Monthly Archives: October 2012

10/22/12 #75FACTS posts


If you wish to join in our blog/book chat of #75FACTS, the reflection questions suggested in the book are listed below this weeks submissions. Click on the link to submit your post.

Simplifying Radicals Create the Problem #11

@pamjwilson Always, Sometimes, Never #3

Mathematical Practice –
Were students engaged?
Were you confident/excited about using the FACT?
How did use of the FACT affect the student-to-student or student-teacher dynamic?
Was the information gained from the FACT useful to you?
Would you have gotten the same information without using the FACT?
What added value did the FACT bring to teaching and learning?
Did using the FACT cause you to do something differently or think differently about teaching and learning?
Would you use this FACT again?
Are there modifications you could make to this FACT to improve its usefulness?

Always, Sometimes, Never – #75FACTS


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.

Thoughts on #75facts


As I read SimplifyRadicals #75facts post this morning, it really got me to thinking…about things I do and how I could use “Create the Problem” in my own classroom.

I’ve given students the answer before and asked them to write a scenario that could model the problem.  But reading her refelction and suggestions for modifications helped me realize a couple of ways I could improve the way I’ve done this in the past.

The FACT reminds me of ideas from More Good Questions, Marian Small & Amy Lin.  Give students the answer and they have to come up with the equation/problem.  Example, the slope is 2/3, what are 2 points that could give you this slope?

As suggested in the FACT#11 description, providing students with an open ended task takes their thinking to another level.  Student examples generate whether they know why a computation is performed rather than just knowing a procedure.  But this FACT actually asks them, not to find the computation/problem, but to give a scenario/context where this strategy could be used to solve the problem.

The key, as with many successful strategies, is sharing student ideas.  Not just allowing them to talk about their examples and how their story matches the solution, but the teacher asking the class for feedback on whether it is a match, if not, how could it be changed/made better (pg. 81)?

This reminds me of another FACT I’ve used in class before “2 stars and 1 wish.”  however, when I first saw this a couple of years ago, it was called 2 +’s and a delta…two positives and one thing I’d like to change.  Playing off of My Favorite No, I ask students “What do I know this student understands?  Give me 2 examples of what this student did well.”  By focusing on the correct parts first, especially if I’m using a student’s example (anonymously) – the student can see it wasn’t completely wrong.

Then for the delta (wish), I ask students not to point out the mistake, but to think of a question they could ask the student to help the student realize their mistake.  Sometimes, this is a tough task, depending on the mistake that was made, but by asking a question, students, again, are having to think on a different level.

In several of the Formative Assessment Lessons from the MARS site (Solving Linear Equations in Two Variables) – the lesson format actually allows students in small groups to evaluate different levels of student work.  On a slide in the projector resources for this lesson, Assessing Student Work, students are given these questions to guide their discussions:

You are the teacher and have to assess this work.

Correct the work and write comments on the accuracy and organization of each response.

•What do you like about this student’s work?
•What method did the student use?
Is it clear? Is it accurate?  Is it efficient?
•What errors did the student make?
•How might the work be improved?
My thinking, use the FACT #11 – Create a Problem as an exit slip.  Divide the responses into different levels.  On overhead, share different levels, both correct/incorrect, as well as different approaches, using the above questions as a guide for class discussion.  Then present students with solution(s) and ask them to create a problem.
Thanks to Simplifying Radicals for getting my brain to churning so early this morning!


#myfavfriday paper thermometers


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.


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!

Vertex Form of a Line? Really?


I read Glen’s post Writing Linear Equations about a month ago.  I remember thinking…  hmmm. really?  but a line doesn’t have a vertex, does it? is that legal?  can I do that?  Will it always work?  So I tried some.  Several.  It made perfect sense. 

Please take a moment to read his post…

Anyway, I reread within the week and wondered if I should give it a try – I mean, it did make sense.  A lot of sense.  But I was afraid it would confuse the students, I was afraid to step out on the limb.  I wasn’t sure how to introduce it.

After seeing a tweet from @druinok, I decided to give it a try.  I shared the form y=a(x-h)+k and asked the students if they had ever seen it before?  In the functions unit – transforming functions (focus on quadratics, absolute values and radicals/square roots) – they were familiar.  I graphed a line with a given slope, then translated it (a point marked at then origin) the given point (h, k) –  to begin as a visual.

Anyway, within 3 examples – EVERY single student was doing it – writing equations of lines…CORRECTLY!  yes.  Thank you Glenn & Druinok! 

In my geometry classes, I still had a handful of students struggling with this “algebra 1” skill.  I pulled them off one-on-one and simply said, lets try it this way, explaining the vertex form.  They are all running with writing equations of lines now~  AWESOME!  I am a believer in vertex form of a line.  Give it a try.  Go ahead don’t be afraid.  It works, beautifully.   

#Made4Math Monday – Parallelogram Foldable


Its been a while since I’ve sumbitted #made4math Monday post.  I really like the idea of foldables – a kinesthetic graphic organizer…I believe they have a positive impact on student learning when used purposefully.

This one (found here parallelogram foldable) for parallelograms, rectangle, square and rhombus.  I wanted a foldable that somehow showed all were all in the parallelogram family, but still kept them separate – I chose a trifold.


When I saw an example of the tri-cut Venn Diagram, I knew I wanted to incorporate it somehow to show squares as the overlap of rectangle and rhombus.  This picture does not show the cuts between rectangle/square and square/rhombus, but I think its visible in the last picture.


The file is simply the skeleton, please feel free to make it your own (ha, just don’t go selling it as your own!)


I am still debating what should go in the center – thinking of examples / non-examples.   Possibly even giving students a couple of example problems using properties of quadrilaterals.  Istuck area formulas in at the last second – but think it may be more effective to let students discover area of a rhombus on the own.  Suggestions are always welcome!