Vehicle weights

Vehicle weights

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about solving mathematical problems involving weight.
illustration: cars on a car transporter truck
A car-transporter is allowed to carry no more than 8 vehicles, up to a maximum total weight of 8 tonnes.
A small car weighs 800 kg and a station-wagon weighs 1200 kg. (1 tonne = 1000 kg)

Question

a)  Which three of these loads would not be allowed? Select three options.

    • 4 station-wagons and 3 small cars

    • 7 station-wagons

    • 9 small cars

    • 3 station-wagons and 5 small cars

    • 5 station-wagons and 3 small cars

Question 2Change answer

Here is an equation to describe the load of the transporter: (800 × m) + (1200 × n) = p
i)  What does the m stand for?
ii)  What does the p stand for?

Question 2Change answer

c)  If 2 station-wagons are put on the transporter, what is the largest number of small cars that can be loaded? 
 small cars [Remember the 8 vehicle maximum and the weight limit of 8 tonnes.]

Question Change answer

     Show how you worked out your answer in the space below:
Task administration: 
This task is completed with pencil and paper or online.
Copyright: 
illustration: cars on a car transporter truck
Copyright: Alex Borland | Public Domain Photos | Public Domain
Level:
4
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
linear equations, algebraic expressions, pronumerals, story problems
Description of task: 
Students solve mathematical problems involving weight. They also identify parts of the related linear equations.
Curriculum Links: 
Key competencies
This resource involves communicating how a student solved a simple linear equation. 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
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (04/1997)

Y9 (04/1997)
a)   (ii) [7 station-wagons weigh 8400 kg – too much]
(iii) [9 cars are too many, even though their weight is OK]
(v) [5 station-wagons and 3 cars weigh 8400 kg – too much]
Must get all 3 correct to obtain this mark.		 difficult difficult
b)   m = number of small cars in the load.
p = total weight of vehicles in the load [in kg].		 difficult
very difficult		 very difficult
very difficult
c) i)
ii)		 6 small cars.
(1200 × 2) + 800m must not exceed 8000, leading to a maximum value of m given by 800m = 5600. This gives 7, but can only have 6 to satisfy the condition that the maximum number of vehicles is 8.		 difficult difficult
Diagnostic and formative information: 
  Common error Likely reason
a) B, E chosen
B, D, E chosen		 8 car limit on option C ignored.
8 car limit ignored and D miscalculated.
b) i)
    ii)		 Metres, mass, mean, etc.
Tonnes (total)		 Alliterative guessing.
c) i) 7 8 car limit ignored. Other calculations correct.
Next steps: 
EXTENSION: (For group discussion)
This example leads to an interesting graphical extension, in which various combinations of numbers of station-wagons and small cars can be plotted on two axes, and the 'legal region' shaded.