In My Own Little Corner

It has been a difficult two weeks.

I have been told what goals I have to fulfill for my two year "self-evaluation" period, and I attended a meeting where a we were scolded for half an hour over several things that did not pertain to me. At the end of all this, I had to help students: some of whom were feeling unsafe and afraid before the election, and some of whom were feeling unsafe and afraid after the election.  Not an easy task when I, too, am feeling unsafe and afraid.  It puts me in mind of how I felt after 9/11:  I just want to gather up my most beloved family, find a little hidey hole and block out the big nasty world.  I am SO grateful for a long talk with my sister who loves and supports me, who understands this visceral need, and who expresses it so eloquently.

But in my own little corner, in 207, we continue to do fun and challenging math.  Thanks to Alex Overwijk at SlamDunkMath we have been playing with bicycle rims to learn about radians, arc length, and such.  Go visit him!  He is the MAN!  And thanks to my son and daughter-in-law who spent a rainy afternoon taking all the spokes out of 7 bicycle tires!

Here are some pix:

G. really gets "into" her work!

M and crew just "hanging" out.

We have a shortened week because of Veteran's Day, so we'll have to play with these some more the next time we get together (I see these students only every other week because we are a vocational school).  We will have only 2.5 days together next cycle, so...not sure how much we can get done.  But it is a safe place where students can work together to explore and to learn.

This is my own little corner.

#Star of the Week!

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 !!

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 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:

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 a will be their target time, the number of seconds they think they can run the lap.  And 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!

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:

(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 waited 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.

O be still, my heart.

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!!!

 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.

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,

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?

First 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.
Second, 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).
Third:  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.
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,

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?

First 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.
Second, 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).
Third:  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.
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

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.

PreCal Wrapped Up

I am following up on my shout for help.  My Pre-Cal students had been working like crazy people as we tried to finish up the curriculum and they came through with flying colors.  As a result, I wanted to make their final exam time a bit more fun, but still really educational.

I put the call out to the MTBoS and as usual they had some grand ideas!  I also chatted with the other PreCal teacher to see what she thought of this idea of creating a game or activity.  We both agreed that our students frequently come to us with areas of weaknesses.  We decided that we would focus this game idea on those areas that needed the most remediation throughout the year.

The topics were

• Positive/negative/rational exponents (switching forms, identifying equivalent expressions)
• Factoring - Quadratics and sums and differences of cubes
• Radians and degrees on the Unit Circle: being able to convert from one to the other quickly
• Parent functions and their transformations

The kids did a great job!  I shared the handout in my previous post.  Here is how they were scored.

And here they are playing the games.

"Mathletics: a Factoring Game"

"Forehead Graphs; Transformation of Functions"
(A student from a different group suggested they call it "Skin Graphs", which I
thought was hysterical, but for some reason they didn't go with it.) 

"M4th Fish:  Exponents"
A  Go Fish game where they tried to get all 4 equivalent cards.
Later they made it into just a match was good enough!

Radian-Degree Matching Game
This game had a bonus round:  after you made 3 matches, you got several
tries with the green cards to see if you could match the coordinates
of your purple degree/radian cards.

I gave them one 80 minute class to do most of the creating.  The second 90 minute class to "test drive" it in their own group and get the rules written up.  Before the class was over, they had to hand their instructions to another group who gave them feedback on the clarity of the rules/instructions.  Edits were made.

On the day of the exam we had 90 minutes.  That meant time to play 2 of 3 games, time for each group to get feedback from the others, and then 25-30 mins for them to type up and submit their reflections.  Worked out pretty well!

Things they all commented on:

• They wished there had been time enough to play all 3 games (not sure how to work this in next year.  Maybe let the group that reads the instructions also do the "test driving" and provide feedback?)
• They really enjoyed working on these topics and reviewing them. ALL agreed these were areas they had struggled with or forgotten about and felt more comfortable with them by the end of the exam time.
• They were incredibly grateful to have done this and not a paper and pencil exam.

This was a really special class.  They worked so hard all year and even in the end, they put effort into creating AND playing the games.  I am going to miss them SO much!

Looking for Feedback on PreCal Final "Exam"

This year I have an option of giving a paper and pencil final exam, or using 2 days plus the 90 minute exam window to have them do something else.  They are SUCH great kids and have worked SO hard this year, I am opting for the latter.

A few weeks ago, I tweeted out a call for what to do and got some fabulous suggestions:

The result is I am going to sort of do a combination of these.  They have seen several activity builders, they have done card sorts, but they have not yet seen WODB.  I will show them Mary's site on WODB and explain how it works.

Then I will give them this paper and let them go at it. 

The topics I am thinking of all have to do with skills that we had to spend more time on than I feel we should have, thus we didn't get as far as we should have in the curriculum:  

• negative and rational exponents (switching between forms) 
• logs and exponential functions (switching between forms) 
• factoring quadratics and sums/diffs of cubes 
• transformations of functions
• radians to degrees (switching between forms)

For any of you who read this, I would love some feedback.  Can we get this done in 2 eighty minute classes and then play them AND reflect on them in a 90 minute block?  (I am expecting that they will assign themselves homework if necessary.)  Can you think of other areas that you find yourself having to review again and again (that they SHOULD have dealt with in Algebra 2?).

Thank you to all who take a moment to read and comment!

Read This Article

This article was tweeted out by @MrVaudrey.  Go read it before you do anything else.

There is nothing more I can add except that I second Jim Doherty's (@mrdardy) thought:

“I hope I never become the teacher who stops learning.”

Jim became involved in the Math Twitter Blogosphere a few years ago, midway in his teaching career.  I met Jim at Twitter Math Camp, where I believe we were both first timers, and coincidentally, had both been teaching for 27 years (I took an 8 year break to raise my tribe of boys, and tutored during those years, so I am not counting them!)

I have learned SO much from becoming part of this on line community.  It has changed the way I teach, changed the way I question students, and changed the way I think about learning.  I have always enjoyed trying something new, but it was exhausting trying to do this for the 5 DIFFERENT courses I was teaching for most of my career (I'm down to 4 different courses this year: Yippee!).

The MTBoS is the most wonderful group of professionals ever to grace the internet.  They share resources as well as ideas.  They toss out thought provoking tweets.  They write insightful blog posts.  They organize professional development (go look up Twitter Math Camp) and charge nothing for it. They hand out virtual hugs.  They find the best places for cupcakes!

I will retire in 6 years.  But I want to make the most of the time I have left in the classroom. And so, like Jim,

“I hope I never become the teacher who stops learning.” 

Binomial Theorem, Pascal's Triangle, Sierpinski Gasket: Oh My!

I love introducing the Binomial Theorem.  I love it so much that I drag it out as warm ups for a couple of days.  We multiply and multiply and multiply.

Finally came the day we gathered all the coefficients and wrote them down row by row.

At first we wrote:

row 0 = 1
row 1 = 1 1
row 2 = 1 2 1
row 3 = 1 3 3 1
row 4 = 1 4 6 4 1

And then we noticed some patterns:  1s at beginning and end, next diagonal says 1, 2, 3, 4, ; there is symmetry to each line.

And we wondered:  1, 3, 6.....is the next number 9?

Today I asked if they could help fill in the 5th row.  They got:

row 0 = 1
row 1 = 1 1
row 2 = 1 2 1
row 3 = 1 3 3 1
row 4 = 1 4 6 4 1
row 5 = 1 5         5 1  but they got stumped in the middle.

I changed it up (to look more like the triangle we all know and love) and said "Well, lots of times people write it like this:"

                                1
                              1  1
                           1   2   1
                        1    3   3    1
                     1    4   6    4    1
                   1   5                5   1

and suddenly a whole bunch of students shouted, "10 and 10!!", while others yelled back, "WHAT?? How did you get that???  Why???  WHAT?????"

Finally we started to put little black boxes over every odd number.  This was going to take a long time figuring out what number was in next line, so we looked at adding two odd numbers, two even numbers, and an odd and even.

"Go forth and color, my cherubs!"  And they did.   And it was good.

Merry-Go-Round Project Revisited

Last March, I did this project for the first time and blogged about it here.  I really liked how it went and decided I would do it again, but this time I got my superintendent to stop by a couple of weeks ago, interrupt my class, and pose the question of refurbishing the hexagonal merry-go-round question to us.

I asked the students if they were willing to take this on.  I told them that we would have to fit it in along with our other work, but that I thought they could do it.  In fact, I was sure they could.  They told him they would and then they peppered him with questions:

• Was it a regular hexagon?
• How big was it?
• How much was the paint?
• How many coats?
• What was the area of the merry-go-round?
• Was it wooden or metal?
• Did the hand railings need painting too?

And on and on.  It was great.  He said he would have to ask the person who had emailed him and he would get back to us.

I let them work on it one day that cycle (we were doing polygons.....what a COINCIDENCE!).  One cherub asked me if this was a real project.

I gave him a deer in the headlights look.....and then said, "oh, Jake.  You know, Mr. H and I have been friends for a really long time.... I am assuming this is real. I don't know that he would take time out of his busy schedule, but you could be right!  Maybe he is pranking me!!"

Today we finally got back to this.  I started by sharing Jake's pondering about the reality of this project.  "But tell you what.  I have arranged for Mr. H to come and listen to us present this.  IF this is a prank, let's prank him back!  Can we find at least 3 different ways to find the area of this hexagon?  That way he will have to sit through THREE presentations!!  Here is the info he sent us."   I had them work in pairs, and conferenced with each pair.  As I found pairs that used a common method, I grouped them into larger groups until we had exhausted methods.

My students found FOUR unique ways to find the area:  Trigonometry, special right triangles, Pythagorean Theorem, and (my personal favorite) Heron's Formula!  I did not let them assume the hexagon was made up of 6 equilateral triangles.  They had to prove it, and they did:  using 2 different methods.

I am really proud of these kiddos.  They really got excited when they found yet another way for solving the area of the small triangles.  The great thing is that not all kids saw 6 triangles:  some kids saw 2 trapezoids, and another saw 3 parallelograms.  In the end, they all had to calculate a height.  Whoot!  Tomorrow we present and I will add pictures.

New Desks = Inspiration?

A long story made short:  I was blessed with four brand new standing work stations.

They are tempered class tops (yeah, makes me a little bit nervous, but we shall see) and they look like this:

Note the fidget bar for a person's foot!!  and it is quiet :)

They take up a bit more space than a normal desk, but they have this cool storage space!  We noticed right away, that if two kids collaborating on something, they fit ok,  We also noticed that white board markers rub right off of this surface.

On first day that these were in my room, I was introducing solving systems of linear equations.  I have been working and working to try to "create headaches", as Dan Meyer suggests, so this is how it started:  

"I may have mentioned to you all that my sister-in-law lives on a farm.  Well, she raises lots of different animals, but they are all pets!  So here is a crazy puzzle from my crazy sister-in-law." (It is actually straight from a Kuta worksheet, as is the next one.)

I asked them for things that they noticed and then things that they wondered about.  I am happy to report that they all agreed that pigs had 4 legs while chickens had 2 each.  I am also proud to report that one kid noted there was no question to answer!

Students did a lot of guessing and checking and with some prompting started to keep track of their guesses.  This helped them do smarter, more organized guessing.

Since the entire sophomore class had gone on a field trip that week, I put this one up next:

It took less time for most of them to make an organized list.  I found fewer making just wild guesses, although some still were.  Some made pictures of buses and cars, labeling how many kids were in each and keeping track of the total.  I made a big deal of this method.   

Other students began creating mathematical models using variables.  I made a big deal of this method.

After the field trip problem, I put up Mary Bourassa's Tim Horton donut and coffee problem (since we live in the land of Dunkin Donuts, I had to explain how big Timmy's is in other parts of the country and in Canada): 

Slide 1:  I had forgotten that last year I added the "Draw a picture." prompt and most kids did not notice it
.

Here is Slide 2.  I asked if this helped them come up with a question we could answer.

I caught one kid doodling on the new desk! :)

I called the other kids over to see what he had done.  One girl GRABBED his pen and did this,

Can you see that she crossed off the 2 donuts and a coffee on each line?

 exclaiming: "OH! I know how much a cup of coffee is!"

and here is the rest of what she did.

And finally one of the students said that he noticed one cup of coffee and 2 donuts cost $3.15, so you could just take that away from the $6.85, leaving the price of 2 cups of coffee.  

All this brilliance because of new desks to draw on!  :)

P.S.  A couple of days passed between the start and finish of this post (Son #2 got married), and TOTALLY forgot how we finished this up (until I got a reply to an email I sent off to Max Ray-Riek on the day it all happened)!  

We finished by using the mathematical models (the ones with variables) that other students had used. We typed these models into Desmos (using x and y....if you use c and d for coffee and donuts it asks if you want sliders) and observed that the two lines intersected.  We clicked on that point of intersection and....Minds. Blown. : the very numbers they had discovered for the cost of a cup of coffee and the cost of a donut!

For those with SmartBoards, here is a link to the Smart Notebook file. 

A Break from Teaching

Son #2 was married this weekend to a lovely lady from the British Isles.  We are so happy for them both.

MTBoS Blogging Initiative: Week 4 - Teach My Lesson

I love Geometry:  especially a little further in the year when you have covered enough topics to make things FUN and INTERESTING.

Last year was the first year I taught this lesson and I blogged about it here.  The gist of it is a fictional merry-go-round that is brought to our school to have the carpentry shop repair and repaint. My superintendent came in and went along with me on this.  The kids were very into accurately calculating the area, amount of paint, and total cost of the hexagonal merry-go-round.

The only info they were given was that it was a regular hexagon and the side measure.

What was fun was the many different ways students came up with the length of the "apothem".

I never introduced that word and these students had never calculated the area of a regular polygon.  My goal was to ensure they had strategies that would work for them during the state test and I knew there was NO way any of them would remember one more area formula!!

Some used the Pythagorean theorem because they realized by angle measures the triangles were equilateral.  Some used special right triangles.  And at least two ended up using trig!!

Here are links to everything I used.  Not all kids got all documents.  I scaffolded as needed since I have a number of students on IEPs.

Student Sheet
Student Help Sheet
Unit Plan
Rubric
Smartboard slides

A Day in the Life of an Educator

The #MTBoS challenge asked us to share One Good Thing or A Day in the Life of an Educator.  I am choosing:

Sunday 1/10/16

Interesting that this comes during this week which is going to be about as crazy as my life gets.  I teach 5 classes, 3 different preps.  I am also the Math Dept. Chair in my school, because I was the last one to my finger to my nose....I have been doing it for years and years, and can't seem to get anyone else to do it, even though as Dept. Chair you get one extra prep period every other week.  I mean, who WOULDN'T want this job?

I am choosing Thursday of this week.

•  4:45 a.m : Alarm smash.  I hit the alarm so it doesn't wake hubby.  Lie in bed and try to remember what day of the week it is!

• 4;55 a.m.  Crank the wood stove, feed cats, make my sandwich, get dressed, "get pretty" as @mathymeg07 says!

• 5:45 a.m. Out the door.

• 6:15 a.m.  Arrive at school.  Turn on my two computers, post the agendas for the day, type up that quick quiz I thought up in the shower.  Dash to the one (yes, one) photo copier in the faculty room, before the science teachers and history teachers get there! :)

• 7:10 a.m. Look over the teacher dashboard of the two classes that did Match My Line on Teacher Desmos yesterday...figure out who is still having difficulty graphing lines.

• 7:35 a.m.  Pre-Cal students arrive in class.  Do review games, practice a little of everything we did.  This class was very interrupted this week because of field trips (2).  

• 9 a.m.   Pre-Cal ends.  I have 1.5 mins to check email before the first kid arrives for the next class.

• 9:03 a.m. High five my Alg 1 kiddos.  Today we are reviewing graphing lines and playing Match My Line (started yesterday, but didn't get too far.)  For those who finish, we'll try Marble Slides!  Very needy bunch.  Am blessed to have an aide in this class (former student of mine, studying to be a math teacher!)

• 10:30 a.m.  Class ends.  This is when my lunch time is scheduled!  Mostly I use this 25 mins. to catch up on emails, enter grades, put hwk up on Google Classroom, OR clean up from the first Alg 1 class and get ready for the next one.

• 10:35 a.m.  Stand at door and high five the next group of Alg 1 students.  Same schedule as the first one, but a smaller class.

• 12:15 p.m.  Tell the Alg 1 kiddos I love them, but it's time for them to move along to their next class.  Now is my prep.  Correct that Quick Quiz I made for the Alg 1 cherubs (to see how they are doing with lines), get ready for tomorrow, send a few emails about our Credit for Life Fair that we do for our entire senior class in the spring.  Realize I haven't used the rest room since 7 a.m, and leave my room for the first time since 7:15 this morning.  Oh look:  there are ADULTS out here!!  Have quick conversation with a couple of them.

• 1 p.m.   Oh look!  Here come the bus drivers to have a meeting in the only empty room in the school:  mine.  They said it was ok if I stay and work at my desk.

• 1:40 p.m.  My second group of Alg 1 students are back in my room for a 45 min. study hall.  I also have seniors here doing a study group for tomorrow's assessment.

• 2:25 p.m.   School is out.  I dash out the door to be ahead of the buses because I have to get to the local university.

• 3:10 p.m.   Arrive at the university, Am presenting to a group of 20-25 teachers grades 8-12. Pray that all the technology will work.  Deep doo-doo if it doesn't!

• 4 p.m.  Sharing the Desmos love to these teachers.  This is the second time we are meeting.  The first time they got to learn how to use Desmos and discovered what it can do.  THIS time we are playing with Teacher Desmos and figuring out how it helps students model mathematics.

• 7 p.m.  Finish up the seminar, go to the dinner that accompanies this professional development. 

• 8:10 p.m.  Drag my butt through the door: greet hubbie and dog.  Unpack my stuff, repack my lunchbox for tomorrow.  Cuddle up to the woodstove and exchange "how was your day"s with hubbie. I see that my "mother of the groom" dress finally arrived!  TOO tired to try it on....

• 8:30 p.m.  Hit the shower, pick out clothes for tomorrow.  Wonder if I actually remembered to print tomorrow's assessment.  Wonder if the million steps I took during the seminar counts toward #FitBos!

• 9:15 p.m.  Sit down to finish typing up my day.  

• 9:45 p.m.   Stop pretending to do anything constructive.  Fill the wood stove so it will make it through the night.  Go to bed.

Please Tell Me I Am Not a Horrible Teacher!

This week I have my senior Pre-Cal students for only four and a half days.  And on one of those days, a third of the students will be on a field trip.

I teach at a Vocational-Technical high school which means I see my students every other week.  Because of the way state testing happens in the spring, administration has to get very creative to make sure the right set of students is in their academic cycle at the right time, and sometimes we have some cycles that are longer than 5 days, and some that are shorter.  It's complicated.

What this means for my seniors is that the last time I saw them was on Dec 18, 2015.  They are coming back to me on Jan. 11, 2016.  And I have them for just 4.5 days. And some of them will missing one of those days because of the field trip!

Here is my dilemma:  I just do NOT have time to have them derive the formulas I need them to have. We are already way behind because of short cycles (holidays) in the fall.  So I am going to just give them the formulas.  Or maybe just show a power point where the work fades in and out.....if I have time to make such a thing.

Just tell me I am not a horrible teacher for doing this......

My Favorite: 2 things

At Twitter Math Camp, one of the BEST times of the day is when people share "My Favorite".  This can be something very simple (a new app or a way to organize) or something earth shattering (high fiving students EVERY DAY in order to help "bond" with students!)

So here is my favorite way of differentiating a quiz.  I have a PreCal class with 17 students.  Because of scheduling issues, I have to teach both the Honors class and the College Prep class at the same time.  All this while also having 3 other courses to teach and be Math Dept. Chair.  When I can cut corners, I do.

We are doing Law of Sines, Law of Cosines (including the ambiguous case), and the area formulas. I knew this was tough for the students and we had to get it all done in 4 days, testing on the 5th, because then they go to their shops for five days (vocational-technical school).

Here are their tests.  The one on the left is the Honors version.  The one on the right is the CP version.

Yes, they are exactly alike.  The Honors has one token, good for 1 question:  they may ask one clarifying question.  The CP version has 2 tokens, good for 2 clarifying questions.   

The End.

P.S.  This is something I shared at TMC15:  Just a way of organizing whiteboards so students can get right to it and I don't have to hand out boards, markers, and wipey cloths.  I hang them on the desks with velcro.  Markers and cloths are wrapped up and put inside.  A little velro button keeps the side closed, so markers etc don't fall out (too much!).

Graphing Linear Functions

Each year I hope that my Algebra 1 students will come to me already knowing how to graph lines.  I KNOW they get taught this in middle school, but for some reason, they just cannot hang on to this.  Worse than coming to me in Algebra 1 and not being able to graph a line, is when I see them in Algebra 2, and they are still fumbling with it!

Well, I refuse.  I have decided that students have to be able to do THREE things to be able to say they passed my Algebra 1 class:

1.  They have to be able to solve "ugly" problems and that includes clearing fractions.

2.  They have to be able to graph a line.  In any and all forms.  Without help.  On demand.  And that includes y = 4 and x = -2.

3.  They have to be able to multiply polynomials using the box method.

To this end, I have been creating and searching for lovely "ugly" problems.  If you have some, please send it to me at tpalmer@ssvotech.org  and I will add it to the collection and post it on Twitter!

I have also been doing Number Talks and encouraging students to multiply large numbers using the area model (aka "box method").  This is in preparation for multiplying polynomials, and hopefully factoring them as well!

As for linear functions, I have been doing lots with Fawn's Visual Patterns and other linear activities like Stacking Cups, but sometimes I just have to make them graph the equations.  To make it a little more palatable I am making a game.

Next week, when my Algebra kiddos come back to me, they will find 24 equation cards, a couple of dice, their individual white boards, some colored cubes, and a game board that looks like this:

Game play is simple:

• No more than 4 in a group.
• 1st player:  Turn over one of the cards.
• Graph the given equation.
• Show the graphed equation to the other members of the group.  If no one challenges you, then you are good to go. Roll the dice and go that many spaces.
• If someone challenges you, they have to explain what they think you did incorrectly, and re-graph the equation.
• Whoever gets the equation graphed correctly gets to roll the dice and go that many spaces.
• In the event no one knows how to graph the line, or the group cannot agree on how to graph the line, they may go (as a group: everyone needs to see what it looks like) to one of the 4 computers in the room and use Desmos.  In this case, no one gets to roll, but it could be a good strategy since there may be multiple cards of that type in the deck.
• Move to the next player.

Game is over when all cards have been used OR someone makes it to the top.  If no one makes it to the top, the person furthest along wins.

I don't want this to take the whole period, and I will give them graphing lines homework to see if this helped at all.  Fingers crossed!