Working out ratios

Working out ratios

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out problems involving ratios.
 



a)

When Beth makes ginger beer she uses a recipe that has 3 cups of gingerbeer mix to every 2 cups of sugar.
If she uses 16 cups of sugar, how many cups of gingerbeer mix will Beth use?
 
__________ cups
 



b)

Jed decided to spend 30 minutes playing computer games after every 2 hours of study.
If he was able to have 1 hour 30 minutes playing computer games, how much study did he do?
 
__________ hours
 
 



c)

Atawhai sorted a bag of gums and found for every 5 red gums she had 4 green gums and 2 yellow gums.
If she had 10 yellow gums, how many red and green did she have?
  
  __________ red gums                                    __________ green gums
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 ratios and proportional reasoning to compute various amounts.
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: 
 

Y9 (05/1997)

Y10 (05/1997)
a) 24 [16 × ] moderate easy
b) 6 [2 × ] easy very easy
c) 25 red gums [5 × ]
20 green gums [4 × ]		 moderate
(for both correct)		 easy
(for both correct)
Diagnostic and formative information: 
  Student response Likely calculation Likely misconception
a) 48
32		 16 × 3
16 × 2		 Doesn't multiply 16 by the proportion .
b) 3 hours 2 × Uses wrong proportion.
c) 50 red 40 green


13 red 12 green

 5 × 10, 4 × 10


5 + 8, 4 + 8

 Uses proportion instead of .

Doesn't use proportional ratio argument.