Math Problem Solving in Context: Part 2

Last week my second graders and I spent our math instructional time trying out a new system for working through math story problems with a partner (Math Problem Solving in Context: Part 1).  It was amazing!  There were definitely some challenges for all of us but, in the end we persevered.

I introduced the Math Buddy Chat system to students on Monday.  We worked with our math buddies to figure out the number of family members that would be attending our upcoming Wax Museum.  Step 1 (independently read the problem, identify important words and numbers and underline the question) went smoothly for each group.  Step 2 (Talk with your math buddy and make a  plan to solve the problem and decide how you will show your work) really through them for a loop.  They all wanted to start solving the problem right away.  I helped them through this step by removing all writing utensils and they reluctantly discussed their plans.

This was a challenging problem because students had 14 numbers to deal with.  Students used a variety of strategies to solve this problem and some chose math tools such as 100's charts, base 10 pieces and unifix cubes to do their figuring. When students finished step 3 (solve the problem on your own, double check your answer) they moved on to step 4 (check your answer with your buddy, if you got a different answer look to see what you did differently and rework the problem if necessary).

After the math buddies discussed step 4 the entire group took a look at each pair of students work and discussed which strategies they used to help them solve the problem.  We began to notice that each group used more than one strategy to solve the problem.  This entire lesson took one hour and twenty minutes.

The following day we used the Math Buddy Chat system again to figure out another problem that was important to us.  We wanted to know how many packages of cookies we would need to purchase if each guest that came to our museum were to have two cookies each.  Students had to figure out how many total cookies we would need and then figure out how many packages we would need if 10 cookies came in each package.  This was a doozy and every single student (struggling to excelling) worked diligently until it was time for lunch!

The second lesson is where I imagined the input/output tables coming into play.  After we looked at discussed each groups strategies I showed them how we could put the information into a table and then we named it.  It was a brief, but powerful introduction.

Things I would do differently next time:

1. Introduce the Math Buddy Chat system with a simpler problem.  Although my students persevered I think it would have been better if they had learned the system with an easier problem first.

2. When students are asked to do step 2, discuss the problem and come up with a plan, make sure they cannot write anything down.  This planning part seemed to be difficult for them to grasp and every single one wanted to skip the discussion piece.

3. Have both partners explain what their plan is before they get started (just until we get the hang of this partnership thing).

And that is it.  I learned a lot about my students understanding of place value during these lessons.  I saw clear evidence that a student I thought had full understanding of place value still held some misconceptions and a student I thought did not really understand place value actually did!

Do you use a similar system for problem solving or have one that you think works well with second graders?  If so I would love to hear about it!

Math Problem Solving in Context: Part 1

I am getting ready to teach my second graders about input/output tables.  Yes, in second grade! This is a new standard for us.  A standard I have not taught before.  I have been racking my brain all weekend trying to figure out how to teach this concept in a way that relates to the lives of my second graders.  

While reading the Teaching Addition and Subtraction Using Contextual Problems section in John A. Van de Walle & LouAnn H. Lovin's book Teaching Student-Centered Mathematics Grades K-3 I had an AHA! moment.  I LOVE those!  The authors tell us that in the United States we don't tend to go deep enough with math problem solving. That we have a tendency to have students solve a lot of problems in a single class period and the focus of most lessons is to get answers right (pg. 71). They suggest however,  that if we want our students to construct a rich understanding of subtraction and addition (or any other operation/concept you might be teaching) we should focus more attention on having students solve one or two problems and then give more time to classroom discussions on the "how" and the "why" rather than simply looking to see if the answer is right. This sounds A LOT, I MEAN EXACTLY, like what the new Common Core State Standards are asking us to do.

After digesting this section of text and thinking about what we are doing in the classroom right now I realized that we had the perfect context for some contextual story problems using addition, patterning and input/output tables.

Currently my second graders are working on a biography research project and are planning to construct a wax museum of historical figures in our gym on Thursday.  We have invited our families and they have returned RSVP's with the number of guests who plan to attend.  We are also planning to serve our guests cookies and punch to celebrate afterwards.  

My plan is to give students the numbers of family guests who plan to attend. I will ask them to work with a partner to figure out how many guests will be attending using the Math Buddy Chat system developed by Laura Candler.  After students solve the problem we will look at the different strategies students used and compare our answers.

On Tuesday I will ask students to help me figure out how many cookies we will need to have if we are planning to have enough cookies for each guest to have two cookies each.  This is where the idea for the input/output table came into play for me.  I will pose the problem to students and have them come up with a plan for solving the problem with their partners.  Afterwards we will analyze the problem solving strategies students used. I will guide students towards understanding how they could put this information into a table format to help them see the information more easily.  We will then name this strategy (make a table) and the type of table that we created (which of course will be the input/output table).

As I am typing this I am thinking of how we can continue problem solving within this context throughout the week.  For example, how many packages of cookies would we need to purchase if 10 cookies came in each package?  How much would this cost if each package cost $1.50?  Etc.

I am excited to try this with my students and see how this goes as an introduction to input/output tables.  I will post the results soon!  

Biography Math Problem Solving