Mini-Math Lessons – fx-991EX and Functions – QR Codes and All!

IThis week I am going to continue my focus on calculators, for a couple reasons. One, I know many students have access to these, so let’s use the tool they might be familiar with and don’t need the internet to use. Two, Casio is extending the free trial for their calculator emulator software until August 31, so teachers can download these and use them to demonstrate and model in remote learning situations. So, this week I am going to be looking at the different ways you can look at functions on different calculators.

Most people think a scientific calculator can’t show you what a function might look like, since it is not a graphing calculator. Not the case with the ClassWiz, one of my favorite calculators. Because of it’s QR code, you can in fact create a visualization of the functions you might be working with, so in the video that supports the two lessons today I demonstrate how to use the QR code to see the graphs of the functions/tables we are dealing with.

The activities today are basic explorations about functions and what they are. Students are using the calculator as a way to explore patterns and develop an understanding of how functions develop from understanding the relationship between the independent and dependent variables. They can look at tables and understand what functions ‘do’ to the input in order to create the output.

Below are the links to the two activities and then a video that shows how to set up tables, how to input functions, and then also how to utilize the QR codes to see the graphs.

  1. Investigating Functions
  2. Investigating Models


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

Here are quick links:

Mini-Math Lessons – Systems of Equations

(The flowers have nothing to do with the math…just thought we could use a little beauty!!)

Today I am in a sense ‘cheating’ again, as I am using a previously made video and activity to share today. It seemed to fit in well not only with the advanced Algebra focus of the week, but also in light of the current pandemic crisis we are in and importance of our medical experts and workers who are giving so much every day. The activity shared today is an activity called “Not Enough Doctors”, and uses real-world data to explore our future supply-and-demand of doctors. What I like about this activity is that you will experience several different functionalities of ClassPad.net – i.e. data/statistics, graphing, text, equations, tables. It is a nice multiple-representation activity and allows students to see different ways to look at data and display data and answer questions about that data. A really important skill.

Here is the link to the activity and accompanying video:


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

Calculate the Love – Valentine’s Day Heart Challenge

This Friday is Valentine’s Day. I know students and teachers around the country are doing Valentine-themed activities, whether that be making cards for parents, or exchanging cards, or doing plot-the-point pictures of hearts, etc. When I was teaching in the middle and high schools, I tried to have some math-related activities, where students were to use mathematics to create Valentine-themed pictures, cards, or art. In geometry, this might be using constructions with compass/protractor or math software. We even made poems a couple years using mathematical language, which were hilarious. Students can be so creative!! (Example: “My love for you is irrational”, and the image was a circle with a heart and the pi symbol inside).

In middle school we might create coordinate plots. In pre-algebra or algebra we might use different functions and the calculators to come up with different representations. It was always quite a bit of fun, so I thought I would pass along the idea.

One really fun challenge that I use to do is to encourage students to construct hearts using equations, inequalities and calculators. This really fosters some creativity, and complexity as well, depending on the level of students, since all sorts of equations can be used. If you have colored calculators you can add in that color-aspect as well. For example, you can use parametric equations, or conics, or inequalities, or plotting points. It is all dependent on the level of student. So – I am encouraging you all to challenge your students this week to come up with creative ways to construct, using equation and/or inequalities, or lists/points to create some different hearts. Maybe have a contest where students, on Friday, share their creations and everyone explores the graphs and then maybe votes on the different ones. You could have ‘most creative’ or ‘most equations’ or ‘best shading’ or best use of color.  This type of activity really forces students to explore equations and inequalities in different ways, having to constrain the domain and/or range, and think about the coefficients.

Here are just a couple examples (using the CG50 Graphing Calculator). Challenge your students and share the love!!

 

The STEM Around Us

NCTM Innov8, the new team-based conference that NCTM is sponsoring, is going on right now in St. Louis, Missouri. Our team is there of hqdefaultcourse, supporting math teachers with our technology and a great team-building session based on the Wheel of Fortune and the probabilities of winning (session is Friday, November 18 at 10:45 am in Room 265/266). St. Louis brings to mind the very famous St. Louis Gateway Arch, something math teachers attending will probably be exploring and trying to mathematically represent – is it a parabola? (In fact, it is NOT a parabola, but rather a flattened catenary). (Cool 3D mathematical model here).

This idea of looking at real objects and connecting mathematics to them is something math teachers do often. It makes complete sense, and, as I have been teaching a geometry course for Drexel these last several weeks, I have really deepened my appreciation for this idea of looking at our constructed world to find the mathematical connections and relationships. What I think we tend not to do with students, and what we should do much more of, is go beyond the obvious “shape” explorations and function fitting to explore the STEM connections.

What I mean is after we identify the inherent shapes and/or functions in ‘real-world’ objects, start asking questions that get students thinking about the why behind those shapes. The why questions lead to investigation and research by students into science, technology, engineering, and math applications that would take them much deeper into understanding the world around them. And, I wager, this type of questioning will engage students in learning and applying what they learn in a much more relevant and interesting way.  Giving them purpose for learning. And, as a result, we might have more students going into STEM fields.

Some examples:

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Why, for example, are most buildings polygon shapes, particularly triangles and rectangles? Why don’t we see more circular or cylindrical shapes for buildings, besides the grain silos or water towers? Is there a reason? This is where engineering would come into play – are certain shapes stronger from an engineering perspective?

science-test-tubes-all-the-ladies-in-washington-zsrurj-clipart

 

Why are science and medical tubes cylindrical? Is their a scientific reason for these shapes/containers? Why not use a prism shape, so then you could set the vials down on a table versus having to store them in special holders so they don’t roll away? Is the shape somehow connected to the way molecules or blood cells behave – i.e. science factors that might determine the tools used.  2791136-image-of-the-motherboard-without-a-pc-processor-closeup

Look at all the different shapes on a computer motherboard – there are cylinders, rectangles, squares, networks of curves/lines of wires, prisms…so many things going on. Students could ask whether certain shapes provide better conductivity? Or heat control? How does the height of a component impact it (notice the different heights of the cylindrical components). I don’t even know the questions to ask here, but this is a great example of where technology comes into play.

I feel that if we allowed students to explore beyond simple things like fitting a function to a curve or identifying shapes in a picture, and really focused on STEM applications and reasons behind the use of those specific shapes, we would be encouraging students creativity, curiosity, and developing research capabilities in order to find solutions. It would be so engaging and really get students interested in those STEM careers, but more importantly, a better understanding of the STEM around them.