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 a page I copied 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!)

Learn Desmos – Tangent Line Slider

From Year 7 to Year 13…

Such a busy week…

But I have written a weekly blog post since January 2011 when I made a New Year resolution to write a blog post every week, a habit I don’t intend to stop, so this week I simply offer two slideshows I created for my students recently.

With Year 7 (age 11-12) we have been studying Algebra. When solving equations, I included for a class of high ability students, equations with the unknown on both sides. Having given them one homework where they were exploring various resources for practising solving equations, a sudent asked in a comment on our homework blog how to use Duncan Keith’s excellent linear equation calculator for practising this type of equation:

The slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.

At the other end of the school, with Year 13 I had completed the various integration techniques required for our exam specification. Aware that students sometimes muddle differentiation and integration, I started the last lesson of the series with one of my ‘self-checks’ / mini tests to see what they could easily recall. I have stressed the importance of knowing the basics with this group. The questions I used are presented in the following slide show – a sort of KS5 mental Calculus test!