Category Archives: radicals

Go Fish! in Math Class


Hey my TMC17 buddy, @kcnorojo!  This post is for you!

As an intro to reducing radicals…  I place students into groups of 3 or 4 and we play several rounds of Go Fish!  This by the way was not my original idea.  I will need to dig some to find the original post.  But I have used it multiple times with all attitudes of students and it has been a great concrete introduction.

Just in case you’ve never played.  Here are the official rules from

Each player gets five cards. If you are dealt a four of a kind, or get four of a kind during game play, those cards are removed from your hand, and you get a point. Moving clockwise, players take turns asking a specific player for a given rank of card.

I actually adjust the rules a bit in each round.  And I believe we start with seven cards as well.  Game ends when someone runs out of cards OR I call time.

Round 1:  Students must have a pair for a match.  Only a pair works.  I allow them to play for several minutes to get the flow of the game.  When the timer goes off, I ask them to count their matches and high five those with the most points.

Round 2:  Students must have a group of three for a match.  Even IF you have the 4th card in the set, you CANNOT lay it down with the match.  Again, when timer goes off, I ask them to count matches and we celebrate the winners.

Round 3:  Students must have an entire set of four cards to complete / lay down their match.  This round goes on just a bit longer.  Timer, count matches, celebrate winners.

Round 4:  I ask them to deal out the cards – and this time they must have a set of 5 to make a match.  A few usually continue to deal out the cards, but several pause and say – but we can’t!  There are only four cards of each type.  Yes!

We have a discussion about which round was their favorite to play.  Which round was toughest?  Which round was their least favorite.  Usually – Round 2…with three in a set, because IF you end up with the last card, you can never lay it down, thus never emptying your hand to end the game.  Hmmmm.

I literally draw a radical on the board and describe how it “sort of” looks like my hand when I hold a bunch of cards.  I make a big deal of the index on the radical – it tells us the rules of the game.  The Go Fish! game lends it to this part very well.  Though these are not the greatest examples, hopefully they will give you a quick idea of what the notes may look like.

We practice several on whiteboards and write a reflection at the end of the work.  Then I have them open their INBs and write out a few examples to complete – notate for future reference / study.  Depending on the class, I may offer a few examples if they are unable to create some on their own.

Depending on the remaining time in class, I will then pass out the Radical Rummy cards to the groups.  I have gone over how we can type in the problems on our graphing calculators – rational exponents, radicals, etc.  I explain that every card will match to form a group of 4.


When a group has gotten their matches complete, I have them create a small poster or use whiteboards to list equivalent expressions.  We then begin a notice / wonder.  I jot down their ideas, testing some as we go along, but letting them decide if their “rule” for the rational exponents holds true.

I like this task after the Go FISH! and simplifying a few radical expressions because it shows them how the rational exponents are simply asking us to find that amount of the factors.  For example, an exponent of 1/3 asks us to find 1/3 of the factors of say 8.  Since 8 = 2*2*2 and we have 3 factors, I want 1/3 of them, so 2 if the 1/3 power of 8.

There are also come GREAT discussions that arise about the negative exponents and what mathematical operations they are telling us to do.

I would love to hear how you approached these same skills and how it goes!

Radical Rummy


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.


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.

Made 4 Math Monday #4 Hole-Punch Game


Has it seriously been a week since I was here? Yep.

Just one quick thought on #TMC12 for today… It was everything I expected and it was nothing like I expected.  Yes – these people are the rockstars they seem to be on twitter… they are genuine in their desire to become better teachers – willing to share – wanting to learn… and give their students the best learning opportunities possible!  But what I was most amazed with – I was there with people I had never met – I guess I was expecting it to be weird meeting everyone for the first time -but everyone was exactly as I expected them to be… oddly as it may be – I felt like I had known them for ages.  I walked in to MICDS in awe of the company – I left MICDS knowing I had lifelong friendships / colleagues from all across the country.  These folks are

To end Saturday, we broke out into content areas.  I was part of the Algebra I group.  There were some great ideas shared – @cheesemonkeysf rational expressions scavenger hunt game;  I’m sorry I didn’t write the name down, was it @msimmons5 (sorry if not) – had this great SURVIVOR review game he uses – within a matter of minutes – there were suggestions shared on what to do with kicked-off / disbanded teams.  Hoping he will actually start a blog and well, blog about the idea in its entirety (sp?).

I shared a snippet of an activity called the Staple Game.  It was shared with me at a KLN meeting this spring.  Since I hate to waste office supplies (staples) – I updated it to the “Hole-Punch Game.”  Simple rearrange a worksheet / practice problems so they are placed around a sheet of paper…see this example:


  • Students work in teams.
  • Each student will complete his/her own work.
  • When everyone has completed 1 problem – they compare answers – to determine which is correct and will be used for the group answer.
  • All team members run over to teacher – teacher checks solution –
    • if correct, hole punch the outer edge of the problem, students return to work space and continue to next problem.
    •  if incorrect, they return to workspace and rework.
  • She also suggested staggering which # each team begins working on.

The teacher who shared said this accomplishes 3 things:

  1. Students must talk / agree on a solution.
  2. Students are physically up and moving.
  3. Sure you could put a check mark, stamp it, etc. but the sound / click of the hole – punch (or stapler) does something crazy and the students – especially for those who are struggling are motivated to keep on working.  Weird, huh?

So for #made4math I am sharing a radical equation hole-punch game.  It could be used as a review or simply as in-class skills practice.


I think you’ll agree this is not a difficult thing to create.  Often times for me, certain classes of students will work harder when a “worksheet” is transformed into a “game-like” activity.  I have also used Tales from the Spring’s Ghosts in the Graveyard activity a couple of times- tweaked for the appropriate season / holiday eggs in a basket, presents under the tree… great discussions occurred every time – students helping students and they completed WAY more practice problems during that short amount of time than I could have ever assigned for them to do otherwise.  The thing I LOVE about this activity – Its not necessarily the fastest, smartest, who completed the most problems that will actually win…

Student Evaluations Part 1


Warning! Long post – more for my reflection / ramblings than for your enjoyment… 🙂

Each year I ask students to fill out evaluations on me – explaining I need their feedback so I can grow as a teacher.  I tell them administrators can come into my classroom and give me an evaluation – but they are with me EVERY SINGLE DAY – they are the ones who know what’s going on and I respect their views / opinions.

I usually wait a couple of weeks after the end of the semester to read through them – but its been over 8 weeks.  Today, I sat down and began reading.  I chose to separate my evaluations – into 2 groups.  This first group was for students who have basicallly met / surpassed benchmark tests in previous grade.  The second group, Part 2, will include students who have some gaps in their learning, are not as intrinsically motivated and may require more support in getting to mastery.  A couple of things really stood out to me.

  • 3 math topics you have mastered this school year.

Top 3 topics (tying) : Linear Functions, Polynomials/Factoring, Quadratics – followed closely by Function Families, Solving Equations/Inequalities and then a dip in responses to Exponents and Systems.  Very Few students listed Radicals and Sequences.

As I look through the entire evaluations – I realize the 3 top units, I successfully incorporated hands-on activities and allowed their learning experiences to be “more open” meaning – I was not so rigid with assignments – actually I gave them assignments & answer keys ahead of time and they chose to work on what they needed to.  (Remind you, these classes were more self-miotivated learners, so this option was successful).   Hands-on learning, games, lab activities – students were up out of their seats and actively engaged.  I have already begun a post about activities/strategies I used in these units and will start to share those soon.

The Radicals is no surprise since its the top of my next list.  Sequences I was disappointed – we separated them into a self-contained unit – but I’m wondering if they should be placed back into the corresponding unit after seeing some of these reponses.

  • 3 math concepts you still have questions about.

Radicals was listed 34% of the time! Wow.  That’s huge. (Makes me feel like failure. 😦 ) Systems – specifically elimination was listed 11% of the time ( surprise to me) and Exponentials 8% (this one was a surprise also since these students performed so well on their unit assessments).  There were 14 other random topics listed – meaning only 1 or 2 students listed each one.

These surveys are really no surprise – their EOC confirms their concerns, strengths and weakenesses.   When I analyzed unit assessments, I often looked at problems that >25% of students had trouble with – to me there may be issues with how I presented the content, thus I revisit the topic/concept.  Radicals is a topic I’ve been looking for resources this summer – knowing I had to improve with this topic!

When we met as a department, we are looking at the first unit Real Numbers – embedding an intro to radicals within the unit – since Rational vs. Irrational was one of the standards we addressed.  I have located a few online resources – like Real Teaching means Real Learning’s post on Teaching Radicals in Less than Five MInutes.  I plan to tweak the “game” a bit – but it uses the basis of Go Fish!  Students play rounds of Go Fish! collecting “books of 2”, next round “books of 3”, 4 and so on…. but with Books of 5 – cannot be done since they only have up to 4 of a kind in their decks.

This leads to examples of square roots, cube roots, 4th root and so on with an expression involving both numbers and variables.

My colleague and I pulled out a deck of cards and tested the game – going through the lesson framing, etc.  We think it will be a success!

I am looking at the use of pythagorean theorem / perimeter of triangles to intro operations with radicals.

I welcome any resources you have found to help students with these topics.

As I finish – I will share just a snipit of the remaining questions I asked students:

  • What are things I do well as a teacher?

 Most of the responses fell within each of these listed.  I would be very satisfied if my child was in a classroom where the teacher did these things well.
  • connects with students (#1 – you have to create a relationship with your students – they have to know you care!)
  • explains math fully / in depth
  • addresses ALL of our questions (tho’ some of them argued I never ANSWERED their question, I did address it!)
  • connects math with us! / real life situations I can aconnect to
  • you teach – you don’t just sit there (students actually wrote this…I found it a bit humorous myself, you mean people don’t teach? Really?  They just, uh, sit at their desks?)
  • offers help before/after school
  • Life Lessons*
 *  I will have to share more on these in a later post!  Students presented me with this poster as a reminder of “all they actually learned in math class.  At the end of the year awards ceremony, I was awarded “The Best Jim Carey Voice Impersonation.”  I’m not quite sure if there is a compliment or a dig in there!  All I can say is – I LOVE MY JOB!  And I get exctied!  Oddly enough, the student who came up with this award is the same one who responded I was moody on things I needed to improve. 
  • What are things I could improve as a teacher?

post attendance (my 1st period – I would get into class and simply FORGET! Clerk was always calling me… ugh. got to do better.)
more in-class time to work on assignments (possibly a shot at flipping this year to address this one???)
more hands-on (I feel I do quite a bit – but they want more!!! )
one student even said I was moody (I promise to stay hydrated, eat breakfast and get more sleep???)
There were other responses like “you do everything well” etc – which makes me feel that I was a success overall as a teacher in general – but truth is, I know there are many areas for growth!  The day I quit asking how can I improve, is the day I need to stop working with students…and get out of the classroom!
  • What activities, strategies, methods did you find most beneficial / effective?

  • Labs / Group Activites! / Hands-on (Battleships / Mines, Bungee Barbie, Marshmallow Catapults – definite winner!)
  • Lab Report (I began this the last month of school to fulfil part of my writing/literacy folders, but with so many responses from students that it was beneficial, I plan to use it with all data labs we complete this school year!)
  • Computer Lab Time – and Lab Journals
  • Creating our own tests! (I wondered if this was really helpful, but even in talking with a couple of parents – this was a strategy that caused students to look deeper in what the learning target was really asking.)
  • Wrong Answer Analysis – mentioned many, many times! YES!!! *fist pump* 
  • Notes
  • I do. You do. We do. (note taking strategy)
  • Songs – I am a Bob Garvey Math Madness fan
  • Rating of online resources we used throughout the school year.

I was in the computer lab one day each week and used this time as RTI – if students were progressing, they were given a specific task to complete online, then were asked to learn all they could about upcoming topics – I tried to use it as a front-loading strategy.  Letting them expose themselves to online resources on topics in the next unit.  I then asked them to journal about their finds – but this year, I think I will play off of I Speak Math’s idea of utilizing a class wikispace and allow students to fill Concept Help Pages with online resources they find helpful.
I gave students a list of most online resources students had used this year, but I am only listing the ones they rated a VERY helpful (9 or 10 out of 10).
Cool Math
Geogebra also check out for teacher-shared resources
Ten Marks as a teacher you are able to set up your classes (free), choose a basic curriclum, assign entire units or specific topics to the entire class or individual students.  It was a good resources for students on home-bound placement or those who had been out for extended days.  I also used it as a resource to share with parents for students who needed remedial work for mastery of standards.  Like any resource, its not and end-all, be-all – but I found it to meet some of my classroom needs.
Khan Academy from a handful of students. – I realize there are debates about Khan – I agree with some arguments – but for certain situations / students it is a great resource.  I had a student who loved math and completed many, many lessons/practice to fill in “downtime” during the lab and on own time at home – just because they wanted to learn more, beyond what I was doing…I see nothing wrong with that.
I often made assignments with Geogebra using investigations and skill/concepts in Ten Marks – so these were probably the 2 they were exposed to most often.  By far the Cool Math was listed as most helpful – students would often go there first as they began to look for help.  Students like the simplistic explanation – they say its easy to follow and they like the crunchers – practice options with some lessons. 
  • Most memorable moment this year…aka in 20 years, what will you remember most about Room 148:

Lots of laughs came from these responses for me.  Several comments on life lessons, finding the sunshine and “Getting Happied” (confetti cannons! still have confetti stuck in my ceiling!) –

…but the one that made me most proud as a teacher… a student responded “Learning!”   And that, folks, is what its all about.