Puzzling Polynomials and Quizzical Quadratics

To help students do a quick review of polynomial operations, I am going to have them complete some polynomial puzzlers as a warm-up and as homework. I found these puzzles on the Illuminations website of the National Council of Teachers of Mathematics which has so many great activities, lessons, interactive applets, and interesting articles. Check out this link to this specific lesson on polynomial puzzlers. Although the concept of polynomial multiplication and division should now be quite routine for our students by their senior year, I still see students make the very common typical mistakes; for example, when multiplying binomials they multiply only the first term to the first term and the last to the last but then miss their middle terms. So I am hoping  that by having this structure of the puzzle that students will catch their mistakes and have plenty of practice with multiplying and dividing polys for homework.

First present page 2 of the flipchart to students and demonstrate how the polynomial puzzlers work. So basically each row and column is multiplied and the product is put on the right (for rows) or bottom (for columns). On page 3, students text in their answer to this very basic puzzler. This is just to see if they get how to solve the puzzlers. Now for the actual warm-up problem on page 4, students should text in their answer for the bottom right corner. This will insure they have solved every section of the puzzle. While students work on this, I will now do my beginning of class routines.

Preperation: Students will need an index card for today's closure.

To close out today’s lesson, present page 5 of the flipchart and have students complete a Cliff Notes, Jr. It is important for students to take a few minutes to summarize all the review they just had and to formalize an individual plan for how they will attack solving quadratic equations in this class. I plan to remind my students again here about  Math Practice 7: Look for and make use of structure. I want them to include in their summary how the structure of a quadratic equation can affect the method of solving we choose.

Assign Homework 1 Polynomial Puzzler from NCTM’s illuminations to help students review basic binomial multiplication and factoring. 

Click here for NCTM's description of the lesson resources.