It is wonderful to be in a school like ours, where staff can so readily apply the best thinking in the field to the benefit of our students.  Current research says that students need to be able to explain procedures and facts, justify and generalize their thinking in order to raise math achievement and increase transfer of math concepts to the real world.  To bolster students' ability to prove as well as develop mathematical argumentation skill, create an environment in which students must regularly explain and justify their thinking. (Hoffman, Brefogle, Dressler 2009).

What Springwater is doing?:

 6^thgrade:  Students are asked to reflect on the following when they come into class:

Explain the Greatest Common Factor - how do you find it?

One student responded:  "It is the biggest factor for (2) numbers you get by going through all of the factors of the numbers and picking the biggest one"

Example: 12: (1,12) (2,6), (3,4)

14:  (1, 14) (2,7),

  Greatest Common Factor is:  2

This student will work throughout his lesson to refine his written explanation and move from PF: Procedures and Facts to Justification and Generalization.

7^th grade:  Applying graphing concepts and graphing calculator skills (pictured above:  Students use on-line graphic calculators to graph equations and solve problems)

7th Grade problem for parents:  A Student Council wants to throw a party for students. They decide to have a breakfast catered and they compare bids of two companies. The Catering Crew charges $8 per student. Urbandale Catering Company charges a set fee of $160 plus $6 per person.

a. Write equations relating total cost and number of students for each catering company.

b. Make a table that shows the costs for each company in cases where 20,40,60,80,100, and 120 students would attend.

c. Plot (number of students, catering costs) on a graph. Use different colors or plotting symbols for points to show the two catering companies.

d. Is there any number of students for which both companies would charge the same rental fee?

e. If 60 students signed up to come to the breakfast, which company should the Student Council select? What if 100 students signed up for the breakfast?

Can you "Justify" your answer?  Explain why by providing mathematical reasoning?  Challenge the validity of an idea by providing mathematical reasoning?  Give a mathematical defense for an idea that was challenged?

Turn in any evidence that you tried the above problem to the office and receive a prize!