New Year – New Start with Hand-held Calculators

Technology is out there in classrooms, but what is available varies widely. We hear so much about 1:1 initiatives, tablets, laptops, and other mobile devices being used in math classes, but, the reality is, most math classrooms access to technology is often limited to the teachers computer/whiteboard, vs. every student having direct access to a computer/tablet. I’ve been trying to research/find hard data, which is difficult and often misleading. There is quite a bit of inequity in technology access as well, whether in devices themselves or in internet access, even within the same school districts and states. Here are some links to research/data I found, though it doesn’t really give a clear picture of what is really out there and being used by teachers and students. Obviously this is just a small sample.

From my experiences around the country, and I have traveled and worked in schools and classrooms in every state over the past 12 years, access to technology in mathematics classrooms is NOT as prevalent as the statistics indicate, and is incredibly inequitable. It’s not ‘computers for every student’ as so many articles and reports imply. It’s getting better – sure. But from my own anecdotal observations, which includes my 2-year doctoral research with several schools and teachers, what I see most are classrooms with one computer (i.e. the teachers), which are more often than not used for teaching/demonstration, occasional use of students on laptops/computers (a couple times a month), whether that be in computer labs or more often, mobile laptop/tablet carts, and more often than not, hand-held calculators as the daily, go-to technology for students. And technology ‘use’ for instructional purposes with students is more as a calculating tool or a game-playing and/or review for practicing math concepts, not for truly learning WITH technology. Again – this is based on my hundreds of experiences working in schools with math teachers around the country, but I think it’s pretty indicative of the reality of what is really available and being used. So, while the rumor out there is hand-held calculators (which can include mobile phones, though those are still not allowed in most schools) are going away, the reality is, based on my experiences, hand-held calculators are still the most-used technology tool in math classrooms and still predominantly used on many standardized tests that have not converted to online platforms. A huge reason is obviously cost – schools can provide all students with access to graphing calculators, scientific calculators and/or four-function calculators at a fraction of the cost of laptops/tablets. And, as we all know, education funding seems to decrease every year, so cost is a factor, which includes replacement costs. Calculators are also portable, don’t require internet access, and students/parents can buy their own for home use inexpensively as well.

With that said, I am going to focus my posts in January for the New Year on calculators and how you can take a new look at a technology that is readily available for students and that can enhance mathematics. This post, I am going to focus on a couple graphing calculators – i.e. the CG50 and the 9750GII to show how even a small device such as these can offer ways for students to explore multiple representations, collect data, analyze information and make decisions using mathematics. These two calculators are very similar, with the CG50 being in color and having 3D, but for the most part, you can do the same things on both. For this reason, I am going to use both to demonstrate different parts of the same activity to show that you can use either and accomplish the same discoveries with students.

The activity I am focusing on is one called Life Expectancy, available for free as part of the free lessons/resources from Casio Education. You can access Life Expectancy and others in the Fostering Series Sampler (this specific activity starts on page 13). This lesson involves looking at different representations of data to find key information about the data, analyze trends, and compare the representations to make decisions about which are the most appropriate and why (so box plots, histograms, pie-graphs, scatter-plots, and xy-lines). I have provided two videos, one with the 9750GII that shows how to enter data into the statistics menu and make a histogram, and box-plot from the same data; one with the CG50 that shows how to make a scatter plot of the same data, with a linear regression. All the steps for each are in the activity, so the videos are just a visual of what you can do. The steps are the same for both calculators, so whether you have the 9750GII or the CG50, either video will show you how to create the statistical plots (and, bonus, if you have the 9860, it works for that graphing calculator too!!) What I hope you get out of this is that with the use of calculators, you can provide visuals and multiple representations that allow students to analyze the math, make connections, and more importantly learn with the technology instead of just using technology as a calculation device to get a simple solution.


Histograms and Box-Plots on 9750GII (but same steps for CG50 and 9860):


Scatter Plot and Linear Regression on CG50 (but same steps for 9750GII and 9860):



Equations & Art – Winter Fun with Technology

Tree with plotted points

It’s that time of year – countdown until winter break.  As many teachers know, this is often a difficult time to get students to focus and learn, so often we try to keep them engaged with ‘activities’, often that are NOT connected to the subject (i.e. watching ‘holiday’ movies). One thing in math that you can do to both engage, challenge, and still keep learning at the forefront is to do some art with math. Winter-related is always fun (i.e. snowflakes, snowman, ornaments etc.). Often plotting-points on grids to create images is the go-to type of activity, but I also suggest that you take advantage of the technology you might have in your classroom (graphing calculators for MS/HS students, or math software, like You can do both plotting points using technology tools as well as more advanced creations, exploring how equations and domain/range constraints can create some interesting ‘winter creations’.

I have been having a bit of fun this morning playing with equations – linear, conic, parametric, parabolic, and plotting points to come up with some winter images. I’ve shared several images here – done both in as well the graphing calculator, CG50. What you can do with students is challenge them to come up with their own creations. Maybe limit them to only linear equations and inqualities, or only parametric equations, or they have to use a combination. In the process of creating and exploring, students are really deepening their understanding of what the different coefficients in an equation/inequality do to impact the graph. And they can play around with different forms of the equations/inequalities, since some forms control the shape/movement of the graph more efficiently. For example, I like the slope intercept form of the linear in my creations because I can control the slope. I like the standard form of the circle because I can control the center. You will note also that in some of these images, the axes are showing, and some are not. I created them with the axes but then turned them off once I was completed. I also played around with my window/scale.  All of this is using mathematics and trying to really manipulate the domain, range, and using the right equations to create the shapes I wanted. A nice review and extension of prior knowledge and in the process of being creative, students are deepening their understanding of the equations and their graphs.  Here’s a link to all the examples below (free usable activity):

Parametric equations only example (the GIF uses a slider to change the snowflake):

Snowman using circle equations, linear equations with limited domain, and parabolas with limited domain.


Snowflake with circle equations, linear equations with limited domains, plotted points and parametric equation.

Christmas Tree with plotted points, polygons (using geometry tools).

Ready-to-Use FREE Lessons to Spark Math Learning

Integrating technology into math instruction is a way to help visualize mathematics, provide opportunities for students to work with multiple representations, and more importantly make connections that help deepen their mathematical understanding. With time constraints, standards-alignment, and standardized-testing pressures (just to name a few ‘obstacles’), teachers don’t have the time to create these technology-rich activities themselves or even the time to help students ‘learn’ the technology, so instead opt NOT to even attempt to integrate technology or find ready-to-use activities online or in other resources. There are several places to find technology resources for mathematics instruction, but again, often these are not necessarily aligned to learning goals or they require a bit of a learning curve for both teachers and students to implement, and therefore create yet another roadblock. With that in mind, and the team of teachers have been working hard to build our lesson library to support teachers who want something they can do with their students tomorrow.

I’ve been working with from the start to make sure that we are creating a math tool that allows for teachers and students to quickly get into the mathematics and not be bogged down in the ‘learning’ of the tool – instead, the tool and the math work together. Part of this is helping to create ready-to-use mathematics lessons that allow for a teacher or a student to get right into doing math. As a mathematics educator and someone who has utilized technology in all the teaching I have done throughout the years (in middle school, high school, and now higher ed), I value the technology as a tool for supporting math learning. Activities that help students see and do mathematics themselves so they can find the patterns and create the generalizations and understandings is a goal of helping students develop conceptual understanding, and is a great tool for this since it provides a space for multiple representations, including a place for students to share their thinking and justifications.

Those of you who have already created your free account in, and have been exploring it’s capabilities, know that there is the option to share your work, either by URL and/or publicly, where anyone who has an account can search and find relevant, content-related activities that they can use in their classroom, save into their own account, and modify/edit to make it your own. We’ve now made these activities easier to find and available for use even if you haven’t created an account, meaning you can work on them yourselves or if you want students to work on them, they can, even if they are not logged into a account. As long as you have a device (computer, tablet, phone, etc) you can start doing the math. Obviously, if you want to save your work or save the activity for later use, you will want to create an account so there is a place to save it to, but you can also just work on it and explore and test things out without an account. is still brand new – less than a year officially, so we are still building up our library. We have a team of teachers who are working on activities, and then of course, all our users who are creating their own activities and deciding to share them publicly, so the library grows every day. If there are activities you are interested in, please let us know. And please feel free to create your own activities and share them with our worldwide network of teachers and students who are using

This video shows you how to find a current list of activities without needed an account. You can use these activities without an account and any web-browser. But – if you find something you love or want to keep any work you do, you need to duplicate and save the activity into your account. If you still don’t have your free account, I have also provided some video links that show you how to set up your account so you can save things you find, modify them as you see fit, or just create your own activities.


Other related video links:

Halloween – Fun Statistical Exploration Ideas

As I walk down my street and see the spider webs on the bushes, the witches and ghosts flying from the porches, and the glowing pumpkins, it’s hard not to think about Halloween. If you live on a street with lots of younger kids, it’s even harder! On my street, in a small town, Halloween is a big deal – all the neighbors come out, we build a bonfire, adults without kids hang out while those adults with kids walk around trick-or-treating with their children. There are hand-made costumes, adorable family costumes, lots of candy and a few ‘adult’ treats as well. I admit – I tend to dress up just for the fun of it, even though my own children are long grown. All of this has me thinking about the amount of money that people spend on this day of fun – i.e. the decorations, the costumes, the candy. Naturally, this had me out exploring…..

I found several articles, and let’s just say the numbers are pretty astounding:

From one article, it’s estimated that $2.6 billion is spent on candy and $2.7 billion spent on decorations. Wow!  That’s a lot. Though, after looking at the price for one bag of candy, I shouldn’t be too surprised.

Of course, I LOVE when data is displayed visually, since this really helps students in particular see data and make sense of it. Found this chart from Statista about last year’s Halloween and how the spending is divided across categories. The costumes for pets sort of cracked me up!

Infographic: The Shocking Scale Of U.S. Halloween Spending | Statista

As always, I like to think about how this type of information could be used with students. Especially as math teachers, where we are always looking for real-world problems that are in fact real world (not textbook ‘real’….i.e. contrived) and that engage students. Halloween is definitely something that engages students, so there are many ways teachers could incorporate some Halloween real-world data and questions into the math classroom.

There are several articles and places that have data about Halloween, so one way would be to collect data and create graphs of these for comparison. So perhaps comparing the trend of spending over several years and then maybe exploring what might have been happening in the years where spending seemed lower or higher and making some connections there.

Or, having students look at Halloween adds for costumes and/or candy and compare pricing and make some decisions on where they should buy their Halloween supplies, factoring in things such as sale prices, buying in bulk, type of candy, etc.

You could have some fun with candy as well – maybe estimating the number of candy corns in those small bags, and then collecting data (i.e. open several small bags, count the number, record the data, then find statistical measures and graph. Really, same thing could be done with any of those Halloween-size bags of candies, such as M&M’s, Skittles, etc.  A fun exercise in weight vs. quantity.

Students could collect data on costumes (i.e. survey other students in their school on what costume they plan to wear, and see what the trends are for costume type (see chart to the right, where for kids, Princess is #1 and then Superhero).

You could include some health statistics too – i.e. does the number of cavities found in people increase after Halloween?

And let’s not forget about pumpkins!! According to this article, $377.3 million was spent on pumpkins last year (for carving). So – how do farmers plan for the run on pumpkins? How many pumpkins are planted that are not used? Is there a state that grows the most pumpkins? Where are pumpkins grown in this country??There are lots of questions we could ask about pumpkins, so get your students thinking! And, there are lots of statistical plots reflecting the data on pumpkins (and more) that could lead to some really interesting exploration and questions and analysis.

Let your students generate some questions themselves and then help them explore finding information and then presenting the data and their conclusions. There will be a lot of different kinds of math going on, based on the avenue they choose to explore.

Have some fun!!!

Here is a quick video of some data taken from this article that I put into (first as an image, and then I made my own table). Here’s a link to the paper if you want to use it.














You will find more infographics at Statista

Let’s Explore with Geometry and Start the School Year Off Right! (New Features with

I admit it. I am a geometry nut.  It is my favorite subject to teach, which I have been doing for the past 30 years (wow….said that out loud!!). Geometry to me is all about logic and connections and relationships of shapes. It should be hands-on, it should be visual, and with technology, is should be dynamic – meaning you can see and discover relationships through movement and manipulation. There are many good resources out there (for those of you looking for a ‘textbook’, Discovering Geometry has always been my go to – it’s all about learning geometry through hands-on discovery and connections. It’s on it’s 5th edition, and the ebook has dynamic investigation using (formerly used Geogebra), and has made huge strides in advancing it’s geometry functionality, which is what this post is focused on. My goal over the next few posts is to focus on specific geometry explorations using some of’s geometry functionality, but today’s post is an overview of what’s new. has all the tools you would expect a geometry software to have – i.e. points, straight-edge tools, polygon tools, display tools, expressions, equations, etc. It has some others don’t have – i.e. tools for conics for example. Below is a list of some of the added features as we continue to improve the functionality of the software (which is FREE, btw!!)

Quick List of New Functionality:

  1. Compass Tool
  2. Ability to add in images and use them as part of your geometry explorations
  3. Ability to create sliders for transformations (dilations, rotations, translations, reflections)
  4. Trace feature
  5. Multiple Grids, including isometric
  6. Ability to lock constructs
  7. Ability to create a rigid polygon (meaning it won’t change shape once constructed)
  8. Ability to add tick marks to sides and angles
  9. Ability to change the style of points – i.e. dot, square, x
  10. Ability to measure exterior angles explicitly and create angles 0-360
  11. Ability to construct a specific regular polygon (n-gon) by constructing one side and choosing n (number of sides)
  12. Ability to duplicate constructs without have to ‘reconstruct’ them.

I will be creating videos on each of these features and how to use them for future postings, but today, I wanted to show you where you can find the different new features. Be sure to visit and sign up for an account (so you can save any work you do). Both the Free and Basic accounts are completely free and have everything you could need for a classroom (don’t forget there is calculations, graphing, statistics, financial tools, and text as well as geometry!). Below is a quick how-to on finding where all the new features for geometry are – stay tuned for future how-to’s on using the specific features. Meanwhile, why not try and explore things on your own? Have fun!!


Math In Motion – Creating Simulations with

The beauty of dynamic software is the ability for objects to move in real-time and measures and other objects connected and/or controlled by those also move. Basically seeing change over time happen. This allows for the ability to create some interesting simulations – such as simulating cars moving at different speeds and directions to explore rate of change, or objects turning to explore rotational symmetry and angles of rotation. Many possibilities.

Obviously thinking of ways to incorporate simulations into the teaching of more abstract concepts can be time consuming. This post, I am sharing a How-to created by Ismael Zamora, where he shows how to create moving images (using cars) and also provides a couple related papers if you are interested in the activity he created.

The idea of the activity, Math In Motion, is to have students first Notice & Wonder about the movement of the cars and how they are related, what the sliders control, and is it possible to answer the question of when they will meet?

Here are the links to the publicly shared papers:

Below is a How-to video that explains how Ish created the motion of the cars, involving images, and sliders.


Teachers Rock! Show Your Appreciation in a More Personal Way – Tell Them

It’s National Teacher Appreciation Week, for those of you not in the know. In schools everywhere, teachers are probably getting nice little ‘treats’ from parents and students, or having special lunches or breakfasts brought in, or being treated to free ice cream or nice messages or pep rally’s – lots of things to show how much everyone appreciates the work they do. Obviously these celebrations and expressions of gratitude vary around the country, but there is usually, based on my own personal experiences in middle and high school, some recognition for teachers at some point during this week.  Which is great. Teachers deserve to be told how wonderful they are and what a difference they make in students lives, because they do. They do every day, whether they or you realize it.

It’s the little things that teachers do every day, which often go unrecognized, that really make a difference in students lives and learning. That extra time put in to make a lesson really engaging, that eating in the classroom during lunch to spend time with students who just want to talk or get some help, the personal money spent on supplies and classroom decoration so all students have what they need and to make the classroom a welcoming place, the smile at the door as students enter, the late hours grading, the phone calls to parents to share good news about students (yes, teachers do that!)….there are too many to list here, but every day teachers are providing not only learning experiences, but emotional and physical experiences that help to mold and build students confidence and understanding. This is what I don’t think people who have never been teachers understand – teaching is unlike any other job. You can’t just come in, do the same thing every day, and go home at the end of the work day and forget about it. Teaching is more than teaching content. There is a lot of emotion and dealing with students on so many levels, and navigating that, along with teaching content, makes teaching one of the most difficult jobs out there.

Unlike many other jobs, teachers often never know the impact they had on their students. Sure, we can see grades and scores on tests, but that is a moment in time in a students life, and we don’t often ever know if what we did as teachers has long-term impact (which we hope) as students grow and move on. We think it did. We hope it did. But often, we never know. Unless a student comes back and visits, (or, we are now friends on FB, years later!) – we never really know if the things we thought would make a difference did in fact make a difference. Which makes teaching different from many other professions, who can usually see immediate results or impact of their job. Teaching is a profession of faith – where we believe our efforts are the best we can provide and are something powerful that contributes to our students potential future selves. And though we often never know, we do believe.

What I think would be a really powerful way to show appreciation during this week is for students, current and past, to let a teacher know what it is they are doing or have done that has an impact on them or helped them. Reach out to that Spanish teacher who made class funny, and embraced your obnoxious sarcasm, and influenced your decision to become a teacher yourself, or write that math teacher who helped you survive Calculus and helped you become an engineer, or that teacher who smiled at you every day and gave you a hug so that you loved coming to school. Get your kids to write a note to a teacher (now or in the past) that made school exciting or turned them on to reading or helped them perfect their dunking. It’s those little recognitions’, those personal recollections that really make a teacher feel appreciated and know that what they do is making a difference to someone. Those of you who have been out of school for a while, it’s pretty easy to locate a former teacher via FB or LinkedIn. Those of you still in school, write a note, even if anonymously – it will brighten that teachers day and reaffirm their commitment to teaching.

The U.S. Department of Education has shared some really great videos of teachers sharing what makes them feel appreciated, so I am providing links to those here:


My favorite is what students say about their teachers though, so I am sharing that video here: