# 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:

Have fun playing!

# Playing Around with Data

Brothers Sisters Casio ActivityI’ve been exploring the different types of graphs that can be constructed using data lists and the Casio graphing calculators. Data collecting is a powerful way to help students use mathematics in a real-world context. It provides students the opportunity to collect data that is interesting and relevant to them, and then make decisions about that data, such as what graph best supports the data, what questions can we answer from the data, what predictions, if any, can we make, etc. Students apply so many mathematical skills when working with data. What to do with the data once it is collected is obviously a major part of the process, and being able to visualize the data to help answer questions requires students to understand what the different types of graphs mean and show about the data, and, depending on the question asked, which graphical representation is best.

To help me in my exploration, I used one of the activities from our Fostering Mathematical Thinking in the Middle Grades with Casio Technology resource book (Dr. Bob Horton, 2013), as it has some great real-world activities and sample data that allowed me to explore a variety of graphs. Casio calculators can create many graphical representations from a single set of data. All the calculators function the same way, so that’s nice – if I know how to use one, I know how to use them all. Obviously, the Prizm, aside from color, also has some extra features, but no matter which graphing calculator you have (9750GII, 9860GII, Prizm), you can create all these different types of graphs and statistical representations.

The activity I chose, Brothers & Sisters, is one where the data collected from the students in the class is the number of siblings they have, and the two lists created are the numbers of siblings (0 – the highest # in class) and frequency of each.  From this data, we explore box plots, pie graphs, histograms and then measures of central tendency. I have attached a PDF of the activity at the end of this post for those of you who might be interested in trying it with your own students. It includes the keystrokes for the Prizm, but as I said before, all Casio graphing calculators use the same keystrokes, so even the \$50 version can do powerful things.

I am not going to explain the whole activity, since I have attached the PDF that you can peruse at your own leisure. But, I did create a short video clip using the 9860GII version of the graphing calculator, to show the steps. I started with sample data already entered so that I could get right to the various graphs more quickly.

Start playing with data with your students, if you have not done so already. Provide students an opportunity to collect their own data, make decisions on how to represent and use the data, and see how much math happens!

# Histograms with ClassWiz & QR Codes

Students should engage and be hands-on with mathematics as much as possible. One of the activities I loved was the Sum of Two Dice, whether in my middle school classes or in my Algebra classes. That’s the great thing about mathematics – you can take an activity/concept and make it more or less rigorous depending on the questions you ask.

I am sure many of you have done this activity – I am choosing it for this post because it’s a nice way to demonstrate how the Casio ClassWiz (fx-991EX) scientific calculator allows you to create frequency tables and with the QR code, see an online visualization of the data.

First thing – have students roll two dice and collect some data – i.e., the number on each die and then the sum of the two together. If you don’t have die (or don’t want to hear all the noise!) you can utilize the random integer option on the calculator to simulate rolling die. I usually had my students in pairs to do this – one record, one ‘roll’. Then have them tabulate the frequency of each sum and create a new table with possible sums & frequency.

The next step is to have them make a histogram of their own frequency table and then compare to other students.  In my example, students only rolled 24 times each, so everyone’s graph will look different and not be what we expected (more 7’s). Great discussions can come from these observations.

Hopefully, discussions lead to the idea that each group only collected a small sample of rolls, and that if we had more samples,
perhaps the distribution of data would be more what we expected – i.e. more sums of 7 appearing. Here’s where having a class emulator is a great tool – you can display one frequency table and collect the class data.  So – same sums, but combine each groups frequency to get a total frequency for the whole class.

Once you collect the class data, you can then create a new histogram. With the ClassWiz you can easily do so just by creating a QR code of the table data, and, with the emulator, go directly to the visualization. You can also do this with the SmartPhone App Edu+ if you have that option. The nice thing about the emulator is you can immediately pop the visualization up and begin discussions and comparisons of whole class histogram versus individual groups. Being able to immediately see the visualization with only a scientific calculator, is powerful, especially as you can quickly compare between previous “one-group” histogram and current “whole-class”.

There are so many ways to use this activity – I use to use it with TinkerPlots, graphing calculators, students hand-drawing the graphs. The ClassWiz and its ability to create QR codes and online visualizations is another way to help students make meaning out of the math they are doing, especially when they only have a scientific calculator to use, as most middle school students do. Hopefully this gives you some more options.  I have included a short video clip on how to actually create the frequency table, QR code, and online graph using the ClassWiz fx-991EX. Try it!

# G-Shock Your Casio Calculator Love

When I hear Casio, the first things I think of are calculators, G-Shock watches and musical instruments. Obviously, since I am working on the educational side of Casio, I have been focused on the calculators, and really learning about how they work and researching ways they support mathematics education. I just recently obtained my own Baby G-Shock watch and am still exploring all the features of this (and fighting off my daughters’ attempt to “procure” my watch!)  I’ve yet to explore the musical instruments, but can tell you that my youngest daughter is campaigning for a Casio Synthesizer under the Christmas tree this year!

In my own hands-on learning, I have expanded my appreciation of the Casio calculators. I’ve been have a great time making videos about how the calculators work and exploring the different features of each. As a former TI-calculator user, I am coming to understand the differences between the two and experience how much easier it is for me to work with the Casio and remember things. Granted, I am still learning and comparing, but like many teachers I have talked to and worked with, once you try Casio you want to stick with it over the TI. Which explains why Casio is trying to get new users and converts to show their new-found love for Casio calculators and reward them for doing so.

If you haven’t heard of the Casio Testimonial Contest, you definitely need to check it out. Simply by writing a review about one of Casio Calculators at ShopCasio.com (click a calculator and then click “write a review”), taking a screen shot of your review, and then posting it on Twitter (@casioprizm #CasioEduTestimonial #entry) you are entered into the 12-week giveaway for a Casio G-Shock watch. 12 winners possible, so that’s pretty easy stuff for a simple review.

And what’s so great about a G-Shock watch? Like I said, I myself just obtained a Baby G-Shock, so I am learning about it myself. There are a lot of cool things about the G-Shock that I have discovered in my research. With my mind always focused on how can I connect to mathematics, here are a few cool things about the G-Shock that would be of interest in the math class:

1. The creator of the G-Shock watch (g stands for gravity), Kikuo Ibe, a Casio Engineer, based his design on a rubber ball he saw bouncing in a park, which would surround the outer layer of the watch. The watch was designed to withstand the “triple-ten ideal” –  able to withstand a ten-meter drop, be water resistance up to ten bars, and have ten years of battery life. (How deep is ten bars? What is the force on impact of a ten-meter drop?)
2. The official promotion shots of the G-Shock watch always show 10:58 as the time because it takes up the most watch ‘ screen real-estate’ (so how much is that?!)
3. They are the unofficial watch of the Navy SEALS.  (Cool!)(Why? Cost? Durability?)
4. The G-Shock Premium has Wave Ceptor Radio-Controlled Technology which means it receives regular signals from atomic clocks all over the world so it will only be out by one second every three million years.

There are more obviously – (you can click the links provided to get more information). For me, I am still just trying to figure out what all the buttons on my Baby G do, but that’s half the fun, isn’t it? Figuring out what calculators and watches can do to support what you need. We’d love to hear how you are using your calculators to meet your learning needs and maybe that will G-Shock you! Contest runs until January 30, so Review. Submit. Win!

# Dynamic Graphs – Using Color & Motion w/Casio Prizm

I have been having such a great time playing around with the Dynamic Graphs on Prizm that I wanted to share how to do this for those of you who haven’t yet explored this feature. You can actually do Dynamic Graphs on all our graphing calculators, but the added feature of color with the Prizm makes it even more powerful.

Why Dynamic Graphs? As a Sketchpad enthusiast, I always tried to use dynamic sketches to help my students visualize mathematics, from geometric shapes to graphs. Dynamic mathematics allows students to make conjectures and quickly test them out and see how changing parameters (lengths, angle measures, coefficients in equations, etc.) impacts the shape/function.  It allows for a deeper understanding of mathematics and provides a visual, which is very powerful. Having that capability on a graphing calculator, which is a technology tool that a majority of high school students have access to (as opposed to computers/tablets where Sketchpad might be available), allows more students to work with dynamic mathematics. The Dynamic Graphs feature on Casio graphing calculators provides that ability, and the Prizm allows for the added color feature, which makes things like comparing dynamic graphs to their parent function easy to do, providing visuals to make deeper connections.

Here is a video I made using the parent sin function and using both the modify graph feature and the Dynamic Graph feature to explore how the coefficients in the standard form Asin(Bx +C) effect the graph, allowing students to visually see how these coefficients change the amplitude, period and phase shift of the sin function.

# Random Numbers to Spark Student Thinking

In my last post, I mentioned attending a session presented by Jennifer N. Morris on making math meaningful. (She is presenting two times at #NCTMRegionals Nashville – Session #244 for 9-12 and Session #275 for 3-5, which is the Origami/Fraction/Random Number session – BE SURE TO CHECK HER OUT – She is AWESOME!). One of the activities in her session incorporated the fx-55plus calculator and using the random number generator to spark engagement, problem-solving, numerical thinking and communication with students. Simply by hitting the random # key, which creates infinite random fractions (many complex!) and have students (participants) determine if that random number was acceptable if it represented the part of a cookie they would receive led to amazing thinking. What is acceptable? What are target fractions? How are students making their estimates and decisions? How do you know yours is bigger or smaller than the person next to you? Participants were asked to line themselves up in order, least to greatest, using their random fraction, which sparked great discussion and comparison. They checked their lineup by converting the fraction very quickly to a decimal, so equivalency and number sense.

During the discussion about all the different concepts students could be focusing on (number sense, fractions, estimation, equivalence, conjectures, probability, etc.) from this simple random number generation, teachers in the session offered several suggestions for using the random number generator on the calculator.  Here are just a few:

1. Use Random Integer to simulate the roll of a die for data collection (you could use two calculators to simulate two die).
2. Assign every student a number, and then use Random Int constrained to the numbers in the class (i.e. 1-20).  Use Random Int to pick a number, and that student is the one called on
3. In Collaborative Groups, assign each group member a number and use random number generator to determine who in group shares, or leads

Jennifer used the fx-55Plus because she loved how easy it was to generate the random numbers. Someone in the group asked about the scientific calculator and graphing calculators, and did they also have the random number generator. The answer was yes, but it was a bit more involved. So – realizing that using random numbers is useful no matter the grade you teach, I thought I would show a quick video on how to generate random numbers using the Casio calculators. The great thing about Casio is that calculators with the same face-plate layout have the same steps. I’ve listed below the calculators I am demonstrating and then some other calculators that would have similar steps to generate random numbers:

• Fx-55Plus
• Fx-350EsPlus, fx – 300ESPlus, FX115-ESPlus, fx-991EX
•  fx-9860GII, fx-9750GII, fx-CG10Prizm

Go be random!!

# Modifying Graphs with the Prizm – Check it out @NCTM Minneapolis

In preparation for NCTM Regionals in Minneapolis this week, I wanted to do a little show-and-tell with the Prizm. Hoping this sparks some interest and inspires some of you heading to the conference to stop by our booth (#511) at the conference and play with the Prizm.

One of the features of the Prizm that I just love is the ability to dynamically modify graphs, allowing students to visually see the effect of a coefficient on the graph of the function. This ability to modify one coefficient at a time and immediately see the impact on the graph allows students to make conjectures and get a better understanding of the graph and what each coefficient represents.

Here is a little demonstration of how the modify function works on the Prizm using both the standard form and vertex form of a quadratic:

I certainly hope you will stop by the booth Thursday or Friday and come play with us and learn more. I’d certainly love to meet you! Or, drop in on some sessions that utilize some of our products, like the Prizm, Keyboard and fx-55 Plus.

Thursday, November 12

• Session 41 9:45 – 11:00, (M100 DE) Hand-held Technology + Hands-On Activities=CCSS Success -Tom Beatini
• Session 84, 12:30-1:30, (M100 AB) CCSS for Statistics: Paired Quantitative Variables – John Diehl
• Session 101, 1:30-2:45, (200 AB) Thinking Like A Synthesizer – Mike Reiners
• Session 102, 2 – 3:00, (200 C) Connecting the Math through Meaningful Experiences – Jennifer North Morris