Card Sorts for Groups

I love card sorts.  I use them pretty often as a way for my students to show me what they have learned or to reinforce what we are learning.  I typically do card sorts with pairs because both partners remain relatively engaged while they work together to match up or group cards.  I find that card sorts with larger groups are more challenging because I worry that some students will just sit back and watch others do all the work.

After a brief chat on doing card sorts with groups by @samjshah on Twitter earlier this week, I was reminded of a method for doing a group card sort that I learned a couple years ago.  I had completely forgotten about learning this at a school PD day and was thankful for the memory prompt.  The method was presented by an amazing teacher on my campus, Ramy Mamoud.

Okay, let's take for example a card sort involving Linear, Quadratic and Exponential relationships(you could use this Card Sort) and  a group of three students.

Here's how this card sort would work:

1. Instruct the students that there is to be no talking during the first part of the sort.
2. Have the students begin by laying out all of the cards face up in front of them.
3. Instruct them to take the Title labels and lay them out to create three columns that the other cards will be added to.
4. Now silently, without any help from each other, have them take turns placing the cards into the three groups, one student going at a time,  Reinforce that they must remain silent, even if they think one of their group members is making a mistake and placing the card under the wrong title.
5. The first student in the group chooses one card from the pile and lays it under the title in which he or she thinks it belongs. The second student takes a turn and does the same.  The third student follows and the group continues going around, each member laying only one card at a time.  
6. During the silent, no talking time, you can play music for the class.
7. When all of the cards have been placed, have each group sit silently while you wait for all groups to finish.
8. When all groups are finished with this first part.  Have the students take turns again, going one at a time, to move cards that they think may have been placed incorrectly.  
9. If a student feels as if a card was placed incorrectly, they pick it up, explain to the group why they think it was placed incorrectly, and then place in the proper place.  If the group members do not agree, they should discuss and come to an agreement on where it should be placed.
10. Finally, after the groups agree on the final placement of each card, the solution can be revealed.
11. Follow up discussion might include having the groups pick a card or two that they weren't sure about, or couldn't agree upon and discuss as a class why that particular card was a struggle for them.
12. Another follow up option would be to have each member of each group choose a card and then write their justification for putting it into the group that they did.

Some thoughts on why this method of a group card sort is a great activity:  

First off, this activity is very low risk for the student.  Because they must remain silent and cannot point out a card being placed in the wrong group during the first round, students don't have to worry about being called out for being wrong.  By the time the group goes around several time to place all cards, no one remembers exactly who placed which card, so no risk of being called out at the end of the first round either.  

Second, all members are totally engaged.  While one student is placing his card, the other group members are looking over the remaining cards and deciding which one they want to place.  They will typically look for a card that they feel that they can place correctly, so they are spending some time in thought about each card as they make their decision.  

Finally, during the second round, students have the opportunity to move cards and discuss their reasoning for placing in a different group giving them time to look at and discuss cards they maybe aren't quite sure about.

I'm so glad I was reminded of this activity so that I can incorporate it into my plans for this year!

Would love to hear your thoughts!

#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.  

#MTBoS - Favorite Review Game

As part of the MTBoS Blogging initiative, I'm going to share one of my favorite games to play with my students when reviewing.  I'm a little late on this post, but wanted to share anyway.

The game is called relay race and it works almost like the relay races you used to play in gym class as a kid.  I arrange the kids in rows and each row represents a team.  I let the teams pick out a name to represent themselves and we put the team names on the board to keep track of points.  Each student has a small whiteboard and a marker.  I have a set of cards with the questions or problems on them, with the same questions/card for each row.  For example if I have 6 rows in my classroom, I would have 6 cards of each question.

The game starts by me putting the first question card on the first desk of each row, face down.  The first person in each row is not allowed to turn the card over until I say go.   When I say go, the first person in the row looks at the question and writes down all important information they need to solve on their white board, then passes the card to the person behind them.  Students are told to not start working on the problem until they have passed the card to the next person in their row, so that time is not wasted.  The second person in the row then proceeds to write down the information for the problem on their white board, and then pass to the third person in the row.  By the time the last person in the row receives the card, everyone else in their row has seen the problem and is working on the problem.  As students finish the problem, I tell them to keep their board covered so others cannot see their answer, as sharing answers results in a team penalty.

The round is over when the one of the students who is last in their row is finished and stands up.  Everyone now has to put their markers down and the round is over. I then have all the students hold up their white boards and I give a point for each correct answer in their row.  I keep a key for the questions on a clipboard for quick checking after each round.  Points are tallied on the front board.

For the next round, the students that were last in their row now come to the front and are first in their row,  everyone else moves back one seat.  This assures that it is a different person who is last in the row each time, eliminating any complaints about how the slowest person is last,etc.  I also do random bonus rounds which award 2X the points or 3X the points to keep things lively and to give hope to those teams that have gotten themselves really behind.  There is also a punishment for sharing answers, the team loses all the current points that they have. This keeps them pretty honest.

My kids absolutely love this game and it works for a variety of topics from solving systems, to solving equations, to graphing parabolas, etc.  I usually prepare about 12-16 questions,  depending on the topic and that always lasts for the 50 minute class period.

Hope you enjoy!

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!

Function Transformations

So excited about the Desmos Class Activity I created yesterday.  I was inspired by Meg Craig (@mathymeg07) of Insert Clever Math Pun Here after she shared a post about her transformations activity(here).   I was really surprised at how easy it was to set this up and am looking forward to giving this a try in my classes next week after we cover transformations.  We are planning to spend a day on translations, a day on stretching and compressing and a day on reflecting.  I will follow those three days up with this Desmos activity.

Some of these are a bit challenging, but I'm hoping my honors kiddos can handle it, maybe not without a little struggle first though.