Put these together as an extension activity for my students on factoring. Each set is designed so that every polynomial is a possible answer, depending on students’ interpretation and knowledge.

First, credit to Christopher Danielson for the idea and Five Triangles for Set 10 above.

Dowload a PDF here, and access the google doc here (click file – copy to save your own version).

I have a few goals with this. First, I want students to slow down and consider the *properties* of polynomials, rather than just rushing through and factoring. Second, I want them to examine some structures that can allow a polynomial that looks complicated to be factored quickly and easily — these are properties that polynomials have in common but may not be apparent at first glance. Finally, I want students to get practice factoring and analyzing a variety of polynomials. There are a number in here that I doubt they will be able to solve and I put some in for my amusement, but this range would make this a useful formative assessment tool for an Algebra II class or higher.

I think one important part of this activity is to structure it so that students have an incentive to slow down. I would put students in groups, and assign each student a polynomial, asking them to argue for why it doesn’t belong. Alternatively, students could be asked to come to an agreement on which polynomial doesn’t belong before moving on. I could also see this being used in a Talking Points structure a la Elizabeth Statmore, or a gallery walk around the room.

Enjoy! I’ll report back once I’ve used these with students.

### Like this:

Like Loading...

*Related*

howardat58I like this a lot, i had to think hard for some of them.

Regarding factorising (UK speak) quadratics, do you discourage or bar the use of the famous formula. ?

dkane47Post authorFormula is required in my school’s curriculum, but comes at the very end.

I’m not sure how I feel about it. One thing we spend plenty of time doing is answering that question – “what are the zeros of the quadratic” – with technology. Students have a ton of tools at their disposal. While the quadratic formula surely has its place, I teach Algebra I, and I feel much more comfortable with it in an Algebra II context, thinking about the discriminant and its influence on the shape and structure of the function. Just my opinion, though.

Other question is whether or not to have students memorize it. We give it to students (or at least, my final is written for me, and the formula is on the formula sheet). I definitely don’t think every algebra I student in the world should memorize it, but blindly plugging in worries me as well.

In sum, I have no good answer. Glad you enjoyed the problems!

howardat58Here’s a little problem for you:

Integers between -10 and +10 (excluding zero) are picked at random and used as coefficients in a quadratic. What is the probability that the quadratic will have “nice” roots ?

I don’t know !

brianPretty cool, I like it. Great way to bring in some debate too.