Category Archives: #made4math

Flip Chart Review


This review tool from Math Teacher Mambo


and this formative assessment/student engagement reminder tool form Stat Teacher


inspired a chat with @druinok & @gwaddellnvhs during spring semester and led to this flip chart review for AP Statistics.


Ours started at bottom right corner and worked up, then over to bottom of left hand side.  That seems weird to me now, but I think my initial idea was to build the flipchart as we go along, adding cards after each completed unit.

We ended up creating ours late in spring, just weeks prior to AP Exam.  We will create them in one setting, then go back and add information as we complete units.

This was a tool several of my students stated was beneficial to them.  A couple even went on to say, they closed their eyes to visual the flip chart on the exam – which helped ensure all steps on a test or specific details on a response.  They only wished we had created them earlier.

Start with cardstock folded in half.  Wow. That’s exciting.


We attached 26-28 index cards.  Tape first card at bottom.


Next card is placed up just enough to leave space for Chapter & Title.  If using lined cards, you can turn upside down and used top line to add Chapter & Title.


If using pens, make sure ink  won’t bleed through.

The idea is not to include every single detail – but quick reminders, mnemonics, anything they struggled with on the assessment.  I encouraged them to spend 10 minutes each day leading up to the exam.

I also like how Math Teacher Mambo created a flipped video for students to know important things to include.

If I get them started earlier, I will encourage them to spend 10 minutes reading through 3 or 4 times per week.

This envelope attached to inside of INB back cover is perfect for storing the Review Flip Chart.



#made4math Monday: Learning Target Quiz Cards


Last year I wanted a file for each course, with sample questions addressing the learning targets to use as either an intervention or for retake quizzes.

Different suggestions were made in a discussion on Twitter regarding organization, offering different levels of questions.  This morning, I am trying to plan out my format.

Here is what I have come up with so far:



Standards/Learning Targets
Index Cards
Index Card Dividers (Tina suggested coupon organizers for built in dividers)

I chose a standard.  Labeled my divider and thought it might be handy to write out the actual standard.  (Yes, this could be done with printed labels).


I am using level colors that coordinate with our Discovery Ed. Benchmarking system.

  L1-red, is the very minimal; L2-yellow, shows more understanding;


L3-green, is where I want to get everyone (this set came from Illustrative Mathematics Project); L4-blue, are open questions for this example anyway…may need to change this later.


I am including answers on the back for guick-check.


These are a quick, rough sketch…trying to iron out my goal, how I want to use them.

My idea is to have a coupon/photo organizer for each unit I teach.  Use actual learning targets from our unit organizer in order to move Algebra 2 closer to SBG.

Suggestions for improvments or your own experiences are welcomed!

INB Unit Organizer


I wanted to create a unit organizer than encompassed several aspects but would also be narrowed to one page, fiting in to the INB.  Here’s a list of what I wanted:

unit overview/schedule
learning targets
record of assignments
track their own assessments/learning
place to record questions/big ideas
opportunity for end of unit reflection

Here is what I arrived at for a first attempt, copied front to back and folded in half, this is the order students will see the booklet. 

The vocabulary pre-assess was a great tool.  I saw this idea over at Math = Love earlier in the summer.  It went so well. It only took students a couple of minutes to self-assess their vocabulary knowledge.  As I walked around, I was able to see several terms had 3s & 4s.  We compiled a list of our 1s & 2s words.  I explained, as they learned a word or gained better understanding, they should go back and put a +.  Before the end of class, students were asking if they could go ahead and update their chart.

If possible, maybe completemthis part a day before beginning a unit, in order to make needed adjustments based on student responses.


I included the correlated CCSS # for each target.  Eventually, these may be beneficial when looking online for a resource on a specific standard.


I am not fully satisfied with this chart yet. Assignments made for specific targets can be listed, a note if completed (stamp) and place to monitor their assessment for each.  A second line has been included in case RTI/enrichment is needed.


Finally, the back side has a place to record reflection.  Ideally, I would have them complete the reflection at least 2 days prior to unit assessment, allowing to address any needs the following day, prior to assessment.


As always, this is a work i  progress, suggestions and ideas are welcomed!
Foundations in Geometry doc

Intro to Matrices:

Intro to Matrices pdf
Intro to Matrices doc

CCSS Appendix A Traditional Course Outlines #made4math


It seems many are just now beginning the transition to CCSS.  These files may be helpful as you begin outlining your curriculum.  All they contain are the standards as outlined in Appendix A of CCSS – recommendations for each traditional course.

Algebra I CCSS

Geometry CCSS

Algebra II CCSS

These files are only intended to help you ensure you have addressed each standard within your local curriculum.  How you organize your units can vary to district to district, but I am hoping these will help you as you organize with the CCSS.

If you have any issues with the files, please contact me, I can email them directly to you if needed.

#WTPW Simplifying Radical Expressions-Rationalizing Denominators #tlapmath


I am not sure how exciting this lesson is, but I believe the idea beats the run of the mill take notes-practice on a worksheet.  It gives students opportunities to notice patterns on their own, a chance to share and discuss those ideas as well as consider ideas from their classmates.

I appreicate Math Equals Love Walk the Plank Wednesday post and will definitely use some of her ideas with the “why” we do this.

My goal is for my students to be able to determine if expressions are equivalent, so I am beginning with a simple card matching task.  As students enter the room, they will receive a card with a radical expression either simplified or not (similar to set A).  As we begin class, they will be asked to find their match…without verbal communication…while I post attendance, etc.  They will come to me with their match and I will confirm if they are correct.  Yes, I will allow calculators.  I know, not too high level on the thinking scale.


I will have several sets of cards similar to those they matched.  Each group will then be asked to complete an open-card sort.  This simply means, I do not give them any direction on how to sort their cards.  The only stipulation is they are ready to explain why they chose to sort them as they did.  When the timer goes off, we will share sorts (both volunteers and any I find that are interesting to me).

Part C, I will have concept attainment cards placed around the room.  Each card will contain examples of radical expressions labeled simplified and expressions labeled not simplified.  Students will carousel to different cards, noticing patterns, trying to develop their own rules.  After a set time, they will do a quick pair-share to summarize their findings before we have a whole class discussion. 

Hopefully their ‘rules’ will encompass all we need to know, but if not, I can always use their ideas to lead us to our goal.

We will create a set of notes for our INBs.  Part of their HW will be a LHP assignment to give examples of expressions that are simplfied and not simplified from their earlier carousel work.  Ideally, they would create their own expressions.

If students need practice with skills, an idea from a workshop several years ago…on a page of say 30 problems, I pick 5 I want them to do, then they pick another 5 or 10, whatever I/they feel is necessary.  By giving them this option, I have more success getting them complete the practice.  I would much rather have 10 complete than 30 incomplete or not even attempted.

An idea for formative assessment…return to card sort from Part B.  They should sort into groups of simplified/not, even match up equivalent expressions.  One person stays with the sorts, while others go to different groups to peer assess.


Possible written assessment questions, a) give a bank of expressions to match equivalents, noting simplified terms; b) given a simplified expression, create an unsimplified, equivalence.

This is a very generic layout, but I can use the sequence with whatever level of Algebra I am working with.

I will post again when I have sets of cards completed. 

Feedback to move forward, ideas  for improvements are welcomed.

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

Happy Birthday #Made4Math !!! Formative Assessmemt Reminder Cards


First, just let me say a big THANK YOU to @druinok for beginning #made4math and to all of the generous folks who have openingly shared their classroom ideas, lessons, tips over the past year.  I was overwhelmed with how quickly it took off!  Still, today, I am amazed at the generosity of this community.  I have learned so much and my classroom was definitelh impacted by your awesome ideas!

My share for today was initially a result of a convo with @rachelrosales and @druinok, brainstorming ways to organize reminders for the numerous formative assessment techniques…something simple, at your finger tips. 

I loved @druinok’s post today and her Student Engagement Flipchart.  Very.Nice.  It will definitely be on my to-do list for a future project.  However, I am choosing to share a similar idea, just a bit different format.  I cut down index cards to fit sports card pages… pack of 10 for $1.  I am able to display up to 90 of these reminders ranging from formative assessment techniques to various strategies for student engagement, reflection, etc. 

Front side of card has title, with some information…


Back side of cards has description, suggestions, reminders…


I have placed the pages in a small 3 ring binder which can easily hold more pages.  Currently, I am trying to include summaries/reminders of techniques I have used or see being easily modified for math class.

Looking forward to learning and sharing more FA techniques with my amazing PLN!!!

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

All Student Response Cards #made4math Monday


In reading Embedded Formative Assessment (Wiliam, 2011), there have been several practical techniques presented in each chapter.  While discussing chapter 4, @druinok suggested creating response cards this summer, based on the technique All Students Respond.

  I had seen a set made by an elementary teacher in my leadership network.  She had several cards labeled with letters, hole-punched and attached to a 3 inch ring that could be opened and placed around the metal frame on student desks. She explained students always had access to them.

I kept thinking about how to accomplish the same idea for my classroom.  I had a package of name badge holders I had picked up at our Mighty Dollar in town, but never found a use for them.  Basically, I put this example together quickly, to have something for #made4math today. Its not innovative, but for anyone who does not have a “clicker system” or devices to use with Poll-Everywhere, etc., its an option that I believe could prove as a useful tool.

My idea is to have a single card, with all responses.  I would need to ‘train’ students how to hold their cards allowing me to see their response clearly.  Mine is double sided, this could easily be accomplished with cardstock printed, then laminated if you didnt have the badge holders.  Each student could clip one into a pocket of their INB and have them on hand when its time to use them.  Or they could be clipped either to a hanging ribbon or the side of a magnetic cabinet, even placed in a basket if you only had one classroom set.


The first side includes a favorite of mine…always, sometimes, never…color coding green, yellow, red, respectively.  The student places their hand, so only the response they choose is visible and located at the top of the card when they hold it up for me to see.  I didn’t have the color circle stickers here at home, but I believe they may help in the visual for me to see.  By keeping responses color coded, I can quickly scan the room to see where students are, then make a decision as to what type of question follows or if we should procceed with discussion of why they responded as they did…supporting their claims with mathematical evidence, of course.

Notice, the QUESTION response.  A student may have a question or require some clarification, this choice doesn’t allow them to opt out, but provides a way to say, I need some help.


On the back side, there are simply color-coded (different from other side) multiple choice responses, again to allow a quick scan before deciding how to proceed.  If multiple answers are chosen, begin by asking students to give possible reasons why a student may have chosen A or D-the other answer, if I chose A, could I figure out how someone else would have chosen D?  I also like to ask, noone chose B or C, what is a possible reason why someone would not have chosen  ___?




Like I said, I plan to use color circle stickers which allow me to see student responsesmfrom across the room.  I am debating on howmto do true/false.  Would
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Trig Ratios – #made4math


Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for students.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my KaganCooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Trig Ratio Cards

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

  • 1. Students are out of their seats and active.
  • 2.  Students are talking about math.
  • 3.  It allows them to both self-peer assess in a low-stress situation.
  • 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.


To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

Quadrilateral Diagonals Properties


Over spring break, I was surfing online resources, searching for ideas and suggestions on how to plan and be more purposeful with the Mathematical Standards, which I have realized this year just how key these are to the success of CCSS. As I looked through Inside Mathematics , I ran across some PD training materials. I watched clips from Cathy Humphrey’s class. The Kite Task, an investigation of quadrilateral properties from seemed like a great activity to ease back on day 1 when we returned.

The task in short is for a kite company, who wishes to launch a new line of kites consisting of all types of qudrilaterals. The students are asked to devise a plan for how to cut/assemble the braces for each type of kite. They are only working with the diagonals in the investigation.

Rather than running copies and cutting out, I used my paper cutter to cut 1″ strips one color card-stock lengthwise and 1″strips width wise of a different collor (I didn’t realize how helpful this would be until later on). I created a strip to use as a guide on each strip, placed 7 holes equally spaced. Odd amount is best since they will be looking at bisectors some.
Each student would receive 2 of one color and 1 of another color.

Here are some snapshots of possible braces built.

For anyone who is having trouble visualizing, I’ve added some “sides” to the diagonals:

As we began the 2nd day of class, a few groups needed just a bit more time to wrap up their investigation. Using fist to five, I asked how many they still needed to determine. Most groups only 2 or 3, so I set the timer to keep us on track. I love days like this to walk around and just listen.

As I was questioning one of the groups, trying to ensure an absent student was on track, I asked the group’s members to “fill an order” – pick 2 sticks and construct the diagonals needed to brace…kite that was a rhombus, then another shape, etc to quiz them for understanding. AHA! Why couldn’t I use this as a formative assessment for the entire class?!?! Perfect.

When all groups had completed and debriefed a bit, I placed orders for kites and the students had to build the braces and pop up to show me for a quick assessment.


These pics were actually a geometrically defined kite. If you look closely, you can see a few wrong repsonses. To address these, I used extra sets of sticks to build a correct example and an incorrect example. To ask for suggestions why one was and the other was not correct. Why was one example actually a rhombus, allowing them to really compare/contrast the two figures.

Another great mistake I saw…when asked to create a rectangle, the top sketch is what I saw from about 6 students. Of course, my initial thought was, they dont understand the diagonals must be congruent.

Then I saw a student trace their shape in the air…second sketch. I literally saw their thinking. They had not used the sticks as diagonals. Clarified and corrected!

A post-it note quiz today, I built the braces, they had to tell me the quadrilateral name. A stop-light self assess, revealed most were confident, of the 10 yellows, 7 got all parts correct. The others missed 1, 2 or 3. All green students had each part correct.

We did a little speed dating to use properties to solve problems. As I listened to their approaches, most everyone seemed on track. Overall, I was very pleased with the results of the lesson.