Valentine’s Day …

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

..and see also “Make Linked Möbius  Hearts“.

Click on the image and move that slider!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
valentine-design

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people you could even use the Desmos API …

Remining with the loving theme you can also express your feelings for WolframAlpha!

I Love YOU

valentine-relay

Valentine Relay – Chris Smith


For some Valentine class activities, try the Valentine Relay from Chris Smith and note all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.

Transum Valentine Puzzle
and here’s a Valentine logic starter from Transum.


 

Circles & Tangents

Circle & tangent

Desmos – Circles & Tangents

Use Desmos to explore tangents to circle through given point

Teaching Year 10 about the equation of a tangent to a circle at a given point I have created a Desmos page. I have also created a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent)

(Also added to GCSE New Content page)

Further Desmos Updates

An early introduction – plot some points and functions
Desmos – points & functions (for PowerPoint file)

 Graphs-GCSE for PowerPoint file

Desmos Activity Builder

A superb new addition – Desmos have created an activity builder for teachers, this enables the creation of interactive Desmos-based classroom activities. A series of pages can be created – any combination of graphs, questions or text. Having created and saved the activity a code is then associated with that  activity which your students enter at student.desmos.com.

CY Desmos Activities

A simple experiment for my first activity – identify the lines x=k and y=k.
Activities are very easy to create, the interface is intuitive; images can very easily be added by dragging them to the page.

This slideshow requires JavaScript.

Once students have tried the activity and submitted answers to any questions a teacher can see all their submitted responses. This is certainly something I will be using with my students in the coming academic year. I have various slideshows for Desmos which I can now create activities for. (For more on Desmos, see these pages).
Student

Desmos & Valentines (& fractions and rotations!)

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

Click on the image and move that slider!

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!
valentine-design

Geeky people you could even use the Desmos API …

Valentine’s Day seems an appropriate time to express love for Desmos!
Two happy discoveries this week (thanks to Twitter):
Fractions - multiplying Rotation
Multiplying fractions and Rotation about a point. Brilliant.


Elsewhere – express your feelings for WolframAlpha!

I Love YOU

Transum Valentine Puzzle
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!

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.

Desmos - simple transformations example

Desmos – simple transformations example


Having used sliders they were able to create
this type of graph page.

I have created the slideshow below to use in class to summarise our work and act as a revision aid for them.

These slideshows are both available here for students.

Filling and Pouring

Some excellent watery demonstrations this week!

Cleo resource

A resource I use regularly to demonstrate ‘real life graphs’ comes from the excellent CLEO Resources (Cumbria and Lancashire Education Online).
Fill the various flasks with water and investigate how the height of the water varies with time.

Archimedes Bath

Archimedes from Colmanweb

Or you might like Archimedes in his bath!

From the Connected Maths Project (Michigan State University) comes this very clear demonstration for exploring the relationships between the volume of various geometric shapes

Connected Mathematics Project

     

Fill a shape with water then drag it to another shape to empty the water into that shape!

(Other activities I particularly like on this site include tessellations and the isometric drawing tool from the 6th grade resourcesVirtual Box from the 7th Grade resources and the Painted Cubes investigation from the 8th Grade resources.)


Desmos Graphing Calculator

I wrote about the (free) Desmos Graphing Calculator in June when I first came across it. Since then I have used it a great deal in the classroom as it is a powerful resource, very simple to use and available for students to use at home. Several new features have been added since I wrote that first post. For my school age students I particularly like the sliders feature, the trace and the option to use degrees as well as radians for angle measure. You can read the latest blog post from Desmos here.

The ability to share pages is extremely useful for students, particularly now with the addition of sliders; students can be asked to explore families of graphs from simple straight lines for the younger students to polar curves for the Further Mathematicians, perhaps some cubics for GCSE / A Level students. (Note that the value you assign to the variables determines the initial set of values possible with the sliders, click on the values on the slider to edit.) Perhaps explore transformations.

It is very easy to demonstrate a variety of functions, for example I was recently studying the modulus function with my sixth form students, looking at modulus equations and inequalities a picture speaks a thousand words! (Just type y=abs…)

absolute value

Thank you Eli Luberoff and team for this amazing resource!

See also Pretty Graphs, Desmos DelightsGraphing Inequalities and these posts on my blog for students: Explore Straight Lines and Explore Graphs.

Graphing Inequalities

Thinking about resources to show students how to graph linear inequalities, I can use Autograph in the classroom as I often do but I am always keen to show them resources they can use at home.

The Desmos graphing calculator handles inequalities very well, unlike many free graph plotters it is easy to plot lines of the form x=k. Click on this image to see these inequalities on the Desmos calculator. See also this post on Mathematics for Students.

Desmos Inequalities
Experiment with these inequalities on the Desmos graphing calculator.

The Holt Online graphing calculator can deal with inequalities (though it cannot plot line of the form x=k) and gives a very clear display.

To enter an inequality, click on the equals sign, then select the required choice:

Up to four inequalities can be entered.

I am puzzled by WolframAlpha currently as I thought this would be an obvious resource to use. The inequalities examples here are fine,  however I don’t think this inequality plot for x+y<5 would help my students much!