Modifying Problems
Unfortunately we haven’t found any curriculum that meets all of our needs. We mostly write our own problems. However, we realize that not everyone has the time or the collaborative community to write their own curriculum. We wanted to share how you can modify current curriculum or other resources.
Here is an example of how we modified a problem from CPM Core Connections 3. The instructional goal of the problem was to address our standard 8.G.A.5 and for students to learn about the Exterior Angle Theorem.
CPM’s Version
Unfortunately we haven’t found any curriculum that meets all of our needs. We mostly write our own problems. However, we realize that not everyone has the time or the collaborative community to write their own curriculum. We wanted to share how you can modify current curriculum or other resources.
Here is an example of how we modified a problem from CPM Core Connections 3. The instructional goal of the problem was to address our standard 8.G.A.5 and for students to learn about the Exterior Angle Theorem.
CPM’s Version
Our Version
Is it possible to find the measure of angle 1 if angle 2 is 78 degrees and angle 4 is 127 degrees? Provide mathematical justification for your thinking. Rational We took out any hints or suggestions as to how the students should approach the problem. We removed the table for several reasons. First of all, the table takes away all the thinking because it tells students to add the remote interior angles and compare the sum to the exterior angle. Additionally the table imposes a specific mathematical structure and organization on students. We feel, that part of developing students mathematical habits is having them figure out their own structure and organization. By starting the problem with “ is it possible…” students are intrigued and wonder if they can find the missing angle? We also opened up the problem by allowing students to reason and think deductively. To get students to see the need for establishing the actual theorem we would simply change the angle values and ask the same question (or perhaps tell them one of the other angles). This would hopefully lead students to discovering the pattern that original table was intending. After observing this pattern, students could write a conjecture and then think about how to prove this pattern holds for any triangle and exterior angle (high ceiling). This is how mathematicians think. They observe patterns, make conjectures, and try to prove them. |