Printing costs

Printing costs

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding which of two companies has the best price for printing.
 

school-magazine-i.png

Airini is organising the printing of the school magazine. She finds the charges for two companies:

  • Weecopy services charge 10 cents per page for any number of copies.
  • Bigpress Print charge $90 for a setting-up charge, then 8 cents per page.  
a) Show how to work out what Bigpress Print would charge for 200 copies of a 30-page magazine.

Working (i):

 


 
 

Answer (ii): $__________

b)
Airini printed another magazine with 45 pages in it. She only got 100 copies of this magazine printed. Show which company would be the cheaper?

Working (i):

 

 


 

Answer (ii): __________

 

Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Key Competencies: 
Using language, symbols, and texts
Keywords: 
linear equations, money, breakeven points
Description of task: 
Students compare the costs of printing a school magazine at two different companies.
Curriculum Links: 
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 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y10 (09/2008)
a) i)

 

   

 Working involving any one of:

  • 200 × 0.08 × 30 + 90
  • $90 + $480 (200 at $2.40 per copy) or
  • other equivalent calculations.

570

 easy

 
 
 

moderate1
a) i) ii)

 

 Working involving any one of:

  • Working  Weecopy Services charge 100 × 0.10 × 45         = $450
  • Bigpress Print charge       100 × 0.08 × 45 + 90 = $450
  • other equivalent calculations.

Both companies will charge the same amount of $450

 easy  
 
 

 

moderate2

Based on a representative sample of 161 Y10 students.

  1.   About 20% of students included all the correct elements but made a computational or place value error.
  2.   About 25% of students make a correct conclusion based upon wrong calculations.
Diagnostic and formative information: 
  Common errors Likely calculation Likely misconception
a) ii) 57 000 or
48 090 or 4890		 48 000 + 9000
200×30×10=48000;
48000 + 90		 Place value errors with money (renaming errors)
Does not convert the cents to dollars.
Mixes cents and dollars.
a) ii)   200×30×10 ÷ 100
200×30×10		 Ignores set up cost
Ignores $90
Ignores the set up cost of $90 and answer in cents.
b) i) Evaluates cost for Weecopy only    

 

Next steps: 

Place value errors with money.
Students need to recognise whether they are working with dollars or cents. They need to make the conversion between the two satisfactorily, using their knowledge that:
      $1 = 100 cents or that
      1 cent = $0.01.
ARB resources Buying electricity and Bank account both show that students confuse dollars and cents.

Ignores the set up cost.
Students need to know that Bigpress Print charge $90 as well as the costs per page of actual printing.
Search for intercepts for resources about "intercepts" which test students' understanding of this concept.