Math As A Teachable Moment: Problem Solving

This activity should really be called Problem Solving & Problem Posing because the students do both.
I generally post a problem on the board or on chart paper (if I'm really on the ball).  Students copy down the problem in their Problem Solving books and then try to answer the problem.  The problem is usually based on a concept we are currently working in math such as:  measurement (g, kg, ml, L, perimeter, area), number operations (+, —,  ÷, X ) or time.  Students get about 8-10 minutes to work on the problem.  When they have solved the problem, they write their own problem using the same format.

There's a lot of sharing out and class discussion about HOW we solved the problem (what strategies did you use?)  Students know that they have to show their thinking...not just write down the answer!

Here are some samples of a problem we worked on a couple of weeks ago.  This was a Friday assessment, so it was on a half sheet of paper, rather than in their books.  Most students understood how to solve the problem and I was pleased to see a variety of different ways that students showed how they solved the problem.

This student decided to break down the numbers into tens and ones and then add them together.

This student broke down the digits in the tens place into tens, but then mentally multiplied the ones.

This student multiplied the 20's by 3 (even though he is showing them as 2's) and then added the ones

This student decided she was going to line them up vertically and add them up...the 'traditional' way.  She surprised me because Math and organization are not her strengths, but her work was very organized AND logical! LOL

This students decided to just add the numbers horizontally...the preferred method with many students

This student decided he wanted to be a 'lazy' mathematician and just multiply (his favourite way of adding up stuff)

This is a student created problem modeled after the problem given

Most of my students are very comfortable with this problem solving format, so I decided to switch it up a bit the other day and give them a different type of problem.  This is an example of the problem I gave them:

I am an even number.

I am greater than 20.

I am less than 50.

My digits add up to 11.

Who am I?

Some figured it out fairly quickly, but others balked at the problem.  So we reviewed what good problem solvers do and what strategies might be appropriate to try.  I was surprised that a number of students did not understand what the word digit meant...which prompted a quick mini lesson! And then I reviewed what an even and odd number were to my math challenged students.  I find this particular problem very useful for incorporating the math vocabulary we want our kids to know.

Now, they enjoy creating their own Who Am I? problems and beg me to use their example for the next problem. I think that's a good indicator of the level of engagement these kids are demonstrating.