Meg Craig (@mathymeg07) is one of those people who make your heart sing. I have learned so much from her and she shares her materials, thought, ideas, and encouragement so freely.

Last summer she announced that she would be perusing the Math Twitter Blogosphere and Twitter to find teachers who are doing cool things. This week she chose several, and I got to be one! If you click on the #Star of the Week button, it will take you to Meg's post.

Dear Meg,

Thanks for your kind words. More importantly, thank you for the encouragement you ALWAYS give and for the humor that goes with it! We love you, Meg!

Yours Truly,

Tina and the rest of the MTBoS !!

# Palmer's Ponderings

## Saturday, October 8, 2016

## Wednesday, October 5, 2016

### Getting Past Those Hurdles!

Algebra 1 and introduction to functions: I have never liked how I did this before, so I scrapped everything and borrowed some stuff I had done when I introduced polygons (developing definitions).

The link to the slides is here, but let me explain what I did at the end that seemed to make a huge difference in my students' ability to interpret a graph of a function. They can easily tell me this is a function (because I always start this unit by doing Hiker on the TI84 which uses the motion detector and they have to recreate some graphs I have created).

I started by showing this graph and asked them to share out some notices.

Then instead of doing wonders, I asked them to sit quietly for a moment and come up with a plausible story for what was going on in this graph. I let them share out stories, and they had to be able to account for what was going on in the various parts of the graph. We recorded a bunch of plausible stories. Some of the stories included manufactured goods, car races, people walking, etc.

After we were done, I tapped the screen and gave them one additional piece of information:

We went through our stories and starred the ones that made the cut, given this new information. We were left with just 2 or 3, and it was getting hard to keep talking about the Solid Line, Dotted line, and Dashed/Dotted Line. I revealed one more bit:

Ah, yes. SO much easier when we are given a key!! We went through the various stories left, accounting for that horizontal piece and the place where A and B cross. They still were voting for a car race, a trio of people walking, and a running race.

I asked what this graph was still missing. It took them WAY longer than I expected, but finally one of my most quiet students threw his hand in the air and shouted: "A TITLE !"

In triumph we showed this slide and there was a chorus of "OH!"s and some fist pumping:

Then I asked them to sit and write the story of this graph, And they were spectacular. We had spent so much time already thinking about causes and effects, they were able to do this SO much better than ever before.

But ONE of my Algebra 1 classes (small, mostly guys) kept saying NO WAY could any one run 400 meters in 60 seconds. They kept thinking about the length of a football field and just refused to believe that these numbers made sense. I had to put them on hold so we could finish the writing. I even told them if they had to change the 60 seconds to another number, I was okay with that, as long as it got incorporated into the story.

Today, I grabbed them all as they came into class and told them to drop their bags we were going outside. We walked the track and I told them that this track is 440 yards (roughly equivalent to 400 meters). As we walked I asked them to take out their phones and google what the world record is for the mile. (A mile is four laps around this track.) What? Under 4 minutes? So about how long to do one lap? They were amazed.

Then we looked up the record for the 400 meter race. Roughly 40 seconds. The world record for the 400 meter hurdles? Only 3 seconds more!

"On Friday, I will time anyone who wants to run one lap on this track. How many of you volunteers think you can get close to 60 seconds?"

When I got home today, I told Hubby about this. He suggested I let them tell me how many seconds they thought they could do it in and then I give them a range that they could be within that guess.

HOLY MACARONI, Hubby!!! You are talking absolute value equations here!!! (He's a pastor, what do they know from absolute value equations? Bloody genius, he is!)

So

I will update after we get through with this, but I am beyond excited thinking how I can introduce absolute value equations, all because I wanted to introduce functions differently!

The link to the slides is here, but let me explain what I did at the end that seemed to make a huge difference in my students' ability to interpret a graph of a function. They can easily tell me this is a function (because I always start this unit by doing Hiker on the TI84 which uses the motion detector and they have to recreate some graphs I have created).

I started by showing this graph and asked them to share out some notices.

Then instead of doing wonders, I asked them to sit quietly for a moment and come up with a plausible story for what was going on in this graph. I let them share out stories, and they had to be able to account for what was going on in the various parts of the graph. We recorded a bunch of plausible stories. Some of the stories included manufactured goods, car races, people walking, etc.

After we were done, I tapped the screen and gave them one additional piece of information:

We went through our stories and starred the ones that could still be plausible now that we had this additional information, and talked about how this domain or input information made some stories work and some not. We went through the remaining stories to be sure the various parts of the graph still made sense.

Then I gave them one more bit of information:

I asked what this graph was still missing. It took them WAY longer than I expected, but finally one of my most quiet students threw his hand in the air and shouted: "A TITLE !"

In triumph we showed this slide and there was a chorus of "OH!"s and some fist pumping:

But ONE of my Algebra 1 classes (small, mostly guys) kept saying NO WAY could any one run 400 meters in 60 seconds. They kept thinking about the length of a football field and just refused to believe that these numbers made sense. I had to put them on hold so we could finish the writing. I even told them if they had to change the 60 seconds to another number, I was okay with that, as long as it got incorporated into the story.

Today, I grabbed them all as they came into class and told them to drop their bags we were going outside. We walked the track and I told them that this track is 440 yards (roughly equivalent to 400 meters). As we walked I asked them to take out their phones and google what the world record is for the mile. (A mile is four laps around this track.) What? Under 4 minutes? So about how long to do one lap? They were amazed.

Then we looked up the record for the 400 meter race. Roughly 40 seconds. The world record for the 400 meter hurdles? Only 3 seconds more!

"On Friday, I will time anyone who wants to run one lap on this track. How many of you volunteers think you can get close to 60 seconds?"

When I got home today, I told Hubby about this. He suggested I let them tell me how many seconds they thought they could do it in and then I give them a range that they could be within that guess.

HOLY MACARONI, Hubby!!! You are talking absolute value equations here!!! (He's a pastor, what do they know from absolute value equations? Bloody genius, he is!)

So

**will be their target time, the number of seconds they think they can run the lap. And***a**b*will be the range I will give them ("You know, you have to be within plus or minus this many seconds and you can still win that candy bar.")I will update after we get through with this, but I am beyond excited thinking how I can introduce absolute value equations, all because I wanted to introduce functions differently!

## Thursday, September 29, 2016

### Intro to Segment Addition Postulate Morphed into SO Much More!

My Geometry students are a really mixed bag of abilities. Just shy of half of them are on IEPs and/or 504s. It makes it challenging to be able to figure out how to get the material introduced in ways that are accessible for all learners, including those who are not native English speakers.

Today we had only 15 minutes at the end of class to introduce the Segment Addition Postulate. I put this on the board:

Then I asked a student to go up to the board and draw how far Max walked.

"How far should I draw?"

"Until you think that is how far Max walked."

It was funny to watch her add a little bit more and then a little bit more. Why? Because she would turn to me with a questioning look and I would say, "OK. Is he done walking now? Finally she just said "Yes, he's done," and I asked a second student to go show how far Maxine walked.

I am grateful when student number 2 drew the other segment,

I asked a third student to put a point where the two met.

We called it P for "Perfect" (said with an English accent....I did that once and they now all mimic me! Whenever someone does something great they all say in unison: "Perfect!" with the appropriate English accent.)

Here is what we had so far:

Next I asked them to

S: "LOOK at it!" he exclaimed. "It's right in the middle!"

Me: "Prove it."

S: "How?"

Me: "I dunno...got any ideas?"

Someone grabbed the yardstick and measured the segments. To make it more "real" we decided to scale it: 1in = 1 yd.

Finally I asked them to come up with some questions we would be able to answer with ABSOLUTE CERTITUDE. These

THIS question led to a spontaneous Number Talk. I had not had an opportunity to do Number Talks with this group of students yet. It was SO cool. These

I particularly loved the very last one. It was SO cool, I made the kids stay quietly in their seats even though the bell was ringing b/c THIS young man noticed that if Max had

O be still, my heart.

Today we had only 15 minutes at the end of class to introduce the Segment Addition Postulate. I put this on the board:

*(Max and Maxine live on the same street.)**My friend Max walked from his house some distance to visit his friend Maxine.**Meanwhile, Maxine decided to walk out to meet him along the way.*Max |

Maxine |

Then I asked a student to go up to the board and draw how far Max walked.

"How far should I draw?"

"Until you think that is how far Max walked."

It was funny to watch her add a little bit more and then a little bit more. Why? Because she would turn to me with a questioning look and I would say, "OK. Is he done walking now? Finally she just said "Yes, he's done," and I asked a second student to go show how far Maxine walked.

I am grateful when student number 2 drew the other segment,

__Maxine__walked all the way to where__Max__seemed to have stopped. I wasn't sure how I would deal with that except to say, "Is she done walking yet? Why/why not?"I asked a third student to put a point where the two met.

We called it P for "Perfect" (said with an English accent....I did that once and they now all mimic me! Whenever someone does something great they all say in unison: "Perfect!" with the appropriate English accent.)

Here is what we had so far:

Next I asked them to

**notice**things in the story that they could say with ABSOLUTE CERTITUDE. One of the notices was that P was the midpoint. I had to intervene here and ask the student to prove it.S: "LOOK at it!" he exclaimed. "It's right in the middle!"

Me: "Prove it."

S: "How?"

Me: "I dunno...got any ideas?"

Someone grabbed the yardstick and measured the segments. To make it more "real" we decided to scale it: 1in = 1 yd.

Finally I asked them to come up with some questions we would be able to answer with ABSOLUTE CERTITUDE. These

**questions**ranged from "Are they friends?" (Yes b/c it says "his friend Maxine") to the one I had hoped for: "How far do they live from each other?"THIS question led to a spontaneous Number Talk. I had not had an opportunity to do Number Talks with this group of students yet. It was SO cool. These

**strategies**ranged from "I did the algorithm" to "I took 4 away from the 19 so that it became 15 + 15 = 30, and then added the 4 back in to get 34."I particularly loved the very last one. It was SO cool, I made the kids stay quietly in their seats even though the bell was ringing b/c THIS young man noticed that if Max had

*and not walked the extra 2 yards, Maxine would have walked an extra 2 yards which means they each would have walked 17 yards and he knew that 17 doubled was 34.***waited**O be still, my heart.

## Wednesday, August 24, 2016

### Getting Ready for Geometry

I am about to meet students from 8 sending towns in my freshman Geometry class. One thing I really HATE spending time on is doing all the basic Geometry vocabulary review. For some students it is nothing new, some others need a nudge or two, and then there are some who need a bit more.

Most of all, I am the one who gets bored. It feels like we could be doing so much more.

To that end, I have developed this activity and tried it out on some fabulous volunteers at the #mathtweetup2016 that happened this past Monday in Boston. They gave me some really helpful feedback. Thanks so much you guys!!!

Most of all, I am the one who gets bored. It feels like we could be doing so much more.

To that end, I have developed this activity and tried it out on some fabulous volunteers at the #mathtweetup2016 that happened this past Monday in Boston. They gave me some really helpful feedback. Thanks so much you guys!!!

It has taken me longer than I care to admit to tweak it and get this post written: I can give excuses about son returning, hubby taking a vacation week, and lastly Dropbox going all weird on me.... But it is still August, so now I can say I have officially participated in the Blaugust challenge!

These are the links to the vocabulary words, the images, and the teacher instructions. Please feel free to add to the images page. These are ones that I grabbed fairly quickly and one that Elissa Miller (@misscalul8) posted today!

Norma Gordon (@normabgordon) also suggested a sentence scramble: it is a way to help groups work together (Each member of the group has some words in an envelope. Together the students have to show and share out their words until each student in the group has a complete sentence.) The Sentence Scramble may be a way to BEGIN all this...Introduces working together, etc. And then as a follow up, do it with the geometry vocabulary words the next day or the day after, just to be sure the vocabulary is sticking.

## Tuesday, July 26, 2016

### TMC16: Just TRY to Explain It to Those Who Ask

Having just experienced my 3rd (and I believe BEST) Twitter Math Camp, I feel as though I should have some profound insights to share. I don't.

Instead, I want to write a letter to myself (kind of like you may have done at camp or at a church youth retreat), to remind myself of the things I learned, the people I met, and maybe even some of the "ah ha!" moments I had in those 4 days. This post is FULL of links to all sorts of things so I can find them easily.

Dear Tina,

Me: "I was a Twitter Math Camp!"

Them: "Hunh? Math Camp? What did you do, sit around and do math problems?"

Me: "Oh that would have been cool! I didn't get to do much of that...maybe a little on patterns and stuff."

Them: "So what DID you do?"

Me: "Hmmm, hard to describe. First we got to spend a day with Desmos! We got to find out all the new things they have added to the graphing calculator. You know Desmos, right? The online graphing calculator that is free? And they also have built Teacher Desmos, a site that is full of activities that are made by Desmos staff, or created and shared by other teachers, OR you can make your own! They had JUST finished creating Card Sort for Activity Builder the night before and we got to try it!"

(Noting the glazing over of the eyes, I add...)

"They gave us cool socks!.....And a pencil.....oh and a Desmos STICKER!"

What I like best about these morning sessions?

Them: "So you had a good time?"

Me: "Yes. You really had to be there. It is going to be in Atlanta next year. If you are a math teacher, you should go."

Now the Last Thing: This is the message that came from Key Note speakers (Thanks Dylan Kane), session leaders, and casual conversations: It is OK to fail. It is OK to fail more than once. It is in the failing that comes the learning. Failure is just one step closer on the path to success. (restated from poster)

Yours,

Tina

Instead, I want to write a letter to myself (kind of like you may have done at camp or at a church youth retreat), to remind myself of the things I learned, the people I met, and maybe even some of the "ah ha!" moments I had in those 4 days. This post is FULL of links to all sorts of things so I can find them easily.

Dear Tina,

**First thing**: please remember what you said to people when they asked you where you had been that week in July.Me: "I was a Twitter Math Camp!"

Them: "Hunh? Math Camp? What did you do, sit around and do math problems?"

Me: "Oh that would have been cool! I didn't get to do much of that...maybe a little on patterns and stuff."

Them: "So what DID you do?"

Me: "Hmmm, hard to describe. First we got to spend a day with Desmos! We got to find out all the new things they have added to the graphing calculator. You know Desmos, right? The online graphing calculator that is free? And they also have built Teacher Desmos, a site that is full of activities that are made by Desmos staff, or created and shared by other teachers, OR you can make your own! They had JUST finished creating Card Sort for Activity Builder the night before and we got to try it!"

(Noting the glazing over of the eyes, I add...)

"They gave us cool socks!.....And a pencil.....oh and a Desmos STICKER!"

"No, really, TMC was the BEST professional development I have ever been to: all 4 days of it!"

**Second thing**: Remember all you DIDN'T get to tell people when you came back:**A.**The morning sessions of Rehearsing Instructional Activities Together with David Wees, Jasper DiAntonio, and Caitlyn Ruggiero (I can't find her Twitter page!). We worked specifically with an Instructional Activity called Contemplate then Calculate. (You can see more of this if you click on the link above then look for that title and click again. EVERYthing they showed us is shared there. Unbelieveable.)What I like best about these morning sessions?

__it ties in perfectly with the problem solving strategies I have been working on with my students for the last two years thanks to Max Ray-Reik and the crew at Math Forum, something I learned at the first TMC I went to.__**First****it ties in perfectly with the Number Talks I started doing with my students last year thanks to Chris Harris from my 2nd TMC (and who persuaded me I really could do this with HS students), and Kristin Gray, and Crystal Morey (who co-led a fantastic on-line Number Talks book study last fall).**__Second__,__: It ties in perfectly to the 5 Practices for Orchestrating Productive Mathematical Discussions book study that several members of the SSVT Math Dept are doing this summer. I got to see the 5 Practices in action at one of the sessions thanks to Tony Riehl and Kerry Gruizenga.__**Third****Fourth:**It can be done in 15 mins using just about any interesting problem you can think of that can have multiple strategies for getting to an answer.**Side Note**: no one I sat with understood what I was talking about when I said that "Contemplate then Calculate" sounds like what the "detectives" on Mathnet (from Square One TV) used to say: "To Calculate and Cogitate" or something like that. (You have to be REALLY old to get all the references to Dragnet, Car 54, etc in this show. The puns and literary references are to groan for. Go find and watch the episodes.)**B.**I need to remember to work in time for students to reflect on their work. I was made more aware of the importance of this in Pam Wilson's session, "Mirror, Mirror on the Wall". She not only shared the different ways you can work students reflecting in to your lesson plan, but also ways in which YOU can reflect on YOUR teaching. Awesome stuff.**C**. The discussions, the friendships, the safe space to be vulnerable: how can I capture these and explain to others? (see Hannah's post or Annie's post)**Back to the First Thing:**Them: "So you had a good time?"

Me: "Yes. You really had to be there. It is going to be in Atlanta next year. If you are a math teacher, you should go."

Now the Last Thing: This is the message that came from Key Note speakers (Thanks Dylan Kane), session leaders, and casual conversations: It is OK to fail. It is OK to fail more than once. It is in the failing that comes the learning. Failure is just one step closer on the path to success. (restated from poster)

**Remember all this, Tina!**Yours,

Tina

### TMC16: Just TRY to Explain It to Those Who Ask

Having just experienced my 3rd (and I believe BEST) Twitter Math Camp, I feel as though I should have some profound insights to share. I don't.

Instead, I want to write a letter to myself (kind of like you may have done at camp or at a church youth retreat), to remind myself of the things I learned, the people I met, and maybe even some of the "ah ha!" moments I had in those 4 days. This post is FULL of links to all sorts of things so I can find them easily.

Dear Tina,

Me: "I was a Twitter Math Camp!"

Them: "Hunh? Math Camp? What did you do, sit around and do math problems?"

Me: "Oh that would have been cool! I didn't get to do much of that...maybe a little on patterns and stuff."

Them: "So what DID you do?"

Me: "Hmmm, hard to describe. First we got to spend a day with Desmos! We got to find out all the new things they have added to the graphing calculator. You know Desmos, right? The online graphing calculator that is free? And they also have built Teacher Desmos, a site that is full of activities that are made by Desmos staff, or created and shared by other teachers, OR you can make your own! They had JUST finished creating Card Sort for Activity Builder the night before and we got to try it!"

(Noting the glazing over of the eyes, I add...)

"They gave us cool socks!.....And a pencil.....oh and a Desmos STICKER!"

What I like best about these morning sessions?

Them: "So you had a good time?"

Me: "Yes. You really had to be there. It is going to be in Atlanta next year. If you are a math teacher, you should go."

Yours,

Tina

Instead, I want to write a letter to myself (kind of like you may have done at camp or at a church youth retreat), to remind myself of the things I learned, the people I met, and maybe even some of the "ah ha!" moments I had in those 4 days. This post is FULL of links to all sorts of things so I can find them easily.

Dear Tina,

**First thing**: please remember what you said to people when they asked you where you had been that week in July.Me: "I was a Twitter Math Camp!"

Them: "Hunh? Math Camp? What did you do, sit around and do math problems?"

Me: "Oh that would have been cool! I didn't get to do much of that...maybe a little on patterns and stuff."

Them: "So what DID you do?"

Me: "Hmmm, hard to describe. First we got to spend a day with Desmos! We got to find out all the new things they have added to the graphing calculator. You know Desmos, right? The online graphing calculator that is free? And they also have built Teacher Desmos, a site that is full of activities that are made by Desmos staff, or created and shared by other teachers, OR you can make your own! They had JUST finished creating Card Sort for Activity Builder the night before and we got to try it!"

(Noting the glazing over of the eyes, I add...)

"They gave us cool socks!.....And a pencil.....oh and a Desmos STICKER!"

"No, really, TMC was the BEST professional development I have ever been to: all 4 days of it!"

**Second thing**: Remember all you DIDN'T get to tell people when you came back:**A.**The morning sessions of Rehearsing Instructional Activities Together with David Wees, Jasper DiAntonio, and Caitlyn Ruggiero (I can't find her Twitter page!). We worked specifically with an Instructional Activity called Contemplate then Calculate. (You can see more of this if you click on the link above then look for that title and click again. EVERYthing they showed us is shared there. Unbelieveable.)What I like best about these morning sessions?

__it ties in perfectly with the problem solving strategies I have been working on with my students for the last two years thanks to Max Ray-Reik and the crew at Math Forum, something I learned at the first TMC I went to.__**First****it ties in perfectly with the Number Talks I started doing with my students last year thanks to Chris Harris from my 2nd TMC (and who persuaded me I really could do this with HS students), and Kristin Gray, and Crystal Morey (who co-led a fantastic on-line Number Talks book study last fall).**__Second__,__: It ties in perfectly to the 5 Practices for Orchestrating Productive Mathematical Discussions book study that several members of the SSVT Math Dept are doing this summer. I got to see the 5 Practices in action at one of the sessions thanks to Tony Riehl and Kerry Gruizenga.__**Third****Fourth:**It can be done in 15 mins using just about any interesting problem you can think of that can have multiple strategies for getting to an answer.**Side Note**: no one I sat with understood what I was talking about when I said that "Contemplate then Calculate" sounds like what the "detectives" on Mathnet (from Square One TV) used to say: "To Calculate and Cogitate" or something like that. (You have to be REALLY old to get all the references to Dragnet, Car 54, etc in this show. The puns and literary references are to groan for. Go find and watch the episodes.)**B.**I need to remember to work in time for students to reflect on their work. I was made more aware of the importance of this in Pam Wilson's session, "Mirror, Mirror on the Wall". She not only shared the different ways you can work students reflecting in to your lesson plan, but also ways in which YOU can reflect on YOUR teaching. Awesome stuff.**C**. The discussions, the friendships, the safe space to be vulnerable: how can I capture these and explain to others? (see Hannah's post or Annie's post)**Back to the First Thing:**Them: "So you had a good time?"

Me: "Yes. You really had to be there. It is going to be in Atlanta next year. If you are a math teacher, you should go."

**Remember all this, Tina!**Yours,

Tina

## Saturday, July 16, 2016

### What I Learned at Twitter Math Camp Today (and it had nothing to do with math)

Today our youngest son leaves for the Middle East via Paris. He is 26. He is an archaeologist and will be doing a dig in Israel.

I am in Minnesota at Twitter Math Camp, he is in Massachusetts. I had to say goodbye to him two days ago.

I am fearful for him. Horrible things have happened in France. Horrible things have happened in the Middle East. I shed a lot of tears last night after I called him, and again this morning when I listened to a "theme song" he posted on Facebook about heading to the Promised Land. I am afraid for his safety. Europe and the Middle East are NOT a safe places for Americans and if I had my druthers I would beg him not to go.

But that is no way for either of us to live.

This afternoon I had the opportunity to hear Jose Vilson, keynote speaker at Saturday's TMC16. His talk was titled "Race, Math, and What We're Not Talking About". There was SO much about his talk that is important, but what

__really__hit me, what really knocked the wind out of me, was this:
Jose's wife was fearful for his safety. She was fearful of him coming to Minneapolis, the place where a black man, Philando Castile, was shot by police just a couple of weeks ago. She was fearful for him, a black man, coming to this city because horrible things happen to black men in Minneapolis. I am guessing if she had her druthers, she would beg him not to come here.

But that is no way for either of them to live.

And this is what I learned at TMC16 today: While I have been shedding tears for my handsome, smart, clever, youngest son who will be traveling OUT of the safety of the United States of America, other mothers and wives are shedding tears for their sons and husbands because they are not safe IN the United States of America.

Tell me, where is the justice in that?

This is no way for anyone to live.

Now I have more that I need to figure out. Things that are MUCH more important than how I will teach quadratic functions to sophomores. I am hoping that this community which is so passionate about math and the teaching thereof, will help educate me. I am hoping that we can join together into a larger and larger community which will create a place where people of all colors and all religions are safe, and where mothers and wives will not have to shed tears because they are fearful for the safety of their sons and husbands.

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