Representing Polynomials is a Mars Assessment Task designed to asses how well students can translate between graphs and algebraic representations of polynomials.
To be successful in the task, students must be able to:
To warm up for the days work and assess what they already know, my students complete the Representing Polynomials Pretest.
I place students in groups of three for the next part of this lesson. These groups are selected so that they are of mixed ability and students who do not normally work together have a chance to collaborate.
Representing Polynomials Matching Activity asks students to match graphical and algebraic representations of polynomials [MP2, MP7]. Students have done work like this before earlier in the unit, but todays activity is more challenging for two reasons.
The first time this activity is used, the cards should be printed out on colored card stock and laminated. This way, students can use a wet-erase marker to draw in their own graphs and the cards can be saved for future use.
As groups work to complete the activity, I circulate around the room, using the 3 Cup System to determine which groups are struggling. Although I do not specifically tells students the correct pairings, I will give small hints to point them in the right direction when appropriate.
When groups have finished matching up the cards and drawing in their own graphs where appropriate, the class comes together for a discussion of the activity. The goal of the discussion is for students to understand each other's matching strategies and make sense of the mathematical logic of each strategy [MP3]. To foster this type of discussion, I ask the following types of questions:
Through this discussion I hope that my students will solidify their understanding of translations of polynomial graphs and the relationship between the verbal and algebraic representations of polynomial functions [MP2, MP7].
After we have thoroughly discussed the activity and my students have had the opportunity to ask any questions, I return the Representing Polynomials Pretest., which they completed at the beginning of the lesson. I ask them to use a different color to correct any responses that they feel differently about. Students turn this in to me for grading when it is complete.