Category Archives: Middle School Math

Radical Rummy

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I received this file about 5 years ago at KCTM in Bowling Green.  Kari from WKU shared it.  I apologize I cannot remember her last name to give credit.

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She actually used it to play a card game style activity.  I copied sets onto different colored cardstock and laminated, I have enough sets we usually do groups of 3 people.

I do this activity along with Go Fish for simplifying radicals. 

There are four different forms of each value.  Students use calculators to match cards with same value.  We create a poster as a whole class.  Then notice and wonder. 

I like how students develop their own understanding of rational exponents, negative exponents and radical forms.  It’s a great intro activity.

https://www.dropbox.com/s/hsywphtj5sty9jn/Radical%20Rummy.pdf?dl=0

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Environment – Shaping a Culture of Thinking #makthinkvis

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This semester I have been participating in an online chat #makthinkvis with @lizdk and others addressing the book Making Thinking Visible by Ritchart, Church, et al.  Its been very challenging at times-pushing me think outisde my norm for ways to integrate these thinking routines into my instruction.  As well as causing me to step outside my comfort zone as I attempt to put them into action.

I had intended to blog about my experiences and reflections as I’ve tried these thinking routines, however, time seems to  evade me.  Hopefully, I can find time here and there before the end of the semester to get a few things shared.

As we finished up chapter 7 this past week, one idea from page 243 keeps coming to mind.  A key force that shapes the culture of thinking is the environment.  Sure, we all come in our classrooms, organizing, putting some thought into the layout, neat desk (maybe on open house night, but definitely not now for me), where/how papers are turned in, supplies, flow of the room, etc.

But if someone walked in my classroom, after hours, empty of students, no teacher around, what would serve as evidence of learning/thinking?  How much could you discern about the thinking and learning that goes on in my classroom just by stepping inside?

Sure, they may see an agenda and “I can” statements posted daily – but is that evidence of student thinking/learning?

What is hanging on my walls? And who put it there?

What does the room arrangement say about student interactions?

Where is my desk? Can this indicate anything about our learning environment?

If there is nothing on my walls, what does that communicate?

If you knew nothing about me, but you walked in my classroom – I wonder…

What you would see?  What would you notice?
What do you think is going on?
What does it make you wonder? What questions do you want to ask?

What does it say about about me as a teacher, about the learning opportunities I provide my students?

I wonder what evidence of thinking and learning you might find…

Pictures to come later…I invite you back to step inside my classroom soon!

Always, Sometimes, Never – #75FACTS

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I’ll be honest, I’ve only truly dug-in to reading the first 6 FACTS of Keeley & Tobey’s book over the past 2 weeks.  Through KLN – Kentucky Leadership Network, I’ve explored several others over the past year.  But I’ve gotten very drawn in to processing the descriptions, suggestions given on the first 6 (by the way, they are listed alphabetically, didn’t know that until someone pointed it out in twitter chat).

This past week, of these 6, I’ve attempted some form of Agree/Disagree (#1), Always Sometimes Never (#3) and Comments Only Marking (#6) in my classroom.  I’ll share more later on A/D and Comments.

Last year, I began experimenting with the Formative Assessment Lessons from the MARS site.  Sorting Equations and  Identities lesson asked students to sort mathematical statements into categories – always true, sometimes true, never true.  Part of the task was to justify their choices.  After using this lesson, I realized students really struggled with these statements.  In fact, they hated them – moaning/groaning each time one would pop up.  Which said to me – they were having to think.  I began embedding them in lessons/notes – class discusses/questions – especially in assessments.  By the end of the year, students were “not afraid” to face ASN questions as before.

This week, I gave geometry students 15 statements about quadrilaterals/polygons, in which they had to answer ASN.  When they arrived in class the following day, I had areas of the room designated A, S, N.

Depending on the FACT, it may help to explain to students why you are using the new strategy.  Part of this discussion was that when someone makes a statement, it may seem true, but we should check it out to determine if in face it always applies, sometimes applies or never applies (page 57).  Through the activity, students were able to share counterexamples if they disagreed with another student’s statement.  Great discussion (even a few semi-heated arguements) occured!

Mathematical Practice – #3 Construct viable arguments and critiques the reasoning of others.

Were students engaged?  Definitely – from the time they walked in, they saw the A, S, N posted and KNEW what was coming.  Most were engaged during the activity.  At least those who didn’t want to think – had to at least choose an area to move to in the discussion.  I used my “name cards” to call on students to ensure everyone needed to be ready to share their justifications.

Were you confident/excited about using the FACT? Yes.  I’ve found a new love for always, sometimes and never statements – though I remember detesting them a particular college geometry course – now I realize what a great learning tool they can be.

How did use of the FACT affect the student-to-student or student-teacher dynamic?  I tried to allow students to share their own counterexamples – but when one was stuck, I would question – referring back to properties we had investigated, drawing figures on the board, presenting a what if… if needed.

Was the information gained from the FACT useful to you?  I realized some students still confused a few of the rhombus, rectangle, square statements.  Mostly, that students often only considered the “obvious” – but this activity was great because others were able to share their “what about…” with their classmates.

Would you have gotten the same information without using the FACT?  In the past, I would have likely made the same realizations but only after giving the unit assessment.  This FACT helped clear up some misconceptions during the learning process rather than at the “end of the learning.”

What added value did the FACT bring to teaching and learning?  Students had to think about their thinking, jusitfy their reasoning, could be critiqued by classmates’ thinking – great opportunities for discussion / sharing!

Did using the FACT cause you to do something differently or think differently about teaching and learning?  During the task, I was able to use student comments as a springboard for whole class discussion, pointing out examples that made it true and examples that made it false (great piece of learning to impact understanding of counterexamples).

Would you use this FACT again? Yes.

Are there modifications you could make to this FACT to improve its usefulness?  This FACT lends itself well to written work, whole class & small group discussions.  Follow up is key – probing students and guiding them to consider other examples – if not shared by classmates first.  Even after arriving at what seems to be class consensus, ask again – challenge their thinking – don’t settle for the first correct responses – ask why – let them justify their reasoning.

#myfavfriday paper thermometers

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A super quick post – @wahedahbug tweeted looking for data for Algebra I students to collect / put into a table and work with.  One of my favorites is creating a paper thermometer.  Most students know water freezes and boils at 0 and 100 degrees Celcius and 32 and 212 degrees Fahrenheit.  So that’s where I start with my students, asking them to leave a few spaces between the values on our “thermometers”.

Next, I ask them to find the “middle” of each of the values, and again the “upper and lower middles”.  Most will simply average to find the mean.  We record these values, then use differences to compare to find our rates.  9/5!  If you like, sure, change it to a decimal – whatever works best for your students.

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I’ve been using the “vertex” (h, k) model for lines – so, pick a data point and create your equation to model your data.  Pick a different data point…does it give you the same equation? 

I remember the very first time I ever did this activity at an Algebra for All workshop – I was amazed…it was the conversion equation between Fahrenheit & Celcius! LOL – really?  I should have known that! duh.

I love using this because the students recognize the equation from science class and now they “know” where it came from!

#75facts Book Chat Begins Monday 9/24

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

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!

Online Book Chat – Math Formative Assessment

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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

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!

#myfavfriday Who Is Robert Wadlow & Super Size It!

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“My Favorite” was probably my favorite part of #TMC12, literally.  The snippets were quick ideas you could easily tweak for your own classroom.  So when @misscalcul8 suggested we continue – I was excited.  That is until I started thinking about what I would share.  How do I pick my favorite?   My favorite what?  I have a whole list of things I want to share – but today…a favorite unit I’ve used many, many times successfully with my students.

Sadly (for me), with CCSS, we have shifted the ratios/proportions completely to the middle school, so one of my favorite units Who Is Robert Wadlow? is no longer included in our Algebra I curriculum at the high school.  I would leave students with the question at the end of class the day before beginning the unit “Who is Robert Wadlow?”  Several would go home and look up – find information.  The following day, we would discuss, share his measurements (most in metric units) and as a class we would determine how to convert to standard units – so it would make the most since to our American Brains.  So my question – was he unnatural?  Or just a bigger version of us?  If you research, you’ll see how he was normal size baby when he was born.  We talk about how you go to the doctor for well-child visits and they measure you – plotting your height/weight on “that curve” and discuss why doctors do that.  How if we’re growing too fast/slow the doctors can run tests to see if something in our growth hormones need to be modified…

Anyway, to end the day we all measure our foot lengths and heights and create a scatterplot…surprised to see – its somewhat correlated (yes 9th graders are growing, so its not perfectly linear…) – then we add RW’s (ft, ht) to the plot…again, surprised to see, he fits the pattern…just a bigger version.  We calculate the height/foot length ratios for the class, then split the data out to boys and girls to see if there is indeed a common ratio…once again, surprised to see how close the ratios actually are.  We talk about people who are clumsy in while growing – what their ratios would look like – if they are too tall for their feet, etc.

I shoudl note I used this as opportunity to teach students how to enter data into lists on TI-84, L1=foot length, L2=height, L3 = (L2/L1) and how to create scatterplots on graphing calculator.

One year I even had students ask if this was related to Vertruvian Man and explore if they were similar to him.

As a final project in this unit, I would assign Super Size It as part of their unit assessment.

Y, B, H with their Super Size It projects.
Special K – scale factor of 5 …125 times more cereal!
Extra Gum – scale factor of 3 … 27 times more gum!
Chocolate Pudding – scale factor of 2 …8 times more pudding!
 
You could easily modify this activity to fit high school geometry – to determine how scale factors affect surface area / volume ratios.
 
Robert Wadlow Ratios & Proportions Unit Organizer
 
A few other files I have used within this unit –

So, for My Favorite Friday – one of my favorite units – I no longer get to use – hopefully one of you can use an idea or two and keep the spirit of Robert Wadlow & Super Size It alive!