#MTBoS - Questioning about Polynomial Functions

The MTBoS blogging initiative this week is about questioning strategies in class.  This is an area that I know I need to improve upon.  This year I have really been focusing on trying to be more of a facilitator and not such a lecturer in class.  I know I have a tendency to talk too much and to spoon feed my students too much.  I really want to talk less and make them think and discuss more.  I want to ask the right kinds of questions to make them really think and probe each other.  Baby steps, I keep telling myself.  I know I can't totally revamp every lesson, especially with incorporating a new curriculum in our district this year, so I am making small changes here and there, with the hopes of adding new ideas each year.

Enter our polynomial functions unit.  In the past, I have simply given notes to my students on all the ins and outs of polynomial functions.  I didn't want to do that this year.  I really wanted them to look at the equations and the graphs and figure out the patterns they saw on their own.  I stumbled upon Dylan Kanes post about Polynomial Tasks and really liked his Characteristics in a Table idea, so took that and revamped it to my needs.

After deciding what I wanted them to find in a table, I then asked questions that would hopefully drive them to discover what they needed to know.  I tried to use questions that started with "What do you notice?"  and "What pattern do you see...?"  The day was amazing.  I spoke very little.  I listened a lot and they talked a lot.

I'll discuss more of the lesson itself later, but what made this day so amazing is that the questioning strategies I chose to use really worked.  Instead of telling them to notice something, asked them what they noticed and you know what?  They ended up noticing and figuring out all of the information I would have given them in a set of lecture notes.  I have to say, it was probably my favorite lesson of  the year.

I really want to get better at asking the right questions, and do it more often than I currently do.  

Polynomial Division - Box Method

After finishing up polynomial long division and synthetic division I wanted to give this polynomial box division method a try.  I was intrigued by this method after I saw Sarah Hagan's post about it on her blog.  It wasn't a method I was familiar with, so I had to first spend some time figuring it out.  Love it!  I really thought this method would be so much easier than long division because it eliminates all the potential sign errors when subtracting in long division.

I was hoping to teach the method and practice one day, then do Sarah's box division activity on the second day.  Unfortunately we just didn't have that extra day for the activity, so we were just going to chug through it in one day.  The day before I spent quite a bit of time working through some problems myself as I didn't want to fumble over my words during the lesson and confuse the kids.  Some of them were already confused enough with all the factoring and division we had been doing.  Then sometime during the middle of the night I woke up thinking about the lesson and decided to change it up.  I decided I wasn't going to teach them this method at all, I was going to see if they could figure it out on their own.

So this is how it went...

When they walked into class I had two polynomial multiplication problems for their warm up and I asked them to do it with the box method.

When they were finished with these two problems I asked them to take the problem given and their answer and turn it into a division problem.  Then I asked them to look at an empty box and tell me where would did the divisor come from, the dividend, and the quotient for the division problem.  We diagrammed the empty box together on the white board.

After this I short discussion, I put up the following seven problems on the board and told them to use the box and see if they could figure out how to do the division problem with a box method.  That was it, all the direction I gave them.

I told them when they think they had the quotient figured out, they then needed it factor it and look for the solution in the scrambled answers in yellow.

After a few initial complaints about me not helping them, they all got busy thinking and discussing.  Talk turned to patterns and how to find each term and it was awesome!

By problem 7 they were all pros at using this method and when I polled them at the end of class on their preferred method for solving, almost all of my students thought this one was easier to figure out.  I guess we shall see on the test tomorrow.

A Soft Re-entry back into Algebra 2

That first day back is hard.  We are all used  to two weeks of staying up late and sleeping in late.  First period was especially tough with lots of sleepy kids and very little energy for thinking.  Well aware of what today would be like for the kids, I planned a fun day where we could rely on some previous learning to slowly get back in the groove.  A soft reentry back into our normal routine, as I told my students.

Before the break we started working with polynomials, even though our polynomials unit isn't until the Spring.  We had to cover a few topics before the break because the spring calendar is packed and with testing coming up later in the spring, some of it had to be moved to the fall.  The two topics covered were adding and subtracting polynomials, and multiplying polynomials, so I was on the lookout for some ideas to do a real quick review of those topics, without just giving them a boring worksheet for practice.  While browsing this past weekend, I stumbled upon Lisa Henry's site and one of her posts about some polynomial review stations she did with her classes.

I decided on three activities, two from Lisa and the other I created myself based upon an activity that Sarah Hagan did with her students using the box method for multiplication.

Activity 1 - Exponent Puzzle

I've actually used some version of the puzzle in the past with factoring trinomials and solving equations, so when I saw Lisa using one for exponent review, I decided to create my own similar puzzle.  Students have to match up the problem and solution eventually forming a 3x4 rectangular puzzle.  You can get mine here.

Activity 2 - Polynomial Cubes

This idea also came from Lisa, but I created my own list of polynomials to work with.  Students roll the two polynomial cubs and the operation cube.  The operation cube tells them to add or subtract the two polynomials.  You establish that the polynomial from the blue cube comes first, so that their work matches the self checking key.  I asked my students to do 12 rolls and they used white boards to work out their problems and check.  You can get my version here.

Activity 3 - Polynomial Multiplication Puzzles

I created 6 puzzles fashioned after a polynomial dividing activity Sarah shared on her blog.  The puzzles are pretty easy at the start, but get progressively more challenging.  I loved the way the students had to think about patterns they saw happening in the boxes.  I'm hoping to do the dividing activity with them too, so this practice will help with the learning curve on the dividing one.  Students were given "the box" as the puzzle board and all the pieces to the polynomial multiplication problem.  They had to arrange the problem parts to find the resulting solution polynomial.  The puzzles can be found here.  I copied each puzzle on a separate colored cardstock to keep them organized.

My largest class is 30, so I had about 8 copies of each activity and I had them work in pairs.  The decided which activity they wanted to start with and when they were finished they returned it to the table and grabbed a new activity.  In all of my classes, after a quick introduction about each activity, I only had 3 groups finish early, about 5 minutes before the end of class bell.  

Here are a few shots of the fun.

Hope your first day back was as fun as ours!