One Question, Multiple Strategies

I've spoken before on the importance of teaching through problem solving, and how it truly benefits the students as it allows them to make meaning from the math, rather than us telling them what to do.  In Paul's Grade 6 class we co-taught a lesson on number patterns. This three part lesson gave us a great understanding of where the kids were at, and where we could take them next.


We began by completing a KWC -P chart with the class.  The "P" stands for plan.  We chose to add this to our regular KWC because he was finding that his students were very reluctant to get started on any type of activity, and thought that if they had some pre-discussion on what to do, they may be more independent and more successful.

As the students were working on their problem (in pairs) Paul went around and visited each pair and probed them on their thinking and ideas.  I worked with one pair a little more closely to help make sure that they were on task, and focused.  We used the assessment for learning tool (A4L) to keep track of what strategies the students were using.  Originally, we thought that they would use one of five strategies.  However, we added a sixth strategy as one group used a strategy we hadn't thought of.










We chose three different groups to share their solutions with the class as part of our whole class consolidation.  One group had the right answer, but didn't have a complete solution as I don't think they picked 13x8 = 104 on their first try!  As the group was telling us what they did, I filled in the blanks for them by using a different colour marker.  We called this "editing."  You can see samples of it below in some of the pictures.

The second group was the pair that I was working with.  We chose to have them share for multiple reasons.  One of the reasons was to build their confidence.  Both students are currently on an IEP and need a chance to participate and show their strategy.  A second reason was that they had put a lot of depth and thought into their answer and gave not only the answer, but a suggestion as to what the leftover money could be saved for.

The third group really blew our minds.  They got an answer of 7.7  At first, I thought they were way off base, but when I began to ask some questions about how the 7.7 came into play, a lot of knowledge and understanding came into play.  The 0.7 of the lawn was because the student has a dog.  Her mom doesn't cut all of the grass each time she mows because the dog likes to have longer grass to play in.  Therefore, if the student mowed her mom's lawn she wouldn't charge the full price for the lawn mowing.   She would only charge 0.7 of what her regular cost is. 

We then had the rest of the groups come and put their work up on the board in a Bansho format.  In total, we ended up with 6 different strategies that were used to solve this problem.  So much richer and more meaningful than us showing the students 1 strategy and making them use it.

Welcome Back!!!!

Welcome Back to the 2010 - 2011 School Year!

During the second last week of August I was lucky enough to be a part of Math E Motion - A week long camp for teachers and students (in Grades 6-9) which focused on teaching and learning through problem solving.  The culminating activity for the students was a hands on project that was based on a math problem they had chosen earlier on in the week.  The students picked "Under The Sea" as the theme for all of their projects.  They showed these problems to their peers, parents and friends at an afternoon long "Math Fair."

Over the course of the 5 days, they worked together in partners to take the problem off the paper and make it come to life.  In total there were 18 different projects.  Each pair had different strengths and weaknesses, and each pair was also working at different academic levels.  The end results were nothing short of spectacular!  The students really worked hard, and put forth some excellent work.  Should the program run again next summer, I highly recommend participating in it.  You will be glad that you did.  If you want to run a "Math Fair" in your school, or have questions about it, please let me know.  I'd love to work with you to make one happen!



This problem was finding out the minimum number of moves you needed to make to cut off the dragon's heads and tails - For if you made one cut, one or two more things could grow.

Probability and logical reasoning are at the heart of this activity where you had to guess which box had 2 blue balloons, 2 pink balloons and 1 blue and 1 pink balloon.

For this game you have to place the numbers 1-8 in a row to find out what the greatest possible sum could be for each row.