## Monday, December 28, 2015

### T'is the Season for Logs...Clothesline Style

I love logs and I love teaching logs.  They are all made more fun with crowdsourcing from Twitter with:
Julie using Zombies as opener to create a need for logs
Kate's discovery activity for Log Laws
Wendy recaps her love of logs
Andrew writes about Clotheslines here with an idea from Chris Shore

I figured I would bring the Clothesline idea into high school in my logs and exponential unit.  I had fun putting together logs and exponents onto a number line.  That would be a fun activity for the kids.  It really made me think.

Log and Exponent Clothesline    I think and hope I fixed my typos and mistakes.

My husband used an old soccer net and screen spline to make this clothesline.  Of course, I added some pink duct tape:  (My Algebra 1 class used it to Limbo)

I made my number line on paper first.  Then, I chose to have 16 cards per group of 4 kids.  I wasn't sure if I wanted to use 2 clotheslines and have a competition between teams, but I decided on 1 clothesline and just compete by time.  I made 6 sets of cards.  The first set is a practice set - no logs or exponents, but still challenging with fractions, decimals, and radicals.  This would allow the class to see how it is done.  It also gave us a quick time to aim for.

I used 4x6 index cards and wrote one problem on each.  I added symbols to each group so if they got mixed up, I would be able to sort them after.  I told them they couldn't write on the cards so I could use them again but they could use the board if needed.

I did this activity on the day before Christmas break.  I returned a quiz and we went over that, then we did this for the rest of the class.  It would work well on a review day when the rest of the class might be working on something else and you call up one group at a time.  I had one group up front and the rest were the audience, planning their strategies for attack.

I teach Accelerated Algebra 2 during period 4 and 5, so I left the time results from period 4 on the board and we challenged period 5.  Rounds were the same in each class so we could compare.  At the end, I asked if anyone wanted to try it individually but no one wanted to.

I asked one group if I could record them.  They happened to be the only group to bump it and knock some of the cards off, but they laughed and had fun.

I used an online timer and let the kids start sorting.  I stopped the clock when they were done and checked their answers.  If they had something wrong, I took those cards off and re-started the timer and they fixed it.

One thing I keep stressing is that a negative exponent doesn't make it a negative number.  Some kids were still doing that.  The fractions with small denominators were hard to put in order :)

Overall, the kids that were sorting were having great conversations and working well together.  I think we all enjoyed it.

## Wednesday, December 23, 2015

### My Teacher-Created Desmos Activity - Graphing Rationals

I love seeing teachers post their own teacher-created Desmos activities on Twitter so I decided to give it a try.  I had a lesson on a worksheet that lent itself well.  Originally, it had kids writing rationals equations on paper but using Desmos, so I made it no paper - all Desmos.  I decided 16 slides would be good and it worked great time-wise.

The students graphed reciprocal graphs and rational graphs as part of their homework by using the parent graph and transformations on paper the night before.  It is a hard concept.  So, I thought this would help them.

We started class with a Desmos-made activity called Polygraph.  I have used it with quadratics and it is great.  We did it with rationals.  I gave them about 15 minutes to play each other and the class was quiet.  It was great to watch their vocabulary on my teacher dashboard.  They didn't want to end, but I directed them to my activity with the pin number.

Almost forgot, here is the link: Graphing Rational Functions

I also had them work on mine as 2-1 (2 kids to 1 computer).  This was a good idea because they helped each other and the discussion was much richer.  It jumped right in with the first slide asking them to write a reciprocal function with 3 asymptotes.  In between I asked them where in the fraction the vertical asymptotes come from, what determines the horizontal asymptotes, the holes, the slant asymptote.  My 2 favorite parts were AHA moments about holes and slant asymptotes.  They had a fraction that when graphed would have a hole.  When they looked at the graph it looks like a solid line but when they hover at x = 2, they see the point says undefined, yeah!  They said "I found the hole!"  So much more powerful than on the TI calculator.

And, then I gave them a function that had a slant asymptote and its graph (slant asymptote was not graphed).  I asked them what it was.  They did division and got the equation of the line and graphed it and voila! it checked out.

Time-wise it went great.  The difficulty level was good for my accelerated algebra 2 class.  Here is a look at some of their work from my dashboard.

j'

Another picture:  (Some misunderstandings and things that need to be addressed)

Slant asymptote question:

I was really happy that it all went so well.  The kids got a lot out of it.  It led to more discussion the next day.  The kids were discovering and engaged.  Thanks again Desmos.

## Monday, December 21, 2015

### Sorting Pennies before vacation

We are still working this week of Christmas.  Each year we sort pennies.  Then, we talk about the data collected.  Here is a picture of the kids sorting and then a picture of our dot plot.  I haven't remembered to collect anymore pennies, so I have none from 2014 or 2015.  I ask kids to predict the year that will have the most pennies represented.  Looking at the data, I ask the kids what they notice.  They usually notice the high and the low.  This class noticed it kind of dipped in the middle.  Then we talk about the HOW.  How would we find the mean, the median, the mode.  They always want to know how many pennies we sorted.  I hand out a random sized handful to each student in class.  In my first period class (not the one here), I managed to hand out exactly 300 pennies.  This class had less kids, but we still sorted 210 pennies.  Our oldest was from 1934!  The kids were working and it provided some good discussion.

## Wednesday, December 9, 2015

### Twitter and My Conference Experiences

I have had to opportunity to attend 3 conferences recently:
ATOMIM – in Maine
PCMITLP – Park City Math Institute Teacher Leadership Program in MA (town right next to me)
ATOMIC – in CT
Twitter has shaped how I experienced these conferences.
Along comes PCMITLP.  Again this happened through Tina.  I applied and got accepted to attend this two day weekend conference.  I had heard about PCMI and its three week summer conference for teachers to do some challenging math all three weeks.  This seemed like the perfect taste so I was excited.  I invited my colleague, Kathy (@kd5campbell), who is on Twitter now too.  Only 35 people were allowed to attend to keep it more intimate.  We would be working together the whole weekend.  When I walked into the room, it was so nice to know so many people already – Tina, surprise – Shawn and Tracy from Maine, Heather (@heatherkohn) from Marlboro, MA, Wendy (@wmukluk) came in from NY (all from Twitter).  And, Beth (@bethdore) was there.  She was my student teacher a few years back, so it was nice to connect again.  We got to work doing some problems that are best explained here in Tracy’s post.  Our groups kept changing and we got to network.  Most people were on twitter so I started following them.  I met Cortni (@cortnij) from CT and turns out she would be at the next conference I was going to in two days in CT– ATOMIC and so was...Shawn from Maine.  Great, the fun would continue.  Overall, it was a great atmosphere and experience and I loved it.