Grocery Games

Course: Grade 10 Applied Math, Topic: Using Elimination to solve systems of equations.

I brace myself for the classic question from students, "But when are we ever going to use this???"  But the question never comes, since they already know the answer: to find the cost of Jujubes and Smarties from a receipt, obviously. 

​Shamelessly appropriated from Alex Overwijk at Slam Dunk Math by my teaching partner and I, this activity is one of our favourites from the semester.  The kids love it too.  They get to problem solve and eat some candy while doing it.

Setting the stage:  I show the students a receipt from Dollarama.  What am I gunna ask you to do?

Aside from the obvious, "Who buys 4 Smarties?"  they come to "How much does one Smartie and one Jujube cost?" fairly quickly.
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So can we figure it out?  After coming up with a few different possibilities for the costs by manipulating the Smarties, Jujubes and "pennies", the conclusion is nope.  There is more than one possible answer.  
What about if I had another receipt from the same store?  Now we're getting somewhere.  The cost of a Smartie and Jujube has to work for BOTH receipts!

The Activity: After working through the example together, receipts from various stores are distributed randomly to each student in the class.  They then have to find their partner (the person who has a receipt from the same store as them) and come up to the front to get actual Smarties, Jujubes and "Pennies" (plastic squares) and then figure out how much a Smartie and Jujube costs at that store by trying different combinations with the manipulatives.  When they have an answer, they check with the teacher and are given 2 new receipts from a different store. ​​

After they solve their required 4 pairs of receipts, they ask for more.  That's when I throw one at them that doesn't have a integer solution, or one that has multiple solutions and let them debate it out amongst themselves.

After the activity: You folks realize you solved some pretty complicated math problems today?  Awesome work.  What about if I gave you a problem like this?

They realize it's not practical to use physical Smarties and Jujubes to solve the problem.  If only there was an easier way...

​Cue Elimination, with a distinct lack of "Why are we learning this."