Introducing Systems

Last Thanksgiving I i was walking around Hobby Lobby and saw some little white gift boxes i was wondering if i could do anything with them in my classroom when I had an idea to use them to introduce systems of equations. I start the class by showing them two boxes like the ones below. One box contains coins and the other contains tickets. I show the boxes to the students and tell them we are going to have a contest to guess the contents of each box.

Then I direct them to these two problems on the board and ask them to solve in any way they can. I usually sweeten the pot and offer candy to the first four who can give me correct answers.

Generally is there a lot of frustration at the beginning since I won't give them any directions. After a lot of hemming and hawing, most get down to work using some type of guess and check. They get pretty frustrated because many can get the coins to add up to the correct money value only to realize they don't have the right number of coins.

Every year I am surprised who gets the answer first. Many times it is a student who struggles with algebra but for some reason perks up with a challenge like this.

After this activity, I take a set of systems word problems that have multiple choice answers and I teach them to make guess and check charts for each problem in order to solve the system.

We will move onto algebraic methods week, but I want them to have an understanding that we are solving for two different variables and they must pay close attention to the wording in the problem.