Tag Archives: factoring

Monomial Partners

“What’s your name, what’s your monomial?”

This is a great activity that was inspired by Matt Vaudrey’s Equation Speed Dating.  In this lesson each student gets to create their own monomial – which I constrained to having to be even and with a variable.  Then they break up their paper into three columns:  Partner / Our Binomial / Our Rectangle.  The students pick a partner and join each others monomials together to create “Our Binomial”.  Then they factor their binomial and represent it as a rectangle by labeling it’s dimensions and indicating the area.  I circulate the room and once it appears every group is finished, I have everyone get up and find a new partner.  I’m demanding here that all students get up out of their seats and move somewhere new.


After a couple rounds I started having them draw their monomial and their partners monomial as separate rectangles, and then draw them together.

I have been focusing on a geometric approach to factoring, so the rectangle column was a great addition to previous times when I have done this activity but only asked for the solution.

The column “Our Binomial” does a nice job reinforcing that a binomial is the combination of two monomials.

The Advice

Don’t require them to say “what’s your monomial?”, “do you agree that our binomials is….  “, but inspire them to say it by modeling it.  A lot of my students were saying it because I was giving them messages that anytime they get the chance to say “monomial” or “binomial” they need to take it.

Tell the students not to move onto a new partner when they are finished.  They need to wait until you tell them to switch partners.

Remind them that you are really counting on the partners to catch any errors! Because you can’t do the problems on the board since every pair is working a different problem.  “And yes, you are the partner I am counting on for someone else.”

“What’s your name, what’s your monomial?”   No that’s not a pickup line for Speed Dating…  or is it?

Factoring Puzzle – Practice Version

The Overview:

I wrote about a factoring puzzle I found online here.  That puzzle is difficult because it has trinomials with a leading coefficients other than 1, as well as special products.  I wanted to create a puzzle that would be a simple review on factoring trinomials where the leading coefficient is always 1, or could be 1 if the GCF is factored out first.  Thus when they eventually challenge the more difficult puzzle, their questions will be focused on factoring, rather that “I don’t get what to do?”.

I did not create a scrambled version, so obviously you will need have a TA cut out the pieces and put them into envelopes.



The Goods:



Update 1:

Thanks to a great comment from John, I have created one that does not have a border, thus allowing us to differentiate for the excelling students.  That puzzle is now included above in the original post.  The puzzle without the border is the exact same on the inside as the puzzle with the border, I will eventually make that different too when I get some time.

Factoring Puzzle

The Description:

The original puzzle can be found here.

The only thing I changed was that I added a border around the outside of the puzzle.

The puzzle above is in the correct order.  Obviously if you are going to have students cut out the pieces, then you have to scramble the order.  I have already done that, and both versions are in The Goods.  Here is what the scrambled version looks like:

I think the puzzle is too difficult if there is no border.  This is because the students might factor an expression, and then not find the answer in the puzzle.  The problem is that this might lead them to believe they have factored it incorrectly.  I believe putting the border around the outside shortens the activity to a better length, and makes for a better overall experience.

The Advice:

– I recommend using having your T.A. cutout the puzzle pieces from the finished puzzle, and then putting the pieces into separate envelops.  I used the scrambled version of the puzzle and had the students cutout the pieces, and I think too much time was wasted cutting out paper, rather that solving the puzzle.

– I recommend first having all the students find the puzzle piece that has the expressions x^2+5x-6 (it’s the top right piece).  Have them glue it on the top right corner of the answer document (under the heading “My Factoring Puzzle’).  Then have them factor it on the answer document (or separate sheet), and you do that problem on the board.  Next have them search for the answer piece (x+6)(x-1) and glue that piece in the proper place.  I would be doing this along with them on the document camera.  Then do another problem  off of one of the pieces they have glued down, so that when you finallly let them work alone, they already have three pieces glued to their paper.

– The above piece of advice is key, because I originally just told them what to do and let them do it, and I got a lot of students saying “I don’t know what to do”.

The Goods: