#made4math Monday! More Kagan, Triangle Center Foldable, Einthoven’s Triangle

A couple of weeks ago, I shared how much I was enjoying some of Kagan’s strategies!  We’ve been working with triangle congruence this past week.  I am a fan of the sequencing they’ve placed within these lessons.  From recognizing missing information, to stating congruencies, justifying each part.  This is an informal way to introduce the proofs, but each activity leads one step closer.

Today, our activities involved more of the Boss/Secretary and Pairs Check formats.  Tomorrow we are doing Blind Sequencing.  The idea is similar to ones I’ve seen others post – I think @misscalcul8 did some proofs on popsicle sticks back in the summer and I loved that idea!

Color Coded Cards for Proofs

I printed the 4 sets of each “proof” on color-coded card stock…notice, I highlighted/circled problem # in corresponding color.  This way students can come up and exchange a set once they  complete it.

Students are “forced” to talk about the math – the questions, discussions, (arguments) I’m hearing is wonderful!  They really like Boss/Secretary and even said they have to think about their choice of words – especially when the Secretary (Assistant) writes something completely different than what the Boss had intended.  The praise and coaching aspect is still a bit awkward for a few of them.  The questions they ask one another are so purposeful – they really want to know.  A great opportunity to observe learning / struggles.

Upon completion of the activty, I pop the answers on the overhead – allowing them to double check, a time for discussion, questions, clarifications.  Very interesting to hear students share different approaches to the same problem…and they want to know if its okay… 🙂

Triangle Centers Foldable

As we finished our triangle centers, students asked if I would make them “one of those cool charts” (aka foldable) to help organize all the names/sketches/special characteristics.  Its mostly blank, my first attempt at actually creating a foldable.  I printed it off, made copies and I had my sides reversed, but life goes on and my kiddos were okay with it.  Triangle Centers Foldable I only copied the front side and let them write the names on the inside of the flaps, so they can have “flashcard” style study tool.

Around the Clock

To fill in the center columns – I let them decide what was important.  I used the “Around the Clock” – is that Kagan or another book?  Sorry.  Students have a slip of paper, draw a circle and write in 12, 3, 6 and 9.  I give them 1 minute to go set up appointments with their classmates.  For example, if I made an appointment with Kelly at 3 – she would have my name on her card at 3 and I would have her name on my card.  I had a few stragglers, but it was a quick fix – asking who had an appointment at 6 open.  When they arrived at their appointment, I would write a specific topic, like median/centroid on the board and they were restricted to those topics at that appointment.  I gave them between 2 & 3 minutes to share discuss.  Time.  Move to your ___ appointment.

They loved it, I think.  And once again, they were TALKING about the math!

Cardiology Technician – application of Triangle Centers

While I was searching for some clipart for the foldable, I ran across a text problem from www.nexuslearning.com, about Einthoven’s Triangle for a person’s heart.  I tweaked it a bit, inserted a bigger graph, gave the students a piece of patty paper (how we’ve done the constructions they’ve needed) and assigned it for homework.  In Kentucky, we have program reviews of our accountability model – we must document/show student work samples that we are integrating Practical Living / Career Studies; Arts/Humanities and Writing/Communication…this will definitely be one of my samples for PLCS.

Cardiology Technician – assignment sheet

I left school today feeling successful for the first time this school year.  I know I’ll be back to treading water soon, so I’ll enjoy this small bit of time – smiling, because I loved what I was doing today!

#75facts Book Chat Begins Monday 9/24

Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learnin

Page D. Keeley (Author), Cheryl Rose Tobey (Author)

They refer to the strategies in the book as FACTS – Formative Assessment Classroom Techniques thus the hashtag #75facts.

If this will be your first online book chat – its simple – read assigned material, log on at designated time and share!  I’ve heard from several of you that you’ve gotten your books in hand – so let’s get started next Monday – September 24.  Meet up on Twitter at 8:30 cst and use the hashtag #75facts in your posts.

I know this will be a great opportunity to share and learn from others!  Several of the FACTS may be strategies you currently use – so there will always be opportunity to share what this looks like in your classroom.  The FACTS may also trigger a new idea on how to modify and improve techniques.

There are 75 FACTS which means this chat has the potential to continue the entire school year – so, if you are new – please join in!  We want you to be a part of this!

Overview:

This book is a bit different than ones we’ve used in the past, so you are encouraged to get started and read ahead – getting ready for implementation – however, we’ll begin our chats by discussing 1 chapter each week.

Chatper 1 Introduction – defines FACTS, shares research, making a shift to a foramtive assessment centered classroom.

Chapter 2 – Integrating FACTS with Instruction and Learning

Chapter 3 – Considerations for Selecting, Implementing and Using Data from FACTS

My initial thoughts are to focus on 3 FACTS each week – you can choose 1 of those 3 to implement (or any prior FACT), reflect and share during our discussions.  We can see how this goes and always modify as we see fit.

Chapter 4 – Getting the FACTS is where the 75 FACTS are presented.  Each FACT covers 2-3 pages, so the reading is not the time factor here – implementation is where your time will be focused.  Don’t let this overwhelm you – if you don’t get one implemented, this by no means implies you should skip the chat!

Each FACT follows the layout:

• Description
• How it promotes student learning
• How it informs instruction
• Design and administration
• Implementation Attributes
• Modifications
• Caveats
• Uses with other Disciplines
• Examples, Illustrations
• Notes/Reflections

If you have not already, please enter your name in the form so we can ensure we keep you posted!

I will get a form in place for you to share any blog posts about #75facts soon!

#MyFavFriday – Kagan Geometry

Last week I stood glancing at a shelf of books left behind by my colleague.  I’m not sure why I didn’t notice it before – but there on the middle shelf was a Kagan Geometry book.

Two days this week I’ve smiled at the end of the day and it felt great.  Becky Bride has compiled simple to implement, engaging activities.  I’ve read snippets about the Kagan books – but never really sat down to read/do any of the activities.

Boss-Secretary

One of the activities this week was using a strategy called Boss – Secretary.  Students work in pairs.  The boss tells the secretary what to write, explaining their reasoning for the steps/work.  IF the secretary sees the a mistake, he/she respectfully points out the mistake to the boss and praises her/him when they corrects their work.  If they work through it correctly, the secretary is asked to praise the boss, vice-versa.  After completing a problem, they switch roles.

The students have been funny with this simple, yet VERY effective activity.  Speaking of resumes, tough bosses, etc.  One asked today – do I really have to praise them when they do it correctly?  I’m really not a praise-y kind of person…  I said a high 5 would suffice.

Here is what I love about this – Students are talking/explaining their work so the secretary can do it.  Secretaries are listening, following directions, hopefully picking up on any mistakes.  I’ve heard multiple times – student exclaim – oh, now I get it.  They’ve all said they like this activity – its helped them really figure out “their thinking” – having to say what they’re doing – is difficult, and sometimes what they say/tell the secretary to write it not exactly what they meant.

This is a great formative assessment activity to observe / listen to students.  I’ve learned a lot about their thinking this week and I believe they have as well.  When students, notice plural, ask to do an activity again because it really helped them, well – isn’t that what we’re here to do?

INB LHP assignment

As a left-hand page assignment in the INBs, I asked them to pick one problem they completed as a secretary – and they had to write out the boss’s diaglogue to solve the problem.  (midsegments or isosceles triangles this week).

Another activity in the Kagan book was something I have completely taken for granted… Processing altitudes.  Students draw one of each type triangle, and are asked to draw an altitude. Pass their paper to the next person, who then draws another altitude, etc.   Even after a couple of examples / illustrated definition for reference…they still struggled with “drawing” it.  What?  If they cannot draw an altitude, how can they actually know what one is in order to use it to solve problems?

Applying Some Brain Research

Its been many, many years since I taught geometry – but I always remember students confusing medians, altitudes, perpendiuclar bisectors and angle bisectors of triangles.  I remember attending a David Sousa How the Brain Learns training several years back.  An example was shared how students often confuse concepts that are closely related because they are often times taught on the same day.  Concepts are stored by similarities, but are retreived by differences.  When we teach similar things on the same day, they are stored together, at the same time – when students are asked to retrieve that information, there’s not enough distinction between the two – therefore, they are often mixed-up, confused.  Hmmm.

So do I choose to teach each of these similar concepts (special lines/segments in triangles) on separate days – but is that even enough space between?  Should I skip a day between them?  Anyone with experience pacing it out this way – please share successes / need to make adjustments!  I really think this is an opportunity, by using Bride’s processing lessons – to make a difference, giving students the chance to build concrete understanding of these other-wise intertwined concepts.

If you’re not familar with the Kagan series – I think its definitely worth checking out.  There is very little prep time – other than working through the lessons yourself.  All blackline masters needed are included in the book!

I am soooooo excited about using more of these strategies in the weeks to come!  🙂

I do. We do. You do.

I am the type of person who would love to go in and observe other classrooms – the problem is, very few actually want you there.  I believe other teachers are our most valuable resource in making our own classroom better.  Listening to them – observing how they interact with students, how they present content, how students respond to different strategies – and reflecting on how their ideas / structure can help make my classroom a better place of learning for my students.

Its been homecoming week – on Friday each year, we have a “cook-out” at the end of the school day – with powder puff football and an anything-goes pep rally.  While outside, you get the opportunity to see and talk with several former students.  One in particular yesterday shared they were really struggling in math this year, I’ll call this student H.  H was a hard one to win over last year – but by 2nd semester – H was experiencing success in math class.

Let me first say – when students start to make a statement that seems to blame the teacher – I redirect to what they are doing to improve their own situation.  H commented the teacher rushed through a couple of examples, then gave them time to work on the material; but that it was impossible to work on the assignment without understanding first how to do it.  So, I redirect by asking H – have you  asked the teacher to help you?  Have you raised your hand during the discussion / lecture and asked them to clarify OR even go through another example?  Have you politely explained to the teacher that your are not “getting it” and asked them to slow down to help you understand?  I always ask – are you giving YOUR BEST EFFORT?  Almost always – students will respond – “No, I could do better.”

As teachers, we all have our own styles – but it was a comment from another student that stuck with me throughout the afternoon “That’s what makes Mrs. Wilson different, she makes sure everyone gets it before moving on.”  I took that as a compliment, but I also wondered – although we may teach differently, shouldn’t this be a commonality in every classroom?

The scenario described by H could have just as easily been me on any given day.  In fact, throughout all my years – I hate to admit – but I’ve probably been the sage on the stage more often than not.

It was @maxmathforum’s tweet late in the afternoon that reminded me – we MUST pause and give students the chance to respond and we MUST listen TO THEM!  Sadly, I think many of us have been guilty of “trying to get the content covered.”

I do. We do. You do.  is a strategy I’ve used for several years – but didn’t know it had a name until about 4 years ago.  My amazing curriculum specialist pointed out what I was doing after an observation and shared a bit of research supporting this easy-to-implement format of direct instruction.  Its one of those things you may or may not pay attention to in your Ed classes – guided practice / independent practice…  I know I’ve mentioned it in previous blogs – but its always a strategy students list as helpful in their teacher evaluations.  I struggle using it at times – because I would much rather students figure out their own way of doing – but for a certain group of students – direct instruction can be most effective.

1.  I do.  Stop what you’re doing.  Eyes & ears up here.

Students put down pencils.  You want their full attention.  When they try to listen, watch and write all at the same time, they often miss out on something.  Explain you’ll give them an example for their notes – you promise!  You know you have those kiddos who want to write EVERYTHING down!  You model the problem, talking through your thinking / strategies, choices for your steps.  You can most definitely ask for student input – the key is, they are not “doing” anything else – they are with your example/discussion.

2. We do.  Students pick up pencils and work through an example with you.

Engage them by asking quesitons and letting them respond with the next steps / explanation of why.  Its imperative you implement WAIT TIME – those 3 seconds that all everyone to at least process, then call on specific students.  I find using a set of index cards with their names on them allows me to include everyone – not just those eager volunteers.  Most definitely – search for different strategies – input from students.

A moment for any questions – allows them the chance to ask for clarification.  Sure you’ll have classes / students who would never ask a question, so that’s when I find it even more helpful to call on specific students and ask them why / how.  Then another student – asking them if they agree / disagree with that reasoning.

3.  You do.  A chance to practice on their own – this confirms their ability to do a given skill / use a concept successfully.

Beginning with one problem.  They practice independently.  The KEY is that you are moving around the room – looking at THEIR work – looking for common errors / misconceptions / confirming their correct work.  A simple yes / no / take another look at this step.  When they’ve had time to complete – ask questions / redirection – I go back up front and share what I’ve seen on their papers.  I intentionally make a mistake (similar to “MY FAVORITE NO”) and call on students to see if they can explain why it wasn’t the correct choice.

This is also the time when I call on students who used a not-so-obvious strategy.  (Probably one of my favorite moments is when I get to highlight the quiet student’s strategy!  This is my chance to win them over to the wonderful world of math – they see they CAN do it!)

If I have several who are struggling – I give another “you do.”  When I see most are on track – I give a “Worst-Case Scenario” – something similar to the problem in the HW/practice that will give them the most trouble.  This allows them to ask the questions while I’m there to help.

Though this is not an orginal concept – it can provide teachers with an easy structure that will allow them to slow-down/pause – giving students time to process, ask questions or even feel successful.  It provides you with an opportunity to “LISTEN 2 STUDENTS.”  I have found the times I use this method – I will have more students attempt/complete a practice assignment than when I rush them out the door without confirming their ability to complete a task successfully.

Let me know how it goes or please share suggestions on how I can improve it!

My Favorite Friday: 2>4 & Tetris Group Costume

Its been one of those weeks.  Well, its been one of those years.  Its definitely not my students – they.are.amazing.  But I just don’t feel like I’m moving forward.  I’m stuck.  And I don’t like it.

Favorite #1 “2 > 4!”

Sitting in my room all alone this afternoon, I pulled up twitter and found this from @maxmathforum and absolutely love it.  SOOOOOOOO worth five miniutes of your time!  It was a wink to remind me – everything will be okay – eventually I’ll find my flow again…  just remember to listen to my students…  they’re the reason I’m here.

@jreulbach @Borschtwithanna @cheesemonkeysf Coloring Pascal’s triangle made me realize I wanted to do math forever: http://t.co/B5LzTwEC — Max Ray (@maxmathforum)

 Favorite #2 Tetris Group Costume

Its Homecoming week – I’ll be leaving to go chaperone the dance in just a bit…

Several of us have often tried to do a group-themed costume…

The Clue Characters – including the envelope.

The Seven Dwarfs

Black-Eyed Peas

 

This year – inspired by a tweet months ago…TETRIS!

6 – posterboards, cut 4 11″ squares out of each color

7 – foam boards

tape – 4 pieces together to form puzzle piece

hotglue to foam board, cut out excess white

elastic or ribbon toattach / hang around your neck

let the most talented one create the gameboy on a foam board (project onto board, trace, color with markers!)

 

Its a quick, cost-efficient costume! 

We met afterschool one day to make our Tetris pieces.  We shared how we so missed the collaboration we once had.  When you have the opportunity to share ideas – when you’ve got a go-to person(s), somehow, it limits the amount of stress.  With changes in schedules / room changes – we are not all in the same wing like we were for nearly 8 years.  We had common planning – and each week we met in what I believe was a true PLC.  Though most of our meetings were focused on students and not content – making sure we kept up with those who were falling behind – making sure we had made contacts home – we shared strategies that worked for certain situations – we made sure we used resources available to keep the students on track…we had the opportunity to share ideas.  Not.Any.More.

It has been so hard – being taken away from something you were a part of from the beginning – a venture you believed in whole-heartedly.

We all agreed that this year seems like…work.  And that makes me sad.

Just like our Tetris pieces – apart, we may seem a bit odd – but together…we made sense.  So a shout-out to my dearest friends – those who encouraged me, challenged me, helped me become a better teacher.  I miss each of you.

#made4math Monday! INB Pics & Triangle Investigation

INB pics of pages with WPapp

So this is nothing fascinating – but after some comments / favorited tweet about it – I thought maybe it was worth a quick post.

Catching absent students up on their INBs could be a headache – but I’ve been snapping a quick pic and using a WP APP on my phone – its only a matter of tapping share and its done.  I have a class blog already set up.  I simply title my post INB 23 Triangles 8/30/12 – all the information they need to get started on that page – page #, Title and date.

I tried it with a blogger APP and it was just as simple.  I am not as familiar with Edmodo app but I’m sure its just as easy.  Maybe @druinok can weigh in using it since she’s implemented Edmodo for her classes this year!

CamScanner

Another APP I discovered last spring was CamScanner – scan any document and create a PDF file – you can share via email or upload to dropbox, etc.  I realize their are many out there, but this one was free and had good ratings when I downloaded it.

Scan a handout and upload – students have access if they forget it at school or heaven forbid…lose it!  Its posted and even absent students can download it if needed.

Its been a lifesaver on several occasions.  At our PLC meetings – scan our sign-in/agendas and email it on the spot rather than waiting and having another item on my to-do list.

Naming Triangles Investigation

Here’s a sample of a last-minute activity I prepared on Friday.  Geometry was taking their first cumulative assessment – since this is my first year back on a block – I forgot they wouldn’t need the entire time in class.  Just as they were leaving for lunch I realized they had another 20 minutes when they returned!  Aaccckkkk!  I CANNOT waste a moment of time!

I remember using something similar to this way back when I used to teach geometry.  Sure they can name triangles by side lengths & angle measures.  But what if they only had the side lengths – could they tell the specific type of triangle?  They were VERY familar with Pythagorean Theorem – and since we know our Inverse, Converse & Contrapositive now (thanks to Susan!) – stating its converse was a cinch!  Now, let’s use it to determine what types of triangles we have…

Triangle Investigation File

Parabola Transformations

Running through files this afternoon, I ran across this one.  Basically, you give a screen shot to students with a variety of parabolas or other type of function graphs.   Their task is to come up with the equations that will result in the given picture.  One of the screens is blank…they create their own picture and give the equations needed to create their design.

Parabola Patterns Transformations

As I think about this, maybe I could use it as LHP assignment.  Students sketch their screen on top of an index card and include their equations underneath.  We could do a peer share/assess maybe.  Other ideas of how to use it are welcomed.

INBs – Graphing Stories LHP Assignment

Following @duinok’s lead, in her Favorite First Day of School post – I checked out Dan Meyer’s Graphing Stories to use as an intro to my first unit.  We viewed 8 of his videos – I asked students to sketch what they thought was the correct graph, then in a different color / style of line – I gave them time to sketch the “correct” graph.  We folded our Graphing Stories sheet and entered attached it to our INB on a RHP.  Within the discussions, we addressed choosing good intervals – a reminder of things our graphs should include from axes labels to titles.  It was a great review of good graphing techniques without actually “reviewing” – students were actually doing.

On the LHP, students were asked to write a brief reflection of their graphing experiences.  The second part to the assignment was one I held my breath on…  would they actually do it.

Create your own video / story.  Include a graph to model it.

The next day, I shared a scoring guide with them.  We talked about reasonable deadlines – I passed around a sheet and they chose their due dates.  With only a handful – who came to meet when they were not going to be able to meet their deadline, they were anxious to turn them in.

Several chose to write a story – but many of them made videos – I had a student running up the side of a house – sitting for a moment before jumping back to the ground (yes, it was interesting), another student running at different rates, someone tossing a ball back and forth in a store, a student doing a standing back tuck, a student swimming laps in a pool.  These are only a handful of videos I saw – but this was exactly what I wanted – students taking something of interest to them and connecting it to math.

My plan is to attach their graphs to the LHP.  I have smiled & laughed a lot while watching their videos.

Online Book Chat – Math Formative Assessment

Are you interested in an online book chat?  If you’ve never participated and wonder – how does that work?  Its simple, we’ll set specific parts/sections to read; meet up online and discuss what we’ve learned; share what we’ve implemented; reflect/collaborate!

Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning

Page D. Keeley (Author), Cheryl Rose Tobey (Author)

They refer to the strategies in the book as FACTS – Formative Assessment Classroom Teaching Strategies thus the hashtag #75facts.

Get your book in hand and we’ll be posting more information later!

INBs – A New Adventure – “Flip 4 Answers”

INBs – A New Adventure

All summer long I searched for ways to improve my literacy in math class – I learned so much chatting with my tweeps during our #lit4math book study.  It helped me redefine what literacy is / should be in math class – not just about reading.  And writing.  Not about creating something completely new – but improving what I already do to emphasize communication – discussing – giving students opportunities to make connections.

As I ran across various posts on the Interactive Notebooks – I knew this was something I wanted to do.  At first I had the wrong perception – thinking the interaction was between student and teacher – I struggled, wondering how in the world would I find the time to “grade” and evaluate that many notebooks efficicently and effectively and keep them in students’ hands for continuous learning???

After reading – mostly from @mgolding – I realized I had it all wrong.   The interaction was between the students and their own notebooks – to provide them with opportunities to engage with the information I gave them.  I was overly excited when I saw @mgolding would be presenting at #TMC12 – then crushed to find out my session was at the same time. boo. and I would miss out.

Listening to conversations that came out of her session and reading more once I returned home only confirmed my decision to move forward with INBs.  My science colleague had decided to pursue this learning tool as well – so grateful to have an in-person to collaborate/share ideas with too!

During the first Global Math Department meeting, she brought calm to me – answering so many of my questions in her session that night – thank you, thank you, thank you @mgolding!!!

I have begun my venture with INBs.  I feel a bit stronger in one class than the other – but I have been upfront with my students – this is a learning experience for me as well.

Some things I’ve quickly learned:

1. I MUST keep my TOC up to date – its easy to get off track if I don’t!
2. I MUST do the INB along with students – having completed the pages myself – knowing exactly what I want to go on them;
3. I MUST practice any foldables / graphic organizers to make sure they’ll fit/work.  I may have a great idea in my head – in theory anyway- but I have to put it to the paper to see if it will acutally do what I need it to do!
4. I MUST think about what I want to accomplish with the LHP assignments.  This is the one I tend to struggle with some…thankfully I have lunch with my colleague and bounce ideas to get feedback.

Flip 4 Answers

I plan to blog my list of RHP ideas later, but for today, I want to share an idea that came from my students.  Its similar to something I saw @mgolding share at #TMC12.  She had used post-its to cover hints/work/solution to an assignment she left with a substittue teacher.

When asked to create a practice quiz, one of my students used an index card to cover their work – thus “Flip for answer.”  When  I shared the student’s example, I never dreamed others would follow.  Yesterday during our first cumulative test – I oberved several others started playing off the concept.

   

As I look at the sample below, a CWP (color with purpose) would be VERY easy to assign…I think on Monday – that may be a good warm-up – turn to page 12 and CWP…  positive or negative or zero or undefined, even identifying which letters model parallel & perpendicular.

 

Another idea I think I’ll lean toward using for my LHP assignments – is the use of “Open Questions” – an idea I got during a book chat last fall from More Good Questions Small/Lin.  The second part of RHP 12 was an example of this…give coordinates of two points: with zero slope, undefined slope, positive slope, perpendicular to the slope in part c.

I believe the INBs require me to be more organized in my example choices.  It helps students be more focused / organized as well.  Looking through INBs yesterday – those who were having some trouble with their INBs / not completing their LHP assignments – seem to be the same (few) students who were struggling to make the connections I need them to.  This confirms to me the choices I am making – since most are finding great success.