Desmos on Android

This slideshow requires JavaScript.

A happy day! Desmos comes to Android and I now have the best handheld graphing calculator I have ever had! As you would expect of Desmos, it just works! Get it on Google play here. (Desmos iOS apps have been available for some time). I will certainly be asking students with Android phones to get the app.

You will find a series of Desmos Slideshows here, (these have been written with students in mind) and more on Desmos on this series of pages.

Photos by David Young

Cubic

Regression

Since I will be studying the Bivariate Data section on one of our Year 13 (UK age 17-18) Statistics modules soon I was rather pleased to see that it is now really easy to use Desmos for Regression. The video shows how simple it it to use.

I tried this with some data from an A level question then also added another expression and table to see the values predicted by the model.

Regression

It is also simple to use Excel – just add the data, insert a chart – choose Scatter, then add a trend line.

Regression using Excel

Regression using Excel

GeoGebra provides us with another option.
Try this ready to use worksheet – find the line of best fit.
GeoGebra Regression
From the GeoGebra manual – FitPoly command  

For another easy to use tool, we could use the PhET simulation.
PhET Residuals

…or we could just pop the points into WolframAlpha and have it do all the work to check our calculations!
Regression

 

Desmos – tangents to curve

At the moment I am introducing calculus to my sixth form classes and I wanted to use Desmos to illustrate drawing a tangent to a curve. A quick search found thisCopying the page to my own account I then modified the page to show a simple quadratic (f(x) = x2).

Desmos tangent

Desmos – tangent to a curve

Something I have been meaning to do for a while is try the folder feature on Desmos, a rather neat way to create a tidy looking set of items.

Desmos page notes

Desmos page notes

Show / hide folder contents

Show / hide folder contents

Folders are easy to create:

Desmos Folders

Desmos - add folder item

Desmos – add folder item

Having created a folder, press enter and the next item will be placed in the folder. If you want to add items later, ‘nudge’ your item into the contents of the folder.

I recommend that students use Desmos to help them understand any questions they do; finding the equation of a tangent to a curve is a good example, Desmos can be used very quickly to illustrate a correct (or not!) solution.

For checking calculus examples students can use WolframAlpha, examples are included in the fourth slideshow here).

 

 

Update ….and along came @Desmos! (select either picture for graph page)
Desmos tangent tweet

Tangent to curve - Desmos improved version

Tangent to curve – fabulous version by Desmos!

Thank you @Desmos! (Think I’ll put in a few requests!)

Functions

Thinking about teaching functions in the next few weeks (to UK Year 12 ages 16-17) I realised that I could use Desmos to illustrate composite functions; the following slideshow illustrates the syntax.

We can also use Desmos to illustrate a function and its inverse. To create the page below (select the image), I started with a graph already online illustrating the general case of a quadratic function and its inverse and simplified it. f(x) and g(x) can be changed to a different function and its inverse. Note that the domain of f(x) can be changed.

Inverse

Further examples: exponential function and basic quadratic (where we need to restrict the domain for an inverse function to exist).

Staying with Desmos, as I have mentioned before, the function notation is excellent for transformations:

(See this page for all Desmos slideshaows).

IFunctions two argumentst is also possible to define a function with more than one argument and use Desmos as a calculator

For some clear examples and a resource to point students to, Functions from The University of Plymouth Mathematics Support Materials is useful. The format used in this series makes the examples clear and all the exercises given have answers.

Functions - Plymouth University

Functions – Plymouth University

Other useful resources (requires Java) include the Wisweb applets, algebra arrows could be used to demonstrate functions and their inverses as shown in the following images.

This slideshow requires JavaScript.