Generating Polynomials: A Math Assessment Project Formative Assessment

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SWBAT demonstrate their understanding of manipulating polynomials through this formative assessment.

Big Idea

Students work together on a seemingly simple yet powerful activity using dot patterns to develop their understanding of manipulating polynomials through this engaging Mathematics Assessment Project Formative Assessment Lesson!

Pre-Assessment: Manipulating Polynomials

Students will complete the Entry Ticket: Manipulating Polynomials on Sequences and equations as outlined in the MARs formative assessment manual.

I have students complete this pre-assessment as an entry ticket at the very beginning of class and use the information to get a baseline of where students are in their understanding.

The Productive Struggle: Manipulating Polynomials

75 minutes

During the middle of the lesson, students use the Card Sort Resources: Manipulating Polynomials to engage in the productive struggle of matching different patterns of dots with matching polynomial equations in addition to creating equations from dot patterns. As a time and paper saver I made laminated copies of the card sets (enough for every 2-3 students) so I can easily replicate the activity in multiple classes and in future years to save copying time and paper. Refer to the formative assessment manual for an excellent description of the activity and common errors to look for in student learning.

Revisiting and Reflection on Manipulating Polynomials

15 minutes

The lesson concludes with students completing the Sequences and Equations (revisited) post-assessment (Exit Ticket: Manipulating Polynomials). This activity has a great pre and post assessment to provide data that can give a glimpse at not only where students started and ended, but taken together how students grew in their understanding of the concepts.

Homework: Idea Organizer and Writing Activity

For homework, I assign students to complete the Homework: Manipulating Polynomials Idea Organzier. The assignment asks students to reply to the following prompt: 

"Produce a summary of the strategies your group used to match the visual (dots) and algebraic (equations) representations of polynomials. Provide evidence to explain your reasoning."

The intent of this assignment is to help students consolidate and summarize their thinking. in addition, I want students to back up their ideas with evidence, a skill that many of the students I work with have relative difficulties with. 

The benefit to this assignment lies in its flexibility. It allows students at various levels of mathematical understanding to access and write down strategies used. The assignment is also flexible in how it can be used in the classroom. For example, a teacher might assign the Idea Organizer as an exit ticket to wrap up this lesson and give students the Sequences and Equations (revisited) post-test either for homework or as an Entry Ticket the next class. 

Students can also come into class the next day, with the Idea Organizer completed for homework, and work on writing up their response in a well-polished multi-paragraph response. 

Some students are reluctant to write in the math classroom, even saying they do not think they need to be able to write about math - my response is writing is a skill that might be the best mortar or glue around - it gives each of us the power to connect and communicate to people with various backgrounds and skill sets. Writing also can help students better understand the content because the process requires students to translate their ideas and understanding into another form. 


Mathematics Assessment Project (2012) Manipulating Polynomials: Mathematics Assessment Project Classroom Challenges: A Formative Assessment Lesson. Shell Center: University of Nottingham. Accessed online on May 26, 2014 at