Michael Ann Franks

Delmar Middle School

michael_ann_franks@hotmail.com

Mathematics

Grades 6-12

-Geometry

-Algebra

-Problem Solving
 

Purpose: This activity will allow the student to look for patterns within a given set of data. The student will be able to form conclusions that can be applied to problem solving by looking at simpler problems within the given problem. By looking for patterns, students will be able to apply algebraic reasoning, organization of data, and learn to express their conclusions in correct mathematical terms verbally, symbolically, and in written form.
 

Materials:

- Activity Sheets

- Scissors

- Pencil

- Paper
 

Time Required: 2-3 days (possibly more if time allows)
 

Lesson Procedure: Students will be placed in groups of two. Each team will be given a packet containing a copy of a checkerboard, a counting squares worksheet, and a clear template for assistance in counting squares. The sheets will assist the students in drawing their own conclusions in the counting activity. Students will be instructed on the procedures required to complete the activities. 

• As students are working in their groups have them explain to you what their thinking is and any conclusions that they are finding as they work through the problems.
• Have students write down any observations they are encountering on a separate sheet of paper to share with the class.
• Have the teams describe in writing how they solved their problem and the patterns that they found while doing so.

 

Upon completion of the activity the teacher will go over the activity with the class and teams. All observations should be listed on the board along with any strategies that the students have applied to their solving the problem. Have students share their prediction for a larger array of squares and try it out while creating a table for them to see.
 

Explorations and Extensions:
 

• Have teams create their own counting problem to share with the class. Teams may even be able to switch problems and try to solve them or come up with strategies for solving.
• http://math.rice.edu/~lanius/domath/page3a.html Great site for trying out all of the available problems in this area of math. (Applets) 

 

• Have students list at least two strategies that they used for solving the problem.
• Have students create a table/visual showing their thinking while solving the problem
• Have teams share their work with the class, showing their understanding of the problem.

 

• Algebra 6 - 8 

• Understanding patterns
• Represent and analyze
• Use mathematical models
• Analyze change

• Problem Solving 6 -8

• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and other contexts
• apply and adapt a variety of appropriate strategies to solve problems
• monitor and reflect on the process of mathematical problem solving

• Geometry 6 - 8

• Analyze characteristics and properties of geometric shapes
• specify location and describe spatial relationships
• Apply transformations and use symmetry to analyze situations
• Use visualization, spatial reasoning, and geometric modeling to solve problems

• Representation 6 -8

• Create and use representations to organize, record, and communicate
• Select, apply, and translate mathematical relationships
• Use representations to model and interpret

• Communication 6 - 8

• Organize and consolidate through communication
• Communicate coherently and clearly
• Analyze and evaluate thinking of others
• Use the language of mathematics to express ideas precisely

Personal Comments: This activity can be used at almost any grade level. I think by using the templates the students will not be as confused at approaching the problem as they would be without. I also believe that by showing the student how to set up a graphic display of the information they will really become involved in the problem solving itself.
 

The website that I would love to incorporate into this activity is great! I had fun solving the problems myself. The only drawback to it is the lack of time. It will take time for the students to find the site itself and familiarize themselves with it. In all actuality, a class could spend a good 2 - 3 days in the lab alone working on the problems. Unfortunately with the state standards we do not have time for such fun.....
 
 
 

February 16, 2003
 
 
 

Peer Feedback: