were there?  __________
 
c)
At the third movie the ratio of men to women to children was 1 : 2 : 5. There were 40 women at the movie.
 
 
i)
 
ii)
How many men were there?  __________
 
How many children were there? __________
 
d)
At the fourth movie the ratio of men to women to children was 4 : 14 : 22. There were 33 children at the movie.
 
 
i)
 
ii)
How many men were there? __________
 
How many women were there? __________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
ratios
Description of task: 
Students use given ratios to determine the number of people at the movies.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y10 (03/2004)
a)   27 moderate
b)   14 moderate
c) i)
ii)		 20 and
100
moderate
(for both correct)
c) i)
ii)		 6 and
21
difficult
(for both correct)
Diagnostic and formative information: 
 
 Common error Likely calculation Likely misconception
a) 15 1/3 of 45   
a) 75 45 × 5/3 Inverts ratio.
a)
b)
c) i)
d) ii)		 43
26
15
25		 45 – (5 – 3)
35 – (15 – 6)
33 – (22 – 4)
33 – (22 – 14)		 Assumes differences in ratios are equivalent to differences between absolute amounts, i.e., sees 3 : 5 as 43 : 45, 15 : 6 as 35 : 26, and
4 : 14 : 22 as 15 : 25 : 33.
c) ii) 200    Uses ratio 1 : 2 : 10.
c) ii) 50    Uses ratio 2 : 4 : 5.