Traveling the Circle – Exploring Arc Length with the fx-9750GII

I went on a bike ride this morning. I have a new app for my phone that keeps track of my distance, route, and speed. It gives me average miles-per-hour, calories, and total time as well. Pretty amazing what these apps do – don’t need to do much thinking. However, it did get me thinking!

Obviously, the app is going off of speed and time, as well as GPS location, since it is mapping the actual route I take (very helpful for figuring out how to get back home). Miles/hr is impacted by my pedaling speed, hills, the gear I am in, and any stopping I do along the way (which trust me, happens – gotta catch my breath after some of the hills!) The size of my wheels and the distance covered in one rotation obviously is involved to some degree, but not something the app is calculating. My husband and I can be on the same bike ride, travel the same distance, go the same speed and number of miles, but his tires are much larger than mine. So my assumption is he is pedaling less than me due to the radius of his tires. Which means, in my perfectly logical way of thinking, I work out harder than my husband (lol)!

But this brings me to today’s mini-math lesson, which is exploring the distance traveled by a tire/wheel of a bike, car, truck, etc. Radius and rotation make a difference. I am using the fx-9750GII graphing calculator and an activity from one of the Casio Resource Books, Geometry ,  called Traveling the CircleThis is  a geometry activity, that looks at the application of distance, circles, radius, degrees, radians, arc, arc lengths and more. Students explore how different radii/diamters and angle of rotation determine the distance covered by different tires. They also use the understanding of arc length to determine distance around a curved track (think a typical high school running track). They look at domes and circular shelving. In the process, they are collecting data, using formulas and applying ratios/proportions and looking at practical uses for needing to know the distance of arc lengths.

 

Attached is the PDF of the actual activity. It includes standards, some calculator tips that are specific to the fx-9870GII but obviously can be used/applied to any Casio graphing calculator since they follow the same steps. There are 4 different sections of the activity, each with questions, so it’s a nice look exploration of circles and arc length and how radius/diameter impacts the distance. There is also a video overview that goes through some of the basic operations/functions needed and used in the activity, such as creating tables, doing calculations, using formulas, etc.

  1. Traveling the Circle – Geometry
  2. Video Overview – Formulas and Table of Values and Rational Number Entry

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

Here are quick links:

Mini-Math Lesson – Statistical Calculations and Fractions with the fx-260Solar

I am finishing out this week of scientific calculator explorations with a look at the fx-260 Solar. On the surface, this calculator looks really simplistic – almost four-function if you look at size and cost. But it can do so much so its looks are deceiving. The old ‘don’t judge a book by it’s cover” comes to mind!

Here are just a few of the capabilities of this little ‘engine that could’:

  • Statistical Calculations (mean, sum of values, sum of the square values, sample standard deviation, population standard deviation)
  • Fraction calculations (including mixed-number) and conversions
  • Constant Calculations (i.e. setting a constant and then using it in several different calculations)
  • Trigonometric and Inverse Functions
  • Exponents and Logarithms

There are more, but what I wanted to focus on today were two of these: Statistical Calculations and Fraction Calculations. I have made two quick videos. Having to use my document camera to record since this calculator does not have emulator software, so apologize if the lighting isn’t all that great. It is hard to record and see what you are doing with a document camera – I am learning a lot!!!

  1. Entering Statistical Data in the fx-260 Solar and Statistical Calculations

     2. Working with Fractions with the fx-260 Solar Scientific Calculator


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

Here are quick links:

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