Odd Jobs

Odd Jobs

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about showing how to increase and decrease amounts by given percentages.

 

Karaka receives $12 pocket money each week. He can choose extra jobs to increase how much he gets each week.

  • He gets an extra 25% of his weekly pocket money if he washes the car.
  • He gets an extra 40% of his weekly pocket money if he mows the lawn.
a) Show how to work out how much he would earn in one week, if he only washes the car.
 
Show how you worked this out.
 

 
 
Answer: $__________
 
b)
 
Show how to work out how much he would earn in one week, if he only mows the lawn.
 
Show how you worked this out.
 
 

 
 
Answer: $__________
 
c)
 
Karaka had $150 of his pocket money in the bank. He took out 10% of this amount. Show how to work out how much he had left in the bank.
 
Show how you worked this out.
 
 

 
 
Answer: $__________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
percentages, discount, money, key competencies
Description of task: 
Students calculate percentage increases and decreases for odd jobs and show their working.
Curriculum Links: 
Key competencies
This resource involves recording the strategies students use to find percentage discounts. 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 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y10 (03/2004)
a) $15
Working that uses the information in the question to show the amount he would get with 25% extra, e.g., any 1 of:

  • 25 ÷ 100 × 12 = 3; 12 + 3 = 15;
  • 1.25 × 12;
  • other working (see common strategies)

[Do not accept 12 + 12/100 × 25]

 easy
easy
b) $16.80
Working that uses the information in the question to show the amount he would get with 40% extra, e.g., any 1 of:

  • 40 ÷ 100 × 12 = 4.8; 12 + 4.8 = 16.8;
  • 1.4 × 12;
  • other working (see common strategies)

[Do not accept 12 + 12/100 × 40]

 moderate
moderate
c) $ 135
Working that uses the information in the question to show the amount he would have after decreasing by 10%, e.g., any 1 of:

  • 10 ÷ 100 × 150 = 15; 150 – 15 = 135;
  • 0.9 × 150 = 135; (1 - 10 ÷ 100) × 150 = 135;
  • other working (see common strategies)  

[Do not accept 150 - 150/100 × 10]

 moderate
easy
Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a)
b)
c)		 3
4.80
15		 25% × 12
40% × 12
10% × 150		 Does not add or subtract the percentage change to or from the original amount.
a)
b)		 37
52
140		 12 + 25
12 + 40
150 - 140		 Manipulates percentages as whole numbers (other wrong answers possible with this misconception).
a)
b)
c)		 For Working
12/100 × 25
12/100 × 40
150/100 × 10		   Applies a formal algorithm without an understanding of percentage. Misrepresents the percentage as a fraction, e.g., for a) gives 12/100 instead of 25/100
NOTE: Students still get marks for a correct answer.

 

Common correct strategies

Strategy name Percentage using strategy*
Fraction of 100
a)  25/100 × 12 = 3 or 25 × 12 ÷ 100
b)  40/100 × 12 = 4.80 or 40 × 12 ÷ 100
c)  10/100 × 150 = 15 or 10 × 150 ÷ 100		 17%
20%
19%
Simple fraction
a)  25% = 1/4 , and 1/4 of 12 = 3
b)  40%= 4/10 , and 4/10 of 12 = 4.80
c)  10% = 1/10 , and 1/10 of 150 = 15		 12%
1%
4%
Statement about percentage
a) 25% = 3 or 12 × 25% = 3
b)  40% = 4.8 or 12 × 40% = 4.80
c)  10% = 15 or 150 × 10% = 15		 9%
9%
9%
Using decimal
a)  25% = 0.25, and 0.25 × 12 = 3
b)  40% = 0.4, and 0.4 × 12 = 4.80
c)  10% = 0.1, and 0.1 × 150 = 150		 9%
9%
9%
Extended decimal
a)  1.25 × 12 = 15
b)  1.4 × 12 = 16.8
c)  0.9 × 150 = 135		 13%
12%
11%
Partitioning
a) 1/2 of 1/2 of 12 = 3 or 12 ÷ 10 = 1.2, 1.2 × 2.5 = 3
b)  12 ÷ 10 = 1.2, and 1.2 ×  4 = 4.80 or 1/10 = 1.20 so 4/10 = 4.80
c)  150 ÷ 10 = 15		 5%
5%
6%

*Results based on a trial of 169 students at Year 10 in March 2004.