Exploding Bottles

Exploding Bottles

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about fractions and percentages of whole numbers.
 
Hohepa made 12 bottles of ginger beer each week for 8 weeks. The bottles are sealed with a special bottle top and stored. Sometimes the pressure of the ginger beer causes the bottle tops to explode.
The table below shows the number of bottle tops that exploded.
 
Number of bottle tops that exploded each week
 
Week 1 2 3 4 5 6 7 8
Bottles of ginger beer made 12 12 12 12 12 12 12 12
Number of bottle tops exploded 3 1 0 4 2 0 1 1
 
a)		  
What fraction of the bottles made in week 7 exploded? __________
 
b)		  
What fraction of the bottles made in week 5 did not explode? __________
 
c)		  
What percentage of the bottles made in week 1 exploded? __________%

d)
What percentage of the bottles made in week 4 did not explode? __________%
 
e)
 
What fraction of the total number of bottle tops exploded over the whole 8 weeks? 
Write your answer in its simplest form.
 
Show your working here:
 
 
 
 
 
 
Answer: __________ 
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
fractions, percentages
Description of task: 
Students use information in a table about exploding bottles of ginger beer to find the fractions and percentages of bottles that exploded or stayed sealed in given weeks.
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)

1/12

1 mark

easy

b)

10/12 or 5/6

1 mark

easy

c)

25

1 mark

difficult

d)

66.6 [Accept 66-67]

1 mark

very difficult

e)

1/8 (solved and simplified).
12/96 , 3/24 or equivalent fraction not fully simplified.
Working indicating summing and construction of a fraction.
[NOTE: to attain a mark for working the answer does not have to be correct]

2 marks
or
1 mark
1 mark

very difficult
difficult
moderate

 

Diagnostic and formative information: 
  Common error Likely misconception
c)
d)		 3
8		 Writes the count not the percentage.
c)
d)		 30
80		 Manipulates whole numbers fractions and percentages incorrectly - constructs a percentage treating the count as a fraction out of 10 (instead of out of 12).
d) 8/12 or 2/3 Does not construct a percentage from a fraction with a non-multiple denominator.
d) 33, 33.3, or 33.333 Solves for the bottles exploded not did not explode.
e) 12 Writes the count not the fraction.

Students found constructing fractions more straight-forward than percentages. As the denominators for these questions were not multiples of 10, students were required to indicate some understanding about the nature of percentages.

 

For similar assessment resources which require working with percentages of whole numbers see Finding percentages  CD music and Percentage complete.