Animal percentages

Animal percentages

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working with percentages.
 
a) Mrs Reihana has 12 Labradors. This is 25% of all of her show dogs. 
How many show dogs does she have altogether? 

Show your working.

 

 

Answer: __________
 
b)		  
10% of all Mr Aziz's birds are parrots. 
If he has 30 parrots, how many birds does he have altogether?  

Show your working.

 

 

Answer: __________
 
c)		  
Mr Savaii has 250 fish in his fish tank.
 If 50 are goldfish, what percentage of his fish are goldfish?  

Show your working.

 

 

Answer: __________ %
 
d)		  
In Mrs Thompson's cattery 40% of her cats are ginger. 
If she has 80 cats altogether, what number of her cats are ginger?  

Show your working.

 

Answer: __________
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Key Competencies: 
Using language, symbols, and texts
Keywords: 
percentages, key competencies
Description of task: 
Students answer questions using percentages to find missing amounts, and writing percentages using given amounts.
Curriculum Links: 
This resource can help to identify students' ability to apply additive or multiplicative strategies flexibly to obtain percentages of whole numbers.
 
Key competencies:
This resource involves recording the strategies students use to find percentages of sets, shapes, and quantities. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 6-7
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y9 (03/2004)
a) 48
Working that uses the information in the question to show the total number of show dogs equalling 48. Any 1 of:

  • 25% = 1/4, so 100% is 4 lots of 12 (or successive addition);
  • 12/? = 25/100 and simplifies (formula method);
  • Other working that shows how to find 100% given 25%.
 moderate
moderate
b) 300
Working that uses the information in the question to show the total number of parrots equalling 300. Any 1 of:

  • 10% = 1/10, so 100% is 10 lots of 30 (or successive addition);
  • 30/? = 10/100 and simplifies (formula method);
  • Other working that shows how to find 100% given 10%.
 moderate
moderate
c) 20%
Working that uses the information in the question to show the total number of parrots equalling 20%. Any 1 of:

  • 50/250 = 5/25 = 1/5 = 20% (simplifying);
  • 50/250 × 100 and simplifies (formula method);
  • 50 "goes into 250 five times", and so does 20%;
  • Other working that shows how to find the percentage of 50 from 250.
 difficult
moderate
d) 32
Working that uses the information in the question to show the total number of parrots equalling 32. Any 1 of:

  • 10% = 1/10 and 1/10 of 80 = 8, and 4 × 8 = 32 (partitioning & multiplying);
  • 80 × 40/100 and simplifies (formula method);
  • 0.4 × 8 (decimal equivalent);
  • Other working that shows how to find 40% of 80.
 difficult
difficult

NOTE: For all working, the final answer does not have to be correct to attain a mark. This mark should be allocated for the communication of the attempted calculation as well as a stepwise sequence that could lead to a correct answer.

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a)
b)		 3
30		 25% of 12
10% of 300		 Treats the part as a whole.
c) 5 250 ÷ 50 Inverts the ratio 50 ÷ 250.
c) 25   Sees 50 ÷ as 1/4 -> 25%.
b)
c)
d)		 40
125
40
30		 10% + 30
50% of 250
80 - 40%
If 50% = 40,
then 40% = 40 - 10.		 Confuses percentages with whole numbers, and manipulates accordingly.
d) 50 40 is 50% of 80. Finds the percentage for 40 out of 80.
d) 20 1/4 of 80 Understands 40% to be equivalent to 1/4.