Math and Multiple Solutions

Image by: Krishnan

For the past few days I’ve been reviewing a math unit and have found that the lessons included have very few problems with multiple solutions.  I have nothing against one correct answer scenarios, although I feel as though students should be exposed to problems with multiple solutions.  There are cases where having one solution in math is mandatory, but there are other cases where multiple solutions are possible.  I believe the project in this blog post isn’t completely “open-ended”, although it does have multiple solutions. The concept of open-ended math is important because I believe that this idea is relevant in and outside of the classroom.  Students often seem more intrinsically motivated to complete open-ended problems, as it’s different than the norm.

Recently, I came across a math activity designed for the upper elementary level, (although it could work at middle school) that offers multiple solutions. Since I didn’t personally create this activity, I’d like to give credit to NRICH Project for the original idea.  Multiple math concepts are found in this project.  The concepts covered in this project include a great amount of number sense concepts: factors, multiples, square numbers, even, odd, prime, composite, and triangular numbers. This assignment covers many concepts and a teacher could informally assess students in the classroom as they facilitate the learning process.

Here’s the process that I used:

1.  Download the Word documents (you can easily edit them to meet your needs).  Here is the Word file.

2.  Review the concepts of multiples, factors, square numbers, even/odd, prime/composite, and triangular numbers.

3.  Pass out the sheets to the students. (I had one of the pages a different color than the other – better for organization)

4.  Students cut out and glue the project together. (my class took approximately 30 – 40 minutes)

5.  Review the project with the students

6.  Have the students journal about their math problem solving experience.  Extension opportunities can be found here.  The reflection and assignment could be used to show growth over time and might even be useful in a student portfolio.

Here are a few possible solutions:

Additional answers may be found here.

If you use this, please let me know how this project works in your classroom.