If Solving Simultaneous Equations with Matrices is the Headache…

I really struggle to think of catchy headings – so I stole this one from Dan Meyer!

My Year 10’s are currently learning Matrices – operations, determinants, inverse matrices, etc. Because this group of students “loves” forming groups and solving problems, I decided to flip the lesson (Japanese style) and start with a problem.

To give the reader some context, 3 out of 7 groups had solved the “Tourists & Guides” problem in about 30 minutes, which I found on Mike Lawler’s blog.

tourists and guides

So I wanted to give my students a big headache, before giving them the aspirin or perhaps paracetamol? Here is the problem:

Three students go into a shop and make purchases. Katie buys 3 packets of chips, 2 cans of drink and a chocolate bar and pays. $10.65. Mark buys 4 packets of chips, a can of drink and 2 chocolate bars and pays $12.60, and Tony buys 3 packets of chips and 3 chocolate bars and pays $10.95. Determine how much each item costs.

Within minutes I had a buzz of noise as students began the problem. From the students point of view:

  1. The problem did not look too difficult – money, chips, drinks and chocolate.
  2. It is real world – students often buy these items.
  3. A simple strategy – trial and error – can be quickly employed.

After 30 minutes, I started to hear groans and comments like “we are only 5 cents off”. After 45 minutes, many students gave up and went off task. At this stage I promised to show them how to use an Inverse Matrix (learned previous lesson) to quickly solve the problem (with the use of a ti-Nspire CAS calculator). Aspirin time!


Student B however, was determined to solve the problem on his own – which he did in a seperate room, taking about 90 minutes in total.


  1. I don’t plan on giving students many problems that they can’t solve in future!
  2. Next lesson we will solve with algebra.

About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
This entry was posted in Pedagogy, Problem Solving, Teaching Ideas and tagged . Bookmark the permalink.

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