Real Life Math Problems

22 Nov

I stumbled upon this post by Matt Ives about Real Life Math Problems and I knew it was something I wanted to try.   Matt’s problems are typical word problems, but with all of the numbers removed.  For example, instead of, “You want to buy a cookie for $2 and some milk for .50 cents.  If you have $5 to spend, how much money will you have left over?” the problem might read, “You want to buy a cookie and some milk.  How much money will you have left?”  Students then need to figure out what information they need to solve the problem, and ask the teacher, “How much money do I have to start with?  How much money is a cookie?  How much does the milk cost?”  If children ask a relevant question, the teacher gives them the information needed.  If students ask an irrelevant question, the teacher asks them to rethink about what’s important and what information would help them.

There are so many advantages to this method of problem solving.  It avoids the classic problem of children grasping on to the numbers in a problem and immediately and randomly trying out different operations.  How many times have we seen students read a word problem and then look at us and say, “I multiply right?  Divide?  Add?  Subtract?” without any clear understanding of why they would be using a particular operation.   They’re desperate to plug and chug.  Without numbers, they have to consider what the problem is actually asking before they dive into finding a solution.

This method is also highly engaging.  Students are talking and brainstorming what possible information would be helpful.  My room was loud, but it was on-task loud, with students trying to figure out what information they needed and then what they could do with it.

Students also remain engaged with these problems for more time.  One group was stuck on the first problem for almost ten minutes.  Ten minutes is an eternity for a nine year old, but they kept trying to find the necessary information and failing, trying and failing, until eventually  they succeeded.  Their exuberance when they nailed it was that much sweeter because they’d been working at it for so long.

What Worked:

Students were placed in groups of three.  I find that 3-4 students per group tends to maximize participation of each person while providing for a lot of different ideas to be heard.   If students struggle to collaborate, I might drop it down to pairs.

The math problems grow in order of difficulty, so students began at problem one and worked down through problem 5.  They wrote what information they needed to gather, and then showed the work they did, with numbers, pictures, or words, to get the answer. Students worked on large whiteboards so they could all see and access their work (and I could see what they were doing at a glance.)  I made these whiteboards by buying showerboard at Home Depot.  They come in 8 x 4 foot sheets, which I had Home Depot cut to 2 x 3 foot boards, and then I wrapped the edges in duct tape.

One norm we’ve established is the idea that all students must “share the pen” meaning everyone gets a chance to record.  For this session, I gave each group one pen, but sometimes I give each member a different color pen, with the expectation that I should see three or four colors on the board at the end of the math period.

I required different members of the group to ask me the questions about additional information, so everyone practiced asking clear questions.  Some students had to go back to their group to clarify what they were asking me, so they got even more practice in listening and speaking to others.

At the end of the session we put the boards on a table and had a “gallery walk” of every team’s work.  Then we debriefed in a circle and talked about what went well about working together on these problems, and what was hard.

Next Steps:

I’d like to incorporate this kind of problem solving about once a week in my math class.  My class does a nice job overall of listening to each other and working together respectfully, but we probably need some more instruction in helping each other with wait time and inviting everyone to take participate, even those shy or more struggling.

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