Casio just unveiled our two new graphing calculators, the CG-50 Prizm and the CG-500 Prizm CAS. Both of these can do amazing things, and both are approved by College Board for use on the SAT, Pre-SAT and AP exams. in particular, These are so new that we are still working on the tutorials and guides (coming soon), and the emulator software is still in Beta, but also coming soon.
3D graphing is a component of both calculators and emulator software. I plan to do several more posts demonstrating new features and the amazing possibilities, particularly with the CAS CG-500, but today, I wanted to wow you with some simple 3D 3D graphing capabilities. As a geometry teacher, having the ability to show some 3D shapes and their equations as well as cross sections makes me pretty excited.
I am using the Beta version of our software for the CG-50 and just learning this new functionality myself, so bear with me! But – it’s hard not to see how cool and exciting this 3D functionality is, and on a graphing calculator, which is still the most commonly used hand-held technology device by math students (because of its accessibility and affordability and the inequity in schools technology resources/internet/mobile devices).
Enjoy and stay tuned for more of these in future posts.
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.
It’s that time of year again where math teachers and students get a little pi crazy on March 14 and celebrate that magical number, pi. It’s a fun day to spend focusing on circles and spheres and helping students discover pi or use pi or just eat pie! Hopefully, of course, as math teachers, we are always trying to focus on the mathematics of pi…not just eating pies or circle-related food, though that certainly does add to the fun of the day.
Rather than reinvent the wheel (nice circle reference), I am resurrecting links from last year’s Pi-Day post to places with some fun ideas and added in a few new ones:
- Pi Day http://www.piday.org/million/ This site lists a million digits of Pi, and then, if you click on the links to the right, you can search the digits of Pi (for special sequences, like your birthdate), Pi puzzle (New York Times), or Einstein Rap. There are lots of other links, so explore away.
- NCTM’s Illuminations: http://illuminations.nctm.org/pifight/
- Exploratorium http://www.exploratorium.edu/pi/pi_activities/index.html has a whole list of lessons/activities that explore Pi in many ways. One is the search digits one as well. Another one I think sounds very interesting is the Tossing Pi (scroll down the list to find this) – calculating Pi tossing toothpicks. Kids would love that!
- Project Mathematics http://www.projectmathematics.com/storypi.htm This has videos you can choose about the history of Pi, uses of Pi, people explaining what they think Pi is. Might be good to warm up your class with.
- Joy of Pi – http://www.joyofpi.com/pilinks.html#articles This page has lot of links to interesting articles about Pi, history, etc. Lots of resources.
- Live Science – http://www.livescience.com/29197-what-is-pi.html Has a video and other resources.
- Edutopia – http://www.edutopia.org/blog/pi-day-lesson-plans-matthew-davis Lessons and activities for elementary students.
- Education World – http://www.educationworld.com/a_lesson/lesson/lesson335.shtml Lessons and activities around Pi – multi-grade level.
- Teachπ.org – http://www.teachpi.org/ Lots of everything about Pi – books, activities, history, etc.
- NEA Resources for Pi Day: http://www.nea.org/tools/lessons/50840.htm
- Geometry Gems https://geometrygems.wikispaces.com/PiDay
- Kathi Mitchell’s Fun With Pi Day: http://www.kathimitchell.com/pi.html
- UTEP Pi Day http://www.math.utep.edu/Faculty/lesser/piday.html
- SimplyCircle https://www.simplycircle.com/11-pi-day-lessons-for-middle-and-high-school-students/
Have fun and be well-rounded tomorrow!
I went to the National Museum of Mathematics (MoMath) today – what else would I do while in NYC?!! If you were unaware, this is yet another great attraction to add to your to-do list next time you are in New York City. I was lucky enough to have a few hours today to myself and thoroughly enjoyed my hands-on experiences – me and several hundred school-age children.
The museum is focused on providing hands-on, interactive mathematical experiences so students can see, create, and play with mathematics. There are games, art exhibits, bikes with square wheels to ride, cars to control around a mobius strip, angles, tessellations, fighting robots, logic puzzles….it was really fun, and there was a lot of ‘learning’ embedded in all of the exhibits, though I did find I was the only one reading – the kids wanted to just ‘do’. But can you really blame them?
One of my favorite exhibits when you walk into the museum is the wall of etchings done on metal plates. There are parabolic lights above them that move and due to the angles the metal etchings are at, it appears the whole display is moving and that the etches are 3D when in fact they are flat. The etchings themselves are beautiful – lots of mobius strips in there!! I tried to capture it on video but it doesn’t do it justice.
Another favorite was the art exhibit showing the amazing geometric sculptures of Miguel Berrocal – famous for creating sculpture puzzles – i.e. sculptures built by pieces fitting together. There are numerous sculptures on display along with puzzle books showing the steps to build some of the sculptures. There are also two hands-on opportunities to try to build some of the sculptures. I tried my hand at the above sculpture, “portrait de Michele”, which they recreated the pieces using a 3D printer and then provide ‘directions’ to build. My results are below….I was very proud of myself!
There was a little bit of everything – I made myself into a human fractal tree (that’s me as the trunk if you look really close). And then I made two 3D shapes (sphere and star) by putting together flat plates with 2D shapes (circles and triangles) in a layered order so that they end up looking 3D. That was a challenge trying to piece the different sized shapes in the right order.
There was a lot more fun to be had – from the square tire bike to the shape challenges to building polyhedra. All in all, a fun-filled few hours doing some math and experiencing students enjoying doing math as well. If you ever get the chance to get to NYC, be sure to include the MoMath in your itinerary!
I saw this really cool GIF on FB the other day, showing a bubble freezing. As I watched it, you could see all these beautiful shapes emerging and eventually covering the whole bubble. (I of course wished that it was cold enough where I live for me to go out and try it myself, but alas….where I live seems to be having a no-snow winter this year.
Watch and see:
It looks like snowflakes appearing on the bubble, and snowflakes are fascinating. They are unique, they have amazing patterns that form naturally. Wouldn’t it be fun to explore snowflakes with students? Especially if you live in colder climates where there is actual snow to collect and study. How could we connect the beautiful patterns and unique qualities of snowflakes to mathematics? I set out to explore and found a few great resources for those of you who are interested in exploring frozen math. Yet another way to bring the real-world into the classroom and help students see the math that exists around them. Even if you don’t live where snow may be, some of these resources provide some great tools for ‘creating’ snowflakes with students.
Here are some links:
- http://www.educationworld.com/a_curr/mathchat/mathchat015.shtml This is a nice site because it has several suggestions – from collecting real snowflakes to creating your own, to analyzing patterns and categorizing snowflakes. Great hands-on activities.
- A wide variety of ‘frozen math’ activities here: http://mathwire.com/seasonal/winter05.html including the Koch Curve/Snowflake, where students experience the iterative process to create a snowflake fractal.
- Some nice examples and how-to-make paper snowflakes: http://mathcraft.wonderhowto.com/how-to/make-6-sided-kirigami-snowflakes-0131796/
- Some nice geometry connections and more paper-snowflake making here: http://playfullearning.net/2015/02/snowflake-math/
- This is a great math/science connection with a lot of further embedded links included: http://beyondpenguins.ehe.osu.edu/teaching-about-snowflakes-a-flurry-of-ideas-for-science-and-math-integration
- Vi Hart and Doodling is always fun to watch, and here she is doodling and folding with symmetry and fractions: https://www.khanacademy.org/math/math-for-fun-and-glory/vi-hart/vi-cool-stuff/v/snowflakes-starflakes-and-swirlflakes
I am sure there are more options out there – these are just a few I stumbled upon in my searching. Don’t let the winter blues set in – get out there and collect some snowflakes and do some frozen math!
As it is the holiday season and most people are out of school and busy getting ready for family celebrations, shopping, and whatever other holiday customs might be of importance to you, I thought it might be fun to look at the math behind a popular Christmas song that I know all of you have been hearing (since Thanksgiving) whenever you walk into any store.
I realize that many of you may not celebrate Christmas – I myself celebrate both Christmas and Hanukkah, so my family has several different traditions. I realize there are many of you out there with your own traditions and customs during this winter break (i.e. Christmas, Hanukkah, Kwanzaa, to name a few). That’s the beauty of this country – you can celebrate and enjoy your own traditions. My focus is as always on math and/or technology, and I happened to find this interesting YouTube video that incorporates Pascal’s Triangle into a very popular Christmas song – The 12 Days of Christmas. Even if you don’t celebrate Christmas, you know you have heard this song (I believe I have been stuck on the elevator more than a couple times with this song being piped through)! Hopefully you will enjoy the math aspect of this and next time you hear the song in the stores you can share the math calculations with fellow shoppers.
How many presents is that? Pascals Triangle can help!
We at Casio wish all of you Happy Holidays whatever you may be doing or celebrating!
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:
- 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.
- 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.
- 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:
- 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.