# Planes, Wind, Velocity, Vectors – (Scientific Calculator fx-991EX ClassWiz and Vectors) Happy Friday! I wanted to end my week of fx-991EX Classwiz focus with something that I have been missing – flying. As part of the work I do, I usually travel a bit each month. Whether that is to speak at conferences, work with schools and teachers on math pedagogy, technology, or traveling for vacation, I spend a lot of time on planes. But – as of March, I haven’t traveled once, for obvious COVID19 reasons. And, since schools and teachers are going through so much uncertainty, the professional development I was scheduled to do this summer is cancelled. And who knows when live face-to-face conferences and events will happen again. I am grounded.  And I miss it!!

As I looked through the menu options for the fx-991EX Classwiz, I saw the Vector menu, which got me thinking back to high school (yes, a LONG way back!!) where we actually learned about vectors. Adding/subtracting vectors to determine the direction a plane would have to fly to get to it’s destination to account for the impact of the planes velocity and the winds velocity. This clearly stayed with me because it made so much sense and I found it fascinating, and to this day, I think about the calculations that must go on by the pilots and the air-traffic controllers to make sure planes get to their destination, counteract wind, avoid other planes, etc., much of which is connected to vectors. I don’t know why vectors was taken out of the geometry curriculum – I think it is now more in upper level courses, but to me it really should still be included in geometry, which most students still take, because it is so relatable and relevant. Students see planes (even if they don’t necessarily go on them) flying above them, and I think it would be a great way to bring in a very real answer to ‘when are we ever going to use this?” Obviously there are more applications of vectors, but planes is the one that really stuck with me.

But, I digress. Let’s get to the focus of today’s post, which is using the Vector menu on the fx-991EX Classwiz to work with vector problems. I am focusing on simple vector calculations in my video related to determining a planes path based on their velocity and direction and the impact on this from the winds velocity and direction. A vector has both magnitude (length/size) and direction (often  includes angle). If visually finding the direction the plane must fly, which is what I remember doing in school,  you place the two vectors (wind/plane)(represented by directed arrows for length and direction) head-to-tail, and then construct the resulting vector (basically making a ‘triangle’ (see image 1).  We describe each vector by it’s x-vector magnitude, and it’s y-vector magnitude (so (x,y)). We add/subtracting the vectors by adding/subtracting the (x, y) vectors magnitudes of each, which results in the the solution (x,y). To find the magnitude of the resulting vector you would use the (x,y) solution and the Pythagorean Theorem. If you look at the image 2, what you should see a connection to the Pythagorean Theorem and a hint at Trigonometric functions if given angles (if given bearing degrees vs. magnitude of vector). You might have to do some trig to figure out those x- and y- vector magnitudes or the magnitude of a given vector if only given it’s bearing degrees.

There are many applications for vectors (navigation, force, displacement, acceleration, etc). What I show you in this video is how to do vector calculations in 2-dimensions (you can also do vectors in 3 dimensions which would be the same process, just choosing 3 dimensions vs. 2). I show adding/subtracting, scalar multiplication, and also the Dot Product.

Be sure to visit Casio Cares: https://www.casioeducation.com/remote-learning

# Mini-Math Lessons – Middle School Equivalent Expressions and Exponential Expressions-fx-991Scientific If we are thinking about equity and getting technology in the hands of students, scientific calculators are powerful tools that can support math discovery and exploration (except graph, though the fx-991EX even does that!) and are really inexpensive (between \$10 – \$20). This week I am going to be showing some of the capabilities of scientific calculators that I don’t think many people realize they can do – i.e. equations, expressions, inequalities, and statistics.

Today I am going to share two  activities that utilize the fx-300ESPlus2, though you could use these with any scientific calculator from Casio (or graphing for that matter). Both these activities focus on expressions with a goal of understanding what expressions are, equivalent expressions, the role of variables. The first activity, It’s All the Same, is about using properties of operations (associative, commutative, distributive) to explore equivalent expressions. The calculator is used as a verification tool, where students use stored values for given variables that then allow them to check that different expressions yield the same result. The second activity, The Variable Game, focuses on exponential expressions, and helping students apply properties and write exponential expressions with given parameters. They use the calculator to store variable values and then use these as either the base or the exponent to try to create expressions that fit specific criteria. This allows them to get a better understanding about exponential rules and working with whole number exponents and bases. Both activities, as you will see, include standards, warm-up exploration questions, suggestions for student discussion and ways to extend. Each activity has an application and then some practice problems.

Here are the links to the two activities and a video overview that goes through some of the functionality of the fx-300ESPlus2 that is needed in the activities.

Be sure to visit Casio Cares: https://www.casioeducation.com/remote-learning

# Mini-Math Lesson-Solving Equations/Inequalities and Normal Distribution w/fx-115ESPlus2 Scientific Calculator

I am always amazed when I remember how much power a scientific calculator has to do high-school and upper level mathematics content. I think, like many, it’s assumed once you get into those higher mathematics courses, you need a graphing calculator. But – you really can do so much with just a scientific calculator, except graphing (though the fx-991EX does that too!).  Today I am exploring just a tiny bit of the functionality that the Casio fx-115ESPlus2 scientific calculator has – specifically, I am going to demonstrate how to use it to verify solutions and to determine probability of a normal cumulative distribution. There is so much more that it can do, so consider this a teaser.

The two lessons I am sharing are ones that utilize the two features I am highlighting. What I love about these activities is it isn’t all ‘using the calculator’. In fact, the calculator is just a tool to verify work or help in the analysis of a situation, which is what we should be doing with calculators. They are not ‘answer givers’, but if used properly and appropriately, they help verify students work, they help them analyze mathematics and make decisions and these lessons do a nice job of making the calculator work with the student rather than do the work for the student. The first activity focuses on solving linear equations and inequalities in one variable and quadratics. In this activity, the calculator in this is a tool to verify student solutions to quadratic equations. The second activity is about representing data in various ways (dot plots, histograms, and box plots), and determining probability. The calculator here is used to here to help students find the area under the normal curve.

The video how-to that sort of goes along with these lessons is using the fx-115ESplus emulator software, which, if you check out the link below for the Casio Cares, is available as a free download with an extend free trial through August 31. Great tool supporting students in this remote learning environment.

Here are the links to the two activities that are overviewed, as well as the video which walks through the two main function needs in the activities.

Be sure to visit Casio Cares: https://www.casioeducation.com/remote-learning