This is a fairly basic warm up. The idea is to let students get used to the structure of the polynomial puzzles. Students have solved another polynomial puzzle dealing with addition and subtraction but not with multiplication and factoring. I will go through the first polynomial puzzle with students. To speed up the process I simply have the students make a square in their notebooks and divide it up like a "tic-tac-toe" board (3 rows/3 columns). You could also print each of these slides and distribute them to students. On the second puzzle, I let students complete it with their partner and then we go over it to make sure all students understand how the puzzles work. Before starting the third puzzle, I encourage students that they are going to have to use the structure of each expression to determine how to fill in the missing boxes (MP7). After letting students try the third puzzle, I will look for a volunteer to explain their thinking to the class (MP3).
Allow students to work in partners to complete each polynomial puzzle. Some pairs of students may come close to finishing in the 25 minutes, others may not make as much progress. In either case, students are forced to think flexibly and abstractly in order to complete each puzzle (MP2). NOTE: Puzzle #3 is typically where students will struggle. Watch for students who are multiplying the binomials but simply multiplying the first and last terms of each expression (example: (x+3)(2x-2) = 2x^2-6). This is a conceptual misunderstanding that you will want to address immediately to prevent issues when factoring trinomials in future lessons.
Students may not realize that they are factoring to complete each puzzle. That is okay. The thinking required is what you want to focus on. For example, when you questions students about their thinking, you may hear them explain it as follows, "I needed to think, what times 15x+6 is going to give me 30x^2+6x?" This type of flexible thinking will really help students as they get further into the factoring portion of this unit.
This ticket out is leveled so that students can work on a task they feel comfortable with. While neither of these options includes binomials, much of the thinking required will be the same. If you have some students that have been extremely successful with the polynomial puzzle activity, you could challenge them to make up a polynomial puzzle that included binomials or even trinomials.