This month for Thursday Tool School, I am featuring graphic organizers. For the past two weeks, I showcased Venn diagrams and how they can be used to encourage critical thinking in the classroom. Missed these fun posts? Check them out here!
Students are accustomed to solving math problems in the classroom. Many teachers even have daily problem solving routines which are intended to expose students to a wider variety of problems. Often times though, the problems that we expose students to most are traditional word problems that are analyzed using keywords or a word problem analysis model. (Read more about using keywords here.) In order to provide students with the best opportunities to become successful mathematicians and develop life-long problem solving habits, we must expose them to non-routine problems as well.
A non-routine problem is one that requires students to use more than the four basic operations to solve it. They are complex and require students to be persistent and persevere in order to find a solution. In addition, non-routine problems may have multiple solutions and/or solution paths. The problem illustrated below is an example of a non-routine problem.
Example of a Non-Routine Problem
All of the students in Ms. Green’s third grade class brought markers with their school supplies on the first day of school. Ms. Green likes to put the markers in one big plastic tub for the class to share. Some of the packs of markers had 8 markers. Some had 10 markers. If there are 23 students in the class and 200 markers in Ms. Green’s plastic tub, how many 8-packs did the students bring to school?
Initially, when students read the problem above, many are confused about the wording and will need to reread it several times in order to determine where to start. This is where the graphic organizer comes in. Students use it to help them analyze the problem and determine the essential information. This particular organizer looks like a traditional KWL chart, but it is slightly different. Instead of there being an “L” for what was learned, there is a “C” to identify special conditions. In this case, in order to solve the problem above, students should know that there are 200 markers that resulted from 23 eight- and ten-packs. The image below shows a completed graphic organizer for the problem above.
What I love most about this tool is that as a teacher, I can easily see if students have selected the right parts to answer the question. If I walk by and they do not have these special conditions written down, I know that they will have difficulty solving the problem or their solution will not match the special conditions. This becomes my opportunity to highlight them and discuss why they are important to this particular problem.
Give it a try! You can find this problem as well as other non-routine problems in my Back-to-School Problem Solving Pack. Click here or on the image below to check it out!
Freebie Alert! Click here to download a free copy of the graphic organizer above.
Sound Off! How might you use a graphic organizer to help your students analyze non-routine problems?