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.
Using the trace feature, we can see for example the solution to a pair of simultaneous equations (select graphs then move along the line or curve, points of interest such as the intersection of the two lines are clearly shown).
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…)
Thank you Eli Luberoff and team for this amazing resource!
See also Pretty Graphs, Desmos Delights, Graphing Inequalities and these posts on my blog for students: Explore Straight Lines and Explore Graphs.
The 1000 Problems site is an excellent collection of resources organised into collections on Number, Algebra, Shape and Space and Statistics. Within each category problems are organised by age and key words and a clear description are given for each problem. For each problem a file can be downloaded which includes the solution.
I have been working on Surds with one of my classes recently, looking at the Extension problems on Number I can see there is a problem on ‘Friendly Surds’ which would make a good starter to review the work we have been doing and extend to generalise – what conditions do we need for surds to be ‘friendly’?
For other Starter ideas see the companion blog Mathematics – a variety of resources to start and end lessons.
This is the first in a series of examples showing the syntax to use for WolframAlpha.
These examples are intended for 11-14 year old students.
All the examples will be added to the WolframAlpha pages where you will find further information.
There are many possible ways of sharing information with students. I recently tried Middlespot again after some time and found it very easy to use and much improved. It is very simple to share for example weblinks, videos and music. I like the facility to add sticky notes and/or text.
The above example includes some resources for my students studying quadratic equations.
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.
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!
There are many excellent resources online for solving equations.
A simple way to see a complete solution to an equation is to enter it into WolframAlpha then select ‘Show Steps’. (Update 2012 – using the free version of WolframAlpha allows you an unlimited number of queries, so excellent for checking any work but you can only use ‘Show Steps’ three times a day!)