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.
 


illustration: ginger beer bottle and glass


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
 


illustration: computer


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
 
 

illustration: pink sweet  illustration: blue sweet  illustration: blue green


c)

Atawhai sorted a bag of sweets and found for every 5 pink sweets she had 4 blue sweets and 2 green sweets.
If she had 10 green sweets, how many pink and blue did she have?
  
  __________ pink sweets                                   __________ blue sweets
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Keywords: 
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 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 pink gums [5 × ]
20 blue 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 pink 40 blue


13 pink 12 blue

5 × 10, 4 × 10


5 + 8, 4 + 8

Uses proportion instead of .

Doesn't use proportional ratio argument.