May 30 2014

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.

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).

I Functions two arguments t 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

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.

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May 11 2014

Plotly

Plotly box plots

A very happy discovery today – Plotly, a collaborative data analysis and graphing tool. Looking at the pricing plans the free plan allows for 10 private files to be saved but unlimited public files; Plotly is free for educational use.

Plotly looks very sophisticated with many options and is certainly something I will return to in future posts as I find out more. The images here show the different types of charts which can be created.

This slideshow requires JavaScript.

Plotly box plot

I was initially particularly interested in box plots as although they can be created in Excel it takes a bit of fiddling around to do so. With Plotly, simply upload your data or copy and paste it in and there are your box plots! Note the outliers shown clearly. Hovering over a plot displays the data.

Plotly Help

To create the box plots illustrated here I initially started with the Math box plot example from the given examples, chose view data, deleted the given data then copied and pasted my own data (with all three columns in ascending order); I then selected all columns, changed the names to display and chose Box plot.

Choosing Help gives you the choices shown here; the instructions are very clearly set out.

If you want to code yourself, you can; see Plotly’s API Libraries. I will certainly be experimenting further with creating charts in Excel with Plotly.

See the Plotly blog for further information; see this post for example on best fit lines in Plotly or try Contour plots, error bars, chocolate, beer, meat and Facebook for a collection of examples showing the great variety, customisation and sophistication Plotly offers.

An update – Plotly Feed – just admire the beautiful graphs and presentation of information.

You can follow Plotly on Twitter or Facebook. (You do not have to be a Facebook or Twitter user to view these pages).

Update: December 2014 Plotly have put together 11 favourite graphs from 2014

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Learn and explore Plotly – there are clear tutorials available on the Plotly site.

Feb 13 2014

Happy Valentine’s Day

Click on the image and move that slider!

In what happily seems to have become an annual tradition Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
Desmos Valentine instructions

This year you can even use the Desmos API …

Elsewhere – express your feelings for WolframAlpha!

and here’s a logic starter from Transum for Valentine’s Day!

Wishing Mathematicians everywhere a happy day and if you are a UK teacher about to start half term – have a lovely week!

Feb 8 2014

Dilbert and Mathematics

Dilbert on WolframAlpha

An accidental discovery today when I came across information on a favourite character of mine on one of my favourite websites! This actually came about because I have completely reorganised and added to the series of pages on WolframAlpha which I hope makes the information here on WolframAlpha easier to find. Note the new slideshow on Statistics; WolframAlpha is useful for calculating normal probabilities for example and illustrates queries with diagrams. I like many teachers I am sure always advise students to sketch diagrams when answering questions on the normal distribution.

Back to Dilbert and we find that associated characters such as the Pointy-Haired Boss are also there!

The Dilbert site may amuse you if you have not seen it before. It is possible to search the site; using a keyword of Statistics returns these strips. Related to Statistics we have made up numbers (I do like that second entry!) or data or try Math. How’s this for a job title? Mordak is the Preventer of Information Services!

Perhaps I’d better get back to some work!

Feb 1 2014

Transformations with the Desmos Graphing Calculator

This week Year 10 (UK age 14-15) have been exploring different graph types and also transformations and graphs.

For homework I asked them to draw just a small number of graphs by hand but wanted them to check their work and explore further graphs using the Desmos graphing calculator. Early in the week I made sure they could all use Desmos including the use of tables so in an IT room they used the slideshow here and created several graphs of their own.

Once all the students were confident to use Desmos to create various lines and curves I asked them to explore a series of graphs so that this coming week we can discuss transformations and graphs. Using Desmos allowed them to explore many graphs in a short space of time and several students chose to take screenshots and make notes for themselves.