Visual Pattern #TMC17 Style

Today was our first day of school.  I have taught Alg 1 and Alg 2 before, so that was good to go.  I am new to teaching Accelerated Geometry and took a stab at repeating what my morning #TMC17 group did with the PCMI teacher group called Rich Tasks - and we dove into a Visual Pattern.  It was not the usual, how many blocks are in Step 43.  Instead, they were asked to fill in the blank - "As the step increases, ______ changes."

I asked them to work individually brainstorming ideas in their notebook.  They thought it was a one and done thing.  I have one word.  I am done.  I asked them to "see" more.  Then, I invited them to turn to their group members and share and grow their list.  Next, I had a big sticky on the board and we recorded all their ideas.  I used questioning techniques to dive deeper into what they were telling me by asking clarifying questions, mostly to have them identify what they meant with their pronoun "it".  Out of this natural geometry vocabulary appeared, area, width, perimeter, side vs edge, vertex vs corner.  It was a great conversation.  They were stuck on the word "block".  They saw the number of "blocks" increasing.  I had to pull some more out of them - I was looking for "squares".  How is the number of squares different from the number of blocks - is it a different thing?  How many rectangles are there?  This lead to the "is a rectangle a square" question and vice versa.

Here is our list:


So, I had them brainstorm individually, then in groups, then as a class.  Next, I had my groups of 3 prearranged using flippity.net and invited them up to work at the board #VNPS.  As a group of 3, they were to pick a category and investigate it more fully.

I had two classes.  I was taking a risk.  Yes, I had done this with a group of math geeks (I mean teachers) at TMC, what would my students do, what would they see, how long would it take them.

So, the first class chose "height" and "levels" in their class brainstorming session and then a few groups chose to investigate those which didn't take them too far or too deep.  I adjusted by my second period and while we did include height on our list, I told them they could not investigate it.

They were done a bit sooner than I anticipated.  I had one member from each group grab a pen or pencil and gave them sticky notes and asked them to do a gallery walk and visit some of the other investigations and notice and wonder.  Write down "I notice...", "I wonder...".  They did a good job meandering about the room.  When I noticed each of my 9 groups had about 3 stickies each, I gave a time warning, two more minutes to finish up.  Then, I asked everyone to return to the their seats and give me the rest of the stickies.

At this point, I am adjusting and winging it.  But, it worked out very nicely.  I then invited each group up one at a time to read the stickies and respond accordingly.  They did such a great job.  It really got some great discussion on the first day of school.

Here is some of their work.
  

 

Gallery walk:


 We did some noticing between the groups and decided "levels" and "height" was the same.  "Area" and "number of blocks" were the same.  They were subtracting and finding 1st and second differences.  They were coming up with equations.  We discussed how on one board there might be a linear equation and on another there was a quadratic equation.

In the second class, one group chose number of rectangles (including squares).  They persevered.  They did not get as far as the others with any sort of table or equation.  A student asked me what the equation was.  I was happy to share that was what I investigated at TMC17 and that we spent 2 hours on it and saw a lot of great patterns, but we didn't come up with any equation or conclusions, just kept digging.  

Two favorite observations:
"I notice you have a lot of notices."
"I notice the height is the square root of the area."  Nice!

Finally, I asked them to come back to their desks and notebooks and investigate the number of squares, not rectangles, just squares.  We had about 7 minutes at this point, but they were doing it.  They were seeing patterns, and then making predictions without having the draw the whole picture!  

Update: Day 2, when I did this with my third class, I realized I heard EVERY Geometry student speak on the first day of school!  My doing the sticky notes, each had to read at least one and maybe answer or comment on it.  They were all heard from.  Wish I could make this happen every day.

My Totally #MTBoS Room - Thank you all!

As I was setting up my room this year I realized how much I use from my MTBoS friends (Math Twitter Blogosphere) and from TMC (Twitter Math Camp).  Thank you!  I am going to share pictures and hopefully include the correct acknowledgements.  If I missed you, please let me know. If I credited the wrong person, please let me know.  I want to give credit where credit is due.  I was almost afraid to #pushsend for fear of being wrong but Carl Oliver @carloliwitter made me do it!

Here's to 2017-2018 and my Lucky? 13th year of teaching: 

My pencil sharpening and sign out area with some reminders.  These are old signs.  I don't remember where they came from:



Next up:  Jigoku from David @DavidKButlerUofA at #TMC17 this summer.


Next up: Signs from Sarah @mathequalslove.



Next up: Marbleslides challenge made by Sean @SweenWSweens at #TMC17, posters by Jessica @Algebrainic1 and of course Desmos @desmos.  I updated my own code, changed "treats" to "prizes" because we aren't allowed to do food, and printed all 36 challenges and put them in page protectors in a binder.



Next up:  Birthday weekly recognition board from Heather @heather_kohn at #TMC16 My Favorites' presentation.
Correction: Hanna   @girl_got_range from #TMC16 presented this idea.  Heather had the idea to have the kids write birthday cards on index cards.  I just did this today.  



Next up:  Here these are all together.  A bit busy but oh well.



Next up: My Equations - not sure who did this one? Glenn W?



Next up:  Vertical and Horizontal around my doorway - again, I don't remember who to credit:
 

Next up: My Claim Is...My Warrant Is... From #TMC16 and Chris @Plspeak and Mattie @stoodle and there morning session called "Talk Less, Smile More" I hope to use it more this year in my geometry class:


Next up:  I had this Power of Yet sign made.



Next up:  This is my favorite poster.  I had it made into a banner.  I found the image online and loved it.  It is from Max @maxmathforum and Annie @MFAnnie.


Next up:  I had this poster made after taking a MOOC by Jo Boaler @@joboaler


Next up: Along my wall of windows, I hung a clothesline and clothespins up high to display my student projects using Desmos and conics to make their Conics' Projects.  Here are three. @desmos


Next up:  This is a Welcome Sign with white boards bought at Target last summer.  I think it was Sarah's idea??? @mathequalslove.  Each day I've gone in it has fallen down because of the duct tape on the cinder block.  Will need to find a new spot? or new holder?


Next up: I rescued this table from the side of the road.  My husband rounded the corners.  I printed of inspirational quotes and painted and modpodged it up.  Students like to work there during group work or free time.  Sometimes I will put a puzzle or game back there too.


Next up:  My calendar.  I keep this at the front of the room.  I just realized I need to add early release and stuff to the days.  The numbers are magnets.



Next up:  I think these are from Sarah @mathequalslove a few years ago.  The 8 Math Practices.  These are under my front board.


And, last, but definitely not least, my back boards ready for #VNPS year 2.  I have border hanging to divide the space and numbers hung up with magnets to represent the stations.  I have enough room for 9 stations with 3 kids each.  I did win a grant to get my homemade ones replaced by permanent ones.  Crossing my fingers installation happens on Monday or Tuesday.  Last year was my first year using #VNPS due to my #TMC16 1 Thing and I loved it.  The idea comes from Alex @AlexOverwijk and Peter @pgliljedahl.  Thank you!



Thanks for reading.  The "learners" (from Glenn @gwaddellnvhs at #TMC17 My Favorites) come next Wednesday.  My room is ready and I am almost ready.

#TMC17 Post 1: My TMC17 Scrapbook Story

#TMC17 Post 1: My TMC17 Scrapbook Story

Table of Contents:
A.) Foreword
B.) TMC17
C.) Links
D.) My Story
E.) TMC18: The Sequel

A.) Foreword: I am writing to capture and reflect on my experiences at Twitter Math Camp 2017.  A huge shout out and thank you to @kd5campbell - my colleague, travel companion, partner in crime, and friend.  Thank you for sharing in this fun week with me!  I took a lot of notes and pictures and will share them here for me to reflect, process, and remember this week.  And to share with my readers - some may have been at TMC, some may have been in #tmc17jealously camp like I was for years, and some may just be learning about TMC.  I invite into my math camp world.  Enjoy!

B.)  TMC17 - Twitter Math Camp 17 was held on Thursday, July 27-Sunday, July 30th, 2017 at Holy Innocents Episcopal School (HIES) in Atlanta - Sandy Springs to be exact.  A huge shout out to this amazing school community and @DanielForrester17 for hosting us.  We stayed at the Wyndhym Galleria Hotel about one mile from the school.  I traveled to Atlanta on Tuesday to do the touristy thing and attended the Desmos Preconference on Wed, July 26th.  There were about 200 teachers, coaches, and education leaders in attendance. 

C.)  TMC Links:
   bit.ly/TMCwiki
   bit.ly/TMCLinks
   http://2017tmc.shutterfly.com
   #tmc17
   #tmcPlans

D.)  My Story's Table of Contents:
Post 2: My Traveling and Touring Tuesday
Post 3: My Morning Sessions 
Post 4: My Favorites, Presentations, and Keynotes
Post 5: My Mentee
Post 6: My Dinner and Evening Activities
Post 7: My Presentations
Post 8: My TMC17 Takeaways

E.)  #TMC18 - Interested?
It will take place July 19 - 22nd, 2018 in Cleveland, Ohio.  Follow @TmathC for more info and look for sign up in early February.  It is so worth it.  It is the BEST professional develop by teachers for teachers!

#TMC17 Post 2: My Traveling and Touring Tuesday

#TMC17 Post 2: My Traveling and Touring Tuesday

My colleague, Kathy, and I were up at 3:15 in the morning on Tuesday to travel to Atlanta.  My son was also up to drive us to the bus to then get the plane.  He wasn't happy but I am thankful.  We arrived in Atlanta around 9:30 am.  We met up with Mary Williams.  We were all new to Lyft and I got the app and ordered Todd.  He was surprised to see the 3 of us and our big pieces of luggage for his little Toyota Corolla.  He asked us to stuff 2 pieces in the front seat and wasn't sure what to do with the third.  He opened his truck and it was full of stuff.  Why is he a Lyft driver?  Kathy rearranged and made it work.

We were too early to check in but left our bags there.  I stupidly decided to take my heavy backpack with me and had to lug it around all day.  We had tickets to do the World of Coke at 1 pm and the Georgia Aquarium at 4 pm.  It took us about 1.5 hours to get there.  Yes, our hotel was in Atlanta and these were in Atlanta.  Atlanta is huge!  We had to take the hotel shuttle to the mall.  We were supposed to then take a bus to the train but luckily the shuttle driver had to go by the Marta (train) so he drove us there.  We took 2 trains and then got above ground only to figure out we had to walk another mile to Coke!

We stopped in Centennial Olympic Park and had lunch at Googie Burger because we liked the name.  It was just a burger.


Next, we finished our walk and met up with a crew that was already there for the Coke Tour.  It was so cool.  I highly recommend it.  My brother lives on Coke, so I bought him a shirt.  Yep, no souvenirs for my kids or husband, but my brother.  I bought a pencil to add to my pencil collection.  We had lots of picture opportunities, went into the vault where the secret recipe is, watched a couple feel-good movies about Coke, saw how it was bottled, and then could taste up to 100 different Cokes from around the world.  So cool!



  

Onto the Aquarium.  I wasn't going to do it because I have been to the Boston Aquarium, but my friend, Diane, told me I HAD to go and she was right.  It was all that.  We saw a full dolphin show, a cute lion show, and walked through an arched glass way under the fish tank with so many cool fish swimming above us.  Heather and I climbed into the penguin pen and took a picture too.
  

  
   

  

 


We had dinner there and then went back to the hotel to check in, meet my mentee, Benjamin, and play some games.  A great, long first day.

#TMC17 Post 3: My Morning Sessions

#TMC17 Post 3: My Morning Sessions

I love the way TMC is designed with its varying lengths of presentations.  There are 3 morning sessions that are 2 hours each, for a total of 6 hours so you can really dive deep into a subject.  Then, there are afternoon sessions that are an hour.  There are "My Favorites" that can be 5 or 10 minutes.  And, finally, we end with a Flex session for anything you might have come up with last minute depending on conversations along the way and this is an hour long.  It is so well designed.

I was torn between two AM sessions, but I ultimately chose Teaching Risks Tasks with Peg Cagle, Cal Armstrong, and William Thill.  These people have been working with PCMI for a long time.  It was so great to watch how they orchestrated their teacher moves around us.  It was like an eloquent dance.

Here is the link to their page.  Link

Day 1 = 1 problem in 2 hours!
Today had us look at this Visual Pattern from visualpatterns.org.  I have used these a lot and always asked the same question - How many ___ in Step 43?

They put a twist on it.  "As the step changes, ______ also changes."



We thought about it individually.  Then, discussed it with our group and added to our list.  Finally, we brainstormed as a class on a big whiteboard and wrote all our ideas down.

I came up with: #rows, #columns, #total blocks, #in each row, #in each column.
Our group added: area, perimter, #line segments, layers, how many moves it would take to make the shape into a square.
Our class added: #bigger line segments, #vertices of polygon corners, # squares - unit vs all squares, #rectangles, #surrounded - touching adjacent sides (we called this sort of like minesweeper), #hexagons, #polygons, #tetris pieces.

We were instructed to find someone one or 2 we wanted to work on one of these attributes with.  I chose to work on the number of rectangles with Marsha and Rachel.  We drew the first 8 steps and started organizing by the dimensions of the rectangles and began counting.  We were a great team.  Marsha wrote, I counted, and Rachel looked for any patterns and noted it.  We noticed a lot of things but did not have enough time to get as far as we wanted.  Note: we spend 2 hours on this class and could have used 2 more hours!

Day 1 Notes:
 

Morning Work Pictures:

AM pics 1: playing with stickies as the squares:    AM Pic 2: our rectangle counting:

 

Great team: Marsha, Rachel, and myself:


Day 2 - Analyze videos of teachers teaching:
We watched videos of teachers teaching.  We saw an American teacher introduce linear group work, followed by a Japanese teacher having the students work on solving a word problem involving systems of equations.  We had great, in-depth conversations.  We looked at the questions themselves.  We looked at the teachers' questions and teachers' moves.  We were critical.  Annie Fetter suggested we audio tape ourselves teaching by turning our phone on for group work and taping for about 10 minutes.   Then analyze it for what did I say, how did I react, what did I do, what are my questioning strategies, write down every question you asked, what type of question you asked, and track T, S1, T, S2, T, S3, etc.  See who does the talking.

Some things we did notice was the American teacher seemed to jump in and save the students.  Tip: Don't hijack the question!  Suggestion, when working in a group and a student has a question for the teacher ask the group if anyone knows.  Teacher then to ask other students for help first.

The Japanese teacher seemed to be more prepared and anticipated the students' strategies.  He had manipulatives ready to be used and titles of strategies to be hung up.  It was more of a lesson on strategies for solving systems instead of just getting the final answer.

We learned that Japanese teachers learn about "kikkon-shido" which means "walking among the desks  - not to save, just to note their work.  They are also taught to use the blackboard - why would you write anything on the board if you just plan to erase it?

Day 2 Notes:

 

Day 3: Rich Task Implementation: Looking at worksheets:
 When looking at an assignment - whether it is a worksheet or activity - list the opportunities to learn that are created and supported for both the student and teacher by both a traditional use of the task an alternative task being suggested.  So, if you have a regular worksheet - it has benefits.  If you want to change it up a bit, how are you changing the learning opportunities.  Are all the changes what you intended?  Are they better than the traditional?

Worksheets 1: We looked at one worksheet with solving systems of equations in the traditional way - solve some by substitution, some by elimination, and some by graphing.  Each problem was picked intentionally.  On the graphing, a slope of 5/7 was chosen so students could "move" slope instead of making a table.  On the other graphing problem, the dreaded x = 7 was thrown in to see how students would do with it.  The second "alternative" worksheet had 16 problems in squares that asked the student to sort them.  Some of them were non-linear.  We suggested students might simply sort into linear/non-linear.  Nothing on this worksheet actually asked students to solve the systems.  Our group suggested one could introduce this at the start of the unit and have students cut and glue their sort to a paper and explain why they chose to sort that way and then collect.  Teach the unit and then do it again and see if their process changed.

Worksheet 2:
The next worksheet was your typical area, perimeter, and circumference review sheet.  Instead of asking students to do the problems, ask them to analyze the problems!  Ask questions like:
Which are the 3 hardest problems?
Which are the most valuable to you in preparing for our quiz?
Which 3 are the easiest?
Which 3 are most challenging to most of the class?
For hmwk: pick the most interesting problem, do it, and write about why you chose it.  How cool!!!!

Asking students to analyze problems will slow down the "grinder students".
"Answer-getting isn't math." ~ Peg Cagle
If you are still concerned they are just trying to get the answers, then give them the answers.  Shift the focus, time, and energy.  This will encourage them to do it and then find their errors.

If you know you will be assigning a worksheet for homework and do have time to start it in class, how about if you switch it up and start with the hardest problem first, then the easier problems will be done at home.

Worksheet 3:
Hand out a worksheet where all the work is done and all have errors.  However, the directions are not to fix the errors, instead..."What is this person confused about that led them to this mistake? Bonus: Give another problem that might help them to see and understand their misconception."  How great.  I have done the fix the mistake.  I love this added explanation.

Side note: Allow students to bring an index card to a test where the students put their common mistakes on the card.  "Mistakes I am Likely to Make Card."

Day 3 notes:



 

Three days that were so full of rich goodness!  Thank you! 

#TMC17 Post 4: My Favorites, PM Presentations, and Keynotes

#TMC17 Post 4: My Favorites, PM Presentations, and Keynotes

Note: This one really should be separated into 3 different posts but I wanted to keep all my posts to 8.  I will try to be short here but there are a lot of pics.  Also note, I am usually a spelling geek but man, I made some spelling mistakes.  Sorry.

My Favorites:  I really think these are my favorites.  It is a 5 or 10 minute presentation about something favorite from the year.  They give us a taste of greatness. 

Thursday PM:
Lisa: Thursday Lunch
Sam: Ring the bell when you feel joy in math class
John: Who is the MTBos and all the ways you can search us
Mattie: DeltaMath for math practice:



Friday AM:
Here I was supposed to present 2nd but my computer choose to freeze, so I spent Tony's trying to get mine to work, then someone went and I missed them, then me, so no notes, and then Karim on Greece, but I was just breathing after my presenting:
Tony: Distraction box in the classroom
Me: 2 uses for Google Slides see My Presentations here
Karim: Greece



Friday PM:
David Petro: Geometer's Sketchpad and his site: engaging-math.blogspot.ca with cool dynamic web sketches.  I am going to be using this in Geometry this year!
Joel Bezaire: Tinkerplots
Pam Wilson: Make a Difference Monday - find and read articles of good stuff kids are doing = 5 Fingers



Saturday AM:
Jonathan: Let's Buy a House: Adulting Project
Kat Glass: Group student interventions
Bob Lochel: how-old.net - give it a try, collect data and analyze it

  

Saturday PM:
Joey Kelly: Playwithyourmath.com  So excited to check these out!
David Petro: Deliberate practice
Benjamin Walker: Peer to Peer Math Partnership



Sunday AM:
Deb Boden: Mixed spaced homework
Anna Scholl: Good things coming to LearnZillion in August
Connie Haugneland: Update on this year's trip to Rwanda
Alli George: How to review for 3 straight hours - brain break - take 90 seconds to draw straight lines across a piece of paper, at least 4 lines, then pass out crayons and start coloring but the same color can't touch.  Ask questions, collect and analyze data.  How cool!  I want to color!
Anna Blinstein: Desmos AB Entrance Ticket asking about last night's homework
Sean Sweeney: Marbleslides.  I have used these but wow, so powerful to challenge the students to create their own.  He also has weekly challenges.
Elissa Miller: Two Nice Things - when someone says 1 mean thing, then must say 2 nice things, also Ask questions on Twitter - don't be afraid to ask or embarrassed.  It's a strength, not a weakness!
Sandra Miller:  Lesson planner at planbook.com
Anna Vance: Difference of Squares original rap (with a beat by Benjamin Walker)
Candace Bell: Designing superhero capes and the entire process
Glenn Waddell, Jr: Words Matter - change "students" to "learners" Change "guys".  Change "all" to "each".  Changing your words can change your behavior.

 



PM Presentations:

Thursday PM 1: Kathy and I went to Max and Malke's presentation.  We thought it was going to be dancing, but we were given rolled up newspaper sticks and tape and told to create.  We made the thing on the left below and when we picked it up, it surprised us all by turning into the shape on the right!

 

We learned about teacher moves.  We analyzed the geometry our groups used and then brainstormed new things to try and were given time to make another.  We made the sea urchin on the left.  So fun!  Going to try this in Geometry class this year.

  

Thursday PM 2:  I went to Mary William's presentation on Informative Formative Assessment.  I did know a lot of it already, but it was fun to learn new things in Kahoot like Jumble mode.  Going to check it out.



Friday PM 1:  I presented.  See this post. 

Friday PM 2:  Time to play math with Jamie, Molly, and Rachel.  They started with the "regular" two special right triangles and then gave us a 36:72:72 triangle and we got to play and discover some pretty cool trig things! 



Saturday PM 1:  I presented.  See this post.  I offered to post twice this year which I really enjoyed but it also meant I had to miss 2 sessions and a lot of goodness :(

Saturday PM 2 (really a flex session):   #clotheslinemath with Chris Shore.  I have used the clothesline in my room but mostly just to put things in order - fractions, decimals, logs, exponents.  He showed us it can be much more powerful and our minds were blown as he shown us vertical angles in geometry.  I couldn't help but think: It was the last Saturday of July at 4:30 pm and there were a roomful of math teachers with our minds being blown. So cool!  This will become my #1TMCThing  to merge it with my #1TMCThing last year of using #VNPS.  I am very excited to spend some time with this and blow my "learners' " minds.

 

4 Keynotes:  

Annie Fetter during Desmos precon:"Using Tech to Increase Conceptual Understanding in Algebra and Geometry".  Teach math as "things to experience" not just a telling of properties.  We looked at an interactive applet with 4 triangles and noticed and wondered about them.  Things do not have to be modern, but instead thoughtful.  First we should make sense --> reason --> communicate!



Grace Chen:  "The Politics ?? of Mathematics Teaching"
Grace's speech was inspirational and I was trying my best to be present and take it all in.



Graham Fletcher:  "All I Really Need to Know I Learned from the MTBoS"
Some of my take-aways:
Surround yourself with people smarter than me.
Adapt.
Be vulnerable.
Size matters.
We looked at the length of an apple peel and played with that a bit.
We looked at the spinning lady (I see clockwise, what do you see?) and he reminded us that my students might see math the other way.
All of us are smarter than one of us.



Carl Oliver: "Hitting the Darn 'Send' Button"
I first met Carl mid July as we were both new Desmos Fellows in San Francisco.  I had just received my mentee's name, Benjamin Walker, and he told me he was rooming with Carl.  So, I introduced myself and told him that Benjamin - his roommate - is my mentee.  Small world.  This was Carl's first time at TMC and I was impressed he was doing a keynote.  I know he was working on it while we were at camp and it was done purposely because it was so up-to-date with the #mtbos/#iteachmath debate and he used his new Desmos computation layer to do an AB activity with estimating how many people tweeted using the #mtbos hashtag.  He even went ahead and made a Roll Call of all people and when they first used the hashtag.  I was so excited to see I jumped on this train early on - in October 2013.   He spoke about "when" are we part of the #MTBoS.  He suggest preMTBoS people wanted to get better, wanted to put stuff together, wanted to be part of the conversation, wanted to open a window their classroom, and wanted to get feedback.  I do remember that feeling - am I part, am I not part.  And, then YOU just decide.  I AM part of #MTBoS.  I love part of his conclusion: "By making himself more vulnerable he actually feels less vulnerable." 



Thanks for reading!