Rescue helicopters

Rescue helicopters

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding and comparing the different costs.
 
 

Grabbem Helicopters Ltd. charges a fixed cost of $600 just to get its rescue helicopter in the air, and then an additional cost of $300 for every hour.

 

a)

 
Show how to work out the total cost of a search lasting 4 hours.
 
  

 

 

Answer: $__________
 
b)

 
 
Show how to work out how long a search would be maintained for a sum of $2 700.
 
  

 

 

Answer: __________ hours
 
c)

 

Another helicopter company, Snatchem and Co. sets up, charging no fixed start-up fee, but simply $400 per hour of in-air time.
Show how to work out which company would give the longer search for a sum of $3 600.
 
  

 

 

 

 

 

 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
linear equations, money, breakeven points, simultaneous equations
Description of task: 
Students calculate the cost of hiring a search and rescue helicopter and compare this cost with another helicopter company's charges.
Curriculum Links: 
This resource can help to identify students' ability to use inverse operations to solve simple linear relationships.
Key competencies
This resource involves showing how to solve two simple linear equations simultaneously. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 4-5
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
      Y8 (11/2004)
a)

 

 1 800
Shows a strategy involving any 1 of :

  • 600 + (4 × 300);
  • repeated addition (600 + 300 + 300 + 300 + 300);
  • other acceptable working.

[Accept 600 + 1 200, but indicate that "show how to" should use the numbers in the question stem and include all steps.]

 1 mark
1 mark		 easy
very easy
b)

 

 7
Shows a strategy involving any 1 of :

  • (2 700 - 600) ÷ 300;
  • repeated subtraction of 300 (7 times) to get to zero;
  • other acceptable working.

[Accept 2 100 ÷ 300, but indicate that "show how to" should use the numbers in the question stem and include all steps.]

 1 mark
1 mark		 easy
easy
c)

 

 Answer includes calculations of charges for both companies.
Grabbem: (3 600 - 600) ÷ 300 = 10
Snatchem: 3 600 ÷ 400 = 9
[Other acceptable methods are possible, e.g., identifying that Snatchem charges $100 per hour more and this would equate to the start-up cost ($600) after 6 hours.]		 2 marks (fully correct)
or
1 mark (1 error in working)		 moderate
easy

Results are based on a trial set of 228 students.

NOTE: In parts a) and b) students can gain a mark for showing their strategy if they use a correct method, but make some computational errors, leading to an incorrect final answer.

Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
a)
b)		 3 600
3		 900 × 4
600 + 300 = 900,
900 × 3 = 2 700.		 Assumes the start-up cost applies to every hour of the operation.
a)
b)		 1 200
9		 300 × 4
2 700 ÷ 300		 Ignores the start-up cost.
For similar resources involving linear equations and comparing costs at level 4 refer to: Washing machine repair and Which taxi?.