Math Fun in San Antonio – NCTM 2017 Annual

Next week is the NCTM Annual Math Conference in San Antonio, TX.  It’s a great time to go to Texas, as the weather hasn’t gotten too hot. I remember the last time NCTM was in San Antonio, when I was still teaching high school, and met up with all my teacher friends. We had such a great time, not only going to different workshops at the conference, but exploring the area (a trip to the Alamo was a must) and eating and shopping along the River Walk. I am going this year as part of the education team for Casio, where there will be a lot of fun to be had at our exhibit booth and sponsored events.  I have been going to NCTM Annuals for over 23 years (what?????), and as usual, I am looking forward to reconnecting with math educators and friends from all over the country, many of whom I only get to see this one time a year. So, it’s more than just a place to learn new ideas and collaborate with like-minded educators, it’s a time to renew friendships and share memories. I certainly am hoping to catch up with as many folks as I can, even if just to share a cup of coffee or a hug as we pass in the conference hall.

Naturally, the goal of attending a conference is to learn new things to bring back to your classroom or to the educators you work with. It’s one of the aspects of these conferences I love the most – the ‘renewed’ energy and excitement that occurs when you see a strategy that you want to take back to your class or you learn a new approach to a familiar concept that you know will resonate with your students, or you find that perfect resource for an upcoming unit. I always consider these conferences as a way to reaffirm why we teach math – seeing what others are doing, sharing stories and ideas, and leaving with at least one or two ideas that are going to spark your students creativity and understanding. For me personally, I always had a key focus (say Algebra, or Geometry or technology or manipulatives) to narrow down the workshops I went to, with the goal to find a few new resources, ideas and strategies to incorporate into my teaching over the summer so that next years classes would be even better. This type of focus helped to make ‘teaching’  a new adventure every year, even if I was teaching the same subjects, and it also made sure that as a teacher, I was always challenging myself to be better and find relevant strategies and multiple ways to help my students learn.

One aspect that I always look for is technology applications and resources. I am a firm believer in the idea that technology, whether it be a calculator, a tablet, a computer, a video, can be a valuable resource to help students both learn and develop mathematical understanding, but more importantly to visualize abstract concepts and explore ‘what if’s’.  I am sure there are many of you out there as well looking for some technology workshops as you attend NCTM this year, so I wanted to share some workshops from some of the amazing teachers that work with Casio, as these are always such great hands-on experiences.


  • Thursday, April 6 – 9:30 – 10:30, Room 213AB Conv Center: Exhibitor’s Workshop What’s New At Casio: Viewing Mathematics through a New Prizm (or Two) 
  • Thursday, April 6, 3:15 – 4:30, Room 217C Conv. Center: Polar, Parametric, Rectangular Graphs – Really See the Connections! with DeeDee Henderson
  • Friday, April 7, 11 – 12:00, Room Presido ABC (Grand Hyatt): Conceptualizing Polynomials with Jennifer N. Morris
  • Friday, April 7, 1:30 – 2:45, Room 224 Conv. Center: Conics – The Ugly Duckling of Algebra 2 with Denise Young & Tracey Zak Johnson.
  • Friday, April 7, 2:o0 – 3:00, Room 008AB Conv. Center: The Probabilities and Mathematics of “Wheel of Fortune” with Mike Reiners
  • Saturday, April 8, 8:00 – 9:15, Room 006D Conv. Center: Hands-on Activities + Technology = Mathematical Understanding through Authentic Modeling with Tom Beatini

We will also be having a fun time at the booth, Thursday – Saturday, playing games, having give-aways, talking and doing mathematics with our hand-held technology, so be sure to stop by and say hi (Booth #631) and come play with math. I will be there most of the time and hope to meet some new math educators and give a hug to old friends!!

The Power of the fx-991EX – It’s Not JUST Solar

I read the Casio Twitter feed and FB feed every day, just to answer questions and see what followers might be saying. Recently there have been some kudos shared about the fx-991EX solar powered scientific calculator that got me curious. In particular. that the fx-991EX does engineering problems so well and they would be lost without it (someone said he uses it in all his higher-ed courses). This was intriguing to me since I assumed engineers, with their complex calculations, would more likely use graphing calculators like the Prizm or ClassPad or even engineering software.  Naturally, I set out to explore some of the ‘engineering’ capabilities of the fx-991EX, since I hadn’t really spent too much time with this aspect of the calculator.

As I refreshed my memory of the menu and capabilities of the fx-991Ex, it kind of boggled my mind how
much this solar-powered scientific calculator can do, and with it’s QR code capabilities, it can even show graphs and printable spreadsheets and tables. (See my previous posts about Graphing & QR code capabilities). After looking a little more closely at all the menu icons and what each does, I understood why this one calculator would in fact be sufficient for engineers, or really anyone. I spent some time playing around with different features that I had not previously explored, and have shared a couple of my explorations in the video below.

For those of you who have not experienced or explored this powerful little calculator, I suggest you do. If you are at NCTM San Antonio this April, stop by the booth and get some hands-on experience, or just explore some of the videos, or download the free 90-day emulator trial and give it a go.  You can access our Quick-Start Guide to get you on your way.

The Last Five Minutes of Class

You teachers out there know that those last five minutes of class – when students are ‘packing up’ even if you are not quite finished with the class activities, or, you’ve finished and they are suppose to be working on their assignments or reviewing – are often  a ‘wasted’ five minutes. In my many years at schools, I saw teachers use that time in various ways – but more often than not, it was simply time to get ready to leave, basically chat time and get your stuff together and wait time. Not productive learning time at all.

It’s easy enough to make these moments into fun, engaging, mathematics problem-solving that students, believe it or not, actually come to enjoy and request. I use to have a few different things that I would pull out – focusing on either logical thinking or number-sense or puzzles. Here are just a couple of things:

  1. I had the 24-game – several different versions.  I(If you have never played this or seen this, you should explore it). So, in those last 5 minutes, I would pull out a card, write the 4 numbers on the board and students would try to reach the target of 24. As an example: 2, 3, 4, 4 and you can add, subtract, multiply or divide using each number one time, to make 24. I often had candy for anyone who could come up with a strategy.
  2. If you don’t have actual cards, you can create your own version of ‘reach the target’.  So, pick 4 random numbers using a calculator, and give students a target number to try to reach (so 24). Or, choose 2, 3, or 4 random numbers with a calculator (or have students give you numbers) and ask students to use all the operations and come up with the smallest outcome and/or the largest outcome.  This is a lot of fun – you get some interesting problems and students have to explain their answers and defend their solutions.
  3. Give the students a logic puzzle.  I actually purchased several logic books, and so would read one out to the students or draw/show the picture on the screen and they could work in pairs/small groups to try to come up with a solution. Great critical thinking and collaboration going on here – and if we couldn’t get the solution before the bell rang, we would take it up the next day with most of them working on it overnight. Here are some good resources for logic puzzles:
  4. Read a story.  Yep. Even with my high school students, I would read stories.  Math related of course. You would be amazed at how they actually enjoyed listening, and of course, once the ‘story’ was finished (which might take a couple days depending on our actual time at the end of each class) we’d discuss the ‘math’. Some of my favorite books:

Students loved the challenge of these last 5 minutes (sometimes it would be more). It was a very competitive yet non-threatening time where they could test their math skills or thinking skills, work together, and have fun with numbers and logic. That time was no longer wasted – it became a time students actually looked forward to and often requested.

As you are nearing the winter break, there is probably a bit more time to spare or a bit more time needed to keep students attention.  Use that time in an engaging way that allows for some critical thinking, collaboration and a game-like atmosphere that challenges students and keeps those last five minutes productive.

Permutations & Combinations – Casio vs. TI

img_3628I share a twin house with my neighbors (i.e. we are attached) and we like to decorate our front porches for the holidays the same, so that our ‘house’ is coordinated.  Every year we do something different, and this year we decided to hang holiday ornaments along with the lights – so a variety of Christmas balls and various large ornaments hanging from the porch.  As we were trying to decide the most ‘pleasing’ order to hang these, I realized we were basically discussing combinations and permutations, which naturally got me thinking about working with this in math class.

Permutations and combinations are often very confusing for students. Basically you have a group of things (numbers, objects) and you are going to pick a certain amount from that group of things, and depending on whether order matters, you either have a certain number of combinations of things you can make or a certain number of permutations. Combinations are the possibilities of things chosen when order doesn’t matter. Permutations are the possibilities of things chosen when order does matter.

As an example:


We have 3 Christmas Balls – green, red, blue.  If I want to choose two, order doesn’t matter, than it’s a combination, so how many combinations will I get?

3 combinations: Green, Red;  Green, Blue; or Red, Blue

But, if order does matter, then we have a permutation, so how many permutations are there?

6 permutations: Green, Red; Red, Green; Green, Blue; Blue Green; Red, Blue; Blue, Red.

Now, there’s also the whole idea of replacement and no replacement, but I am not going to get into that here. Working with students, you would want to start with small numbers of objects so they can create the combinations and permutations by hand. But then, you’d want to lead into more complicated things such as lottery numbers and chances of winning, where finding all the combinations and/or permutations is hard to do by hand, thus requiring a formula to make it more efficient, and then eventually, if you really want to do comparisons and have interesting discussions about many real-world examples, you’d want to incorporate technology to help be even more efficient. Here’s a nice page I found that discusses the differences between combinations and permutations and the different formulas needed and provides some good examples.

Below is how you can calculate permutations and combinations when you know your sample size (n = number of things you have) and how many you are choosing (r) from that group of n things. This video shows how to do this on both the Casio Prizm and the TI-84+CE.

Clearly in my front-porch, neighbor decision making, order actually mattered. We wanted a pleasing arrangement. We therefore were looking for permutations – how to choose six balls from a possible 10, so 10P6. There are a staggering number of permutations – 151,200.  Who knew holiday decorating had so many choices!!!  Needless to say we did not try to look at all of them – but good to know we have so many options for the years to come!

Functionality & Affordability Matter

Another post in my series comparing Casio calculators to TI:

I just came from a meeting at Casio America’s headquarters where we discussed ways to help parents, teachers and students get their hands on Casio calculators. In thinking about the message that Casio is trying to instill in it’s customers – that of “Functionality and Affordability”, I thought perhaps I would clarify what that message means.

Affordability – well, obviously that has to do with cost. Basically, if you go into a store such as Walmart, to buy your child calculator, you see a wide assortment of calculators with varying prices. The prices are remarkably different as you progress to graphing calculators, and TI calculators clearly top the list in expense. It can be confusing if you don’t really know anything about the calculators and are just comparing prices – the obvious choice for our cost-conscious consumers is to go with the less expensive choice, but what often happens is schools/teachers name a specific calculator type or brand, which more often than not is the most expensive one.  The question then becomes what’s the difference? Parents probably ask themselves “Will my student be at a disadvantage if we choose to save money and go with the more affordable option?”  Here’s where “Functionality” comes into play.

Functionality has to do with ease-of-use, processing speed, menu options, memory, etc.  When a student has to use a calculator to do mathematics, how hard is it to figure out the steps, to find the menus, etc. Here is where Casio definitely has the advantage over TI, because Casio calculators don’t require students to remember complicated processes or where menus and operations/calculations are – rather the options appear right on the screen as students are working, not hidden in an app or a button. The processing speed is also significantly faster. So, the more affordable calculators function more quickly and are more intuitive and easy to use and remember compared to the more expensive options. And are allowed on all standardized tests, just like the more expensive options.

As an example, here’s a quick comparison of Casio’s 9750GII graphing calculator, at $47, compared to the top-selling TI graphing calculator, the TI-84, at $102, or the TI-84 +, at $122 (these are all Walmart Prices). You will see that the Casio is menu driven, performs quicker and graphs prettier, than the more expensive TI-84+ option. This is a fairly simple problem – graph a quadratic function and find its root (s). The TI has much more complicated functionality, requiring students to find the right menu, create ‘boundaries’ around the root, and make a guess before getting the coordinates of the root. Then repeat the process if there is more than one root.  Also, notice that on the Casio, you can toggle back and forth between the roots (if there is more than one), it shows the function on the screen, along with the root (s) and word “root” so you know what you are looking at.

So – to answer the question: NO your student will NOT be at a disadvantage if you choose the more affordable option because you are getting better functionality. Seems like an advantage to me.


More than Calculators – Teacher Support & Resources

I received a message the other day from a reader who commented on how much he liked the Prizm, but because 2016-05-13_12-52-22Casio didn’t have any resources to support the learning of the Prizm, he was a little reluctant to try it.  My first reaction was “What?!! We have a TON of resources!!”  My second reaction was to ask myself why might he think this? I was able to answer my own question when I searched for our resources – the issue being they are a bit hidden among all of Casio’s other products, (which, just so you know, is of course in the process of changing as we create a more user-friendly web-page).

In the meantime, I want you to see the great teacher/student resources we have! Let me share with you the resources we have that supports teachers (and students), from complete subject-specific or grade-specific resource books (i.e. complete lessons), so sample lessons and activities (free), to online course for Prizm (free) to webinars (free).  There are teacher-created resources and quick-start guides.  Casio WANTS teachers and students to use their calculators and get the help and support they need to use them appropriately.

  1. Free online activities and sample questions:
    • These include grade-level activities and specific Casio Prizm-vs-TI 84 activities
    • Scrolling down the page you will find sports activities for use with five different calculators
    • Keep scrolling to our Quick Start Guides for 6 of our calculators (including Prizm)
    • Keep scrolling to Subject-specific Teacher Resource Guides and Calculator Tips
    • Scroll further to see all our grade-level and subject-level resource books that contain complete lessons
  2. If you look at our products page, under Software & Additional Products, you will be able to scroll through all our grade-specific/subject-specific resource books:
  3. Here’s a short-link to our Casio Lesson Library (with teacher created activities):
  4. Short-link to Guided tours for the Prizm:
  5. 2016-05-13_12-56-04If you are interested in the Prizm, we have a whole webpage dedicated to Prizm activities and support, which includes lessons, videos, and also has the OS updates. 
  6. We have a free online course for the Prizm (self-paced).  If you complete the course, you get the Prizm (fx-CG) emulator software for free.
  7. Free webinars on many math topics (statistics, geometry, algebra, calculus, etc.)(you do have to register your email to view these, but they are free):
  8. Links to manuals for specific calculators:
  9. And let’s not forget the videos showing you how-to’s and comparisons!  and

As you can see, we have a ton of support for teachers and students wanting to use and learn-to-use Casio calculators to support their instruction and/or math learning. We hope those of you out there excited to start working with Casio calculators start using these supports. We are educators here at Casio and want you to love the calculators as much as we do!!

Curve Fitting with Prizm Pictures

I’ve been thinking a lot about the upcoming NCTM conference in April, the theme of which is “Building a Bridge to Student Success”.  I am excited to be heading back to NCSM & NCTM this year after having a years hiatus from math conferences.  Can’t wait to meet up with old friends and colleagues, check out what’s happening in math and math technology, and be a part of a vendor booth again. Believe it or not, I actually like being in the Exhibit Hall – it’s very invigorating and I get to connect with math teachers from all over and find out where the “points of pain” are, to use the words of my friend Stephen Reinhart.

I’ve been involved in the Casio planning for NCTM, so bridges have been a big part of my thinking these last few weeks. With that in mind, I have been looking at the Casio Prizm calculator and the built-in picture resources, and found one that is reminiscent, if not actually, the Golden Gate Bridge in San Francisco. Which led me to playing around with curve fitting and looking for applicable lessons.  There is a whole lesson sampler for the Prizm available free that provides several curve-fitting to picture lessons. You will find not only key strokes for creating the curves and using the pictures, but also questions and resources for the students.

What I love about curve fitting and using real-world pictures is that students are able to see how the math they are learning is actually used and apparent in the world around them. For example – no bridge is built without a lot of math! Prizm has an amazing number of pictures built in that would fit any level of student working with equations and curve fitting – i.e. linear to trigonometric. You can have them plot points and determine their own regression or have the calculator do it, or a combination of both. Lots of options. The point here is that the pictures and line fitting capabilities allow students to problem-solve in a real-world context.  Always a goal in any math class!

I encourage you to check out the Prizm Lesson Sampler yourself. If you don’t have a Casio Prizm of your own, you can test out the emulator free here (fx-CG Manager Plus).  I’ve included a short video showing the basics of accessing the pictures, plotting points, and fitting a regression line.

If you live in Virginia, you can actually attend a free dinner/Prizm workshop in the next two weeks and experience it for yourself. Should be a lot of fun.  Here are the Virginia workshop/dinner dates and links to register:

  1. February 1: Washington County, VA – click here to register
  2. February 2: Roanoke/Salem, VA – click here to register
  3. February 3: Danville County, VA – click here to register
  4. February 8: Rockingham County, VA – click here to register
  5. February 9: Dinwiddie County, VA – click here to register
  6. February 10: Fairfax County, VA – click here to register

Have fun playing!