On the first day back from Christmas break I decided to jump start the math brains of my Algebra 1 with Math Lab students.  I gave them the following problem:

You have 10 fewer quarters than dimes and 5 fewer nickels than quarters.  The total value of the coins is $4.75.  How many of each coin do you have?

I didn’t tell them until we were almost finished that this is an Algebra 2 Trig problem.  To solve it you need to write and solve a system of three equations with three variables.

I gave them about 10 minutes to work with their group without any help from me.  They could use any method – I even brought in some coins for those that need to “see” it.  You can see some of their efforts on the papers below.  A few solved it by “guess and check.”

After 10 minutes, I started prompting them with the following:

            Which do you have more of: quarters or dimes, nickels or quarters?

            Write an equation that relates the number of quarters and the
                    number of dimes.

            Do the same for nickels and quarters.

            Define variables for the number of each of the coins you have.

            What is the value of one quarter?  What is the value of all of the
                    quarters you have?

            Do the same for dimes and nickels.

            Write an equation that represents the value of all the coins you have.

We ended up finishing the problem together on the board.  And I think most of the students understood the steps and why it worked.

When we finished, I asked them why they thought I chose this problem for today.  They said:

            To get our brains going again.

            To show us that struggle is ok.

            To have us make mistakes and get the synapses firing.

            To encourage us to stick with a really hard problem and not give up.

Yay!  Growth mindset is sinking in!

Notice I didn’t tell you the answer.  Can you figure it out?  I believe in you!  You can do this!