Solving Equations by Flow Chart - Working Backwards

Put the following real world problem on the board for students to solve within their collaborative groups.

Madison drove to the farmer’s market to purchase some apples for a homemade apple pie.  The apples were priced $6.58 per pound and were weighed to the nearest hundredth of a pound for pricing.  If Madison also purchased a cloth bag for $5 to carry the apples home and paid $21.45 total, how many pounds of apples did she purchase?

This is a great equation that requires students to work backwards because the cost per pound is a decimal and so is the weight (2.5 pounds of apples).  Even students with great number sense who guess and check will find this difficult to figure out.  The purpose of this bellringer, which you should make explicit by the end, is that we need a systematic method of finding unknown values in equations.  The numbers are not always going to be pretty whole numbers so we need another method that is always productive and precious for any type of problem and any type of numbers.  Now you have their interest in the activity today.

If you have students who guess and check and students who work methodically backwards through the problem, have both present their work at the board and discuss how easy or difficult it was to find that 2.5 pounds were purchased.

Hold a wrap up session to discuss all questions through number nine (all the flow chart questions with boxes drawn).  Really focus on how and why we work backwards through equations when we already know the end result, the answer.  Assign question 10, which has multiple equations to solve, as homework practice.  I make it a habit to post solutions to homework in Edmodo.com each night so students can check their work as they are working to finish.