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.

## Monday, December 28, 2015

## 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.

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

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.

For ATOMIM – I found out about it on Twitter. I knew Dan Meyer @ddmeyer and
Tina Cardone @crstn85 were both speaking. Dan was the keynote speaker and speaking
to a large group. I went in and grabbed a table up front. There was
one woman there and I introduced myself as Jennifer and that was her name,
too (@michaelismath) (lots of Jennifers in this story). We were checking each other out,
had she heard Dan before, did she know about this or that. Was she on
Twitter? Yes, she was. Did we follow each other? Yes, we did,
how cool. She knew Denis @mathdenisnj from NJ and twitter and he was joining us for
another session. I already followed Dennis on Twitter too, so no need for Jen
to introduce me. (Edited: I had Denis as Bob Lochel from Philly, sorry Denis) Did the rest of the conference and met up with Tina
afterwards. She was meeting Tracy (@tracyzager) from Maine and twitter after to chat,
would I like to come? Of course, I follow her on Twitter and it would be
nice to meet her in person too. She brought along her friend, Shawn (@towlemath) from
Maine. I did not follow Shawn but I added him to my list. We had
some great conversations. Turns out Shawn would be traveling to CT for the
conference I would be speaking at in CT. Great conference, great day,
great connections because I felt so comfortable.

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.

Next up is ATOMIC in CT. My friend, Jennifer (@jensilvermath) from CT and twitter
asked me over the summer if I would like to speak about MTBoS and Twitter as a
PLN. Sure, I would be honored. I spent most of the fall collecting
ideas to share, editing my keynote, adding more as more awesome tweets were
posted and more great ideas were shared. It was the ever changing
keynote. I found out that Rafranz Davis (@rafranzdavis) would be the keynote
speaker. I had heard of her in some circles, so time to start following
her and see what she is all about. At ATOMIC, I was going to present and also set up a MTBoS booth. We had our first one at NCTM in Boston and
it was so fun to connect and meet everyone I follow from Twitter. It was
like instant family. The booth was the place to be. People would
rather hang out at the booth than actually go to the sessions. It was
powerful. Jen and I set up our booth with lots of donations from our
Twitter friends (thanks Max @maxmathforum from Mathforum/NCTM, thanks Desmos @desmos, thanks Andrew
Stadel @mr_stadel from Estimation 180, thanks to Christopher Danielson @trianglemancd for the awesome
tiling turtles and a signed book), thanks to Jen for her proradians, thanks to
Ilana @tchmathculture for her donation of her book). Really, these are amazing math people
doing amazing things and the booth is a way to share that greatness. I
attended Rafranz’s keynote speech and did not know what I was in for. She
spoke to a room of 500 attendees. She spoke about her teaching experience
and how it has changed over time but the biggest change came with MTBoS!
Wow, she mentioned it – to all these people, how cool. And, then she
polled the audience (wow, that is what I was planning to do in my talk).
She asked how many people were on Twitter – about 30 hands out to 500 went
up. I have to admit, I felt a little deflated, but optimistic. Then,
she asked how many people blogged. Interestingly, I raised my hand and so
did the woman next to me. We were the only 2 in the whole room. This
was crazy to me. How were all of these teachers not connected to each
other. Why are they not getting all of the great stuff that twitter has to
share?

The ATOMIC conference is organized a little differently than other
conferences which has its good and bad parts. Prior to the conference you
must sign up for sessions – there were four sessions. It is good because
people are forced to have a plan and know where they are going. It is also
nice for the presenter because they know how much stuff to bring and plan
for. At most other conferences, if it is not interesting you, you can get
up and leave. You can chat with your friends there and decide last minute
what you want to go to. However, you might get shut out of one you really
want to go to because it is full. So, here I had Rafranz setting me up for
a great chance to get people connected to Twitter and the MTBos but I knew I
only had 15 people signed up for my talk. That is okay, you have to start
small. I commended the people who came as they were following her
challenge and taking that first step. I did poll the audience. A few
people had at least heard of Dan. Most people did not know what a 3-Act
was. I think 2 people had a Twitter name. And, 6/12 knew about
Desmos. I used plickers to collect this data so I could show them
those. I planned on starting with the poll so I could know the direction
my talk should go – how much depth to go into (or how simple to keep it).
I had a lot of slides (shhhh, 61) in my keynote, but there is just so much
goodness to share. If the conference were still two months away, I might
have gotten to 100 slides. I put all this goodness at the beginning of the
talk and then the how do I get started on Twitter at the end. Jen S from
CT and twitter who had invited me to speak and was helping me with my talk
suggested putting 3 or 4 fun activities up front, then do the how to tweet
piece, then more sharing ideas. Priceless feedback and it worked
great. I didn’t want to just stand up there and say “this is why you
should be on twitter”. I wanted to share and show them Barbie Bungee ( I
had Barbie waiting on the tables for them), show them cup stacking, show them
solve me puzzles, and we did a 3 act. I wanted them to want more and I
think it worked. And, I did get through all of the slides. I may
have overwhelmed them a bit but when I go to a conference, I like to have
something I can bring back to the classroom and use and that’s what I gave
them. I asked them to take a risk and try something new – not 20 things –
just one thing. Here is my keynote.

Jen S was an organizer of the event which helped to conveniently have our
booth as the first one when you walked in so we could grab (I mean greet) people
on their way in and introduce ourselves. It was also right across the room
from my presentation so I could steer them there as they left. And, as a
side note, she gave me Talk 8 (thanks Jen). People who went to the
presentation did stop by, took some goodies, asked so more questions. Shawn from Maine was at our booth in an NCTM capacity. Cortni kept stopping in to say hi. Rafranz hung out at the booth with us for a while. I have seen a few newbie followers on my twitter feed, so I am following them right
back. It was Max Ray who really gave me the push from NCTM in CT in 2012
and maybe I did that for a few new people
yesterday.

Now for a few pictures of the CT conference:

My table set up with Barbie:

My table set up with Barbie:

Kudos if you made it this far!

## Saturday, November 28, 2015

### I enjoy creating assessments

I really do like creating assessments, shhhhh, don't tell anyone. I went to WGU (Western Governors University) for my Masters program and my favorite class was through BYU (Brigham Young University) and it was on how to write assessments.

I have a whole process and it takes time to create the quizzes or tests I present to my students. After all, it is the way I am asking them to show me all they know to their best ability.

When I create an assessment, there is a lot that goes into this process. Here are some of the steps and questions I ask myself, not necessarily in order, but pretty close:

I have a whole process and it takes time to create the quizzes or tests I present to my students. After all, it is the way I am asking them to show me all they know to their best ability.

When I create an assessment, there is a lot that goes into this process. Here are some of the steps and questions I ask myself, not necessarily in order, but pretty close:

- I start with my unit's learning targets and pull out the big ideas. Will this problem best represent this learning target? (I find my problems from a bunch of different places or just create them myself)
- I have both non-calculator and calculator portions of the assessment. Which part should it go on? Can it be easily done with a calculator but I need them to show me all their steps? - then non-calc. Are the numbers more difficult but I want them to go deeper into a problem past the numbers - then yes, calc, do the numbers, show me the more difficult stuff.
- Do I have the best directions for each question - the details? I want to write it so the kids are clear and don't have to ask me any clarifying questions during the quiz. It does happen. I make note of it year to year, so I can update for the following year. I consider the verbs I use. Do I need to make anything possibly plural (ex. find the x-intercept(s))? How many decimal points? What is the format of the answer (ex. simplified square root form)? What is the method I want them to use or is it up to them? What notation do they need to include in their answer?
- I like problems where they get to pick how to solve something. For example, in a unit on solving systems using graphing, substitution, and elimination, I give them 3 systems set up the "best" way for them. They have to solve each using the 3 methods and explain. Or given three quadratics - solve using factoring, quadratic formula, and completing the square. I make one that is not factorable and inevitably someone chooses factoring for that one, only to answer "not factorable".
- I think about the types of numbers I am using in the problems. I teach accelerated, so they should be able to deal with fractions, decimals, large numbers, imaginary numbers, etc, but do the numbers create too much of a mess that I can't really tell if they understand the process (ex, completing the square - they should be able to do it when a is not one and gasp, b is not even)
- I think about the order in which to present the problems. Sometimes, I like to put the most difficult one first. I have learned that the accelerated kids do not like to work out of order. Must do each problem to completion in order. However, if something is just 2 points and you are stuck on it, move on, skip it, come back later. Maybe something will remind you of how to do it later in the test. By putting a difficult problem that is worth more points, they have a fresh brain to work on it, get into it and hopefully are successful with it versus as the last problem on the test where they are crunched for time and their brain is fried.
- Time is my biggest limiting factor. I try really hard to make it work in a 60 minute class. I apply the 3x rule - it should take the kids 3 times as long as me to do it. I make up the test. I then take it with my phone stopwatch on, as if I am testing, and I see how long each problem takes me. When I am done, I can see if a particular problem or page is too long. Then, I decide, why is that problem too long - is it the numbers - can I change them? Do I need to give more information so they can move along in the problem? Then, I have to start deleting. In Accelerated Algebra 2 right now, I am teaching a big unit on quadratics, polynomials, radicals, and rationals. Last year, I gave 3 quizzes on it, but this year I am consolidating to two. It is tough. It is a lot of material and I need to find the best questions to best represent what they can do. I told the kids I was working on it and I was cutting it down for time's sake but I don't like getting rid of quiz questions because they are like my babies. One students said, "I have another teacher who said the same exact thing yesterday. That's weird."
- I think about how to assign the point values. On a quiz, is that a 2 point question, a 4 point question, maybe it has so many parts it is a 6 point question? I write down the parts and points I will look for within each question. I make note of where I think they will make the mistake (ex, did they forget to multiply by the reciprocal when dividing rational expressions?)
- So, I have cut the questions down. I have checked the formatting which I also like to do. I have taken it. I edit it for typos best I can. I share it with a colleague and ask them to edit it. And, hopefully it is ready to go.
- The truth comes when the kids take it. Did they have to ask me questions? Was time okay? And, of course, how did they do on it? How will this shape what I teach moving forward or if we are heading into the test review, how does that shape what we will need to practice to get better prepared for the test. Again, I make note of these for the following year, so I can make adjustments, so it is formative for this year's students and next year's students as well.

## Monday, November 16, 2015

### Yo, Radical Mistakes Dude!

In Accelerated Algebra 2, we are working on radicals - simplifying and writing in exponential form. I taught two classes and ended the second class with an exit ticket my colleague made. I told the students they would be collected and corrected but not graded (to use them as formative assessment). When I started to look at them, I was amazed at all the different mistakes I was seeing, so I decided to turn it into an opener for the following class (today). I took pictures of the mistakes and put them into a powerpoint. There were 6 questions and I have 6 groups of students, so I invited one group at a time to go over the slide with the mistakes. I let them study it first to see if they could make sense of it, then I asked them to talk out loud about what they saw. The students in the audience were all ready to chime in, but I wanted the students at the board to discuss it. I tried to gently guide them with questions like what did the person do? Is the first step correct? Why did they do that? What should they have done? It really led to some great conversations and I hope the thought process helps clarify it for them for the future.

One that killed me was this:

Here is my powerpoint of Radical Mistakes. Feel free to use.

Yo, Radical Mistakes Dude!

One that killed me was this:

Here is my powerpoint of Radical Mistakes. Feel free to use.

Yo, Radical Mistakes Dude!

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