Some recent discoveries…

Jeffrey Ventrella’s Composite Number Tree

I was reminded this morning of why Twitter can be so useful – I usually check the latest #mathchat tweets and saw Richard Wade’s tweet with a link to the latest Teach Maths newsletteron ‘Ten Great Ideas’. The first item includes this wonderful Composite Number Tree by Jeffrey Ventrella – I’m looking forward to trying that with students after half term. I think it would make a great starter. Students could work out themselves how the tree is being formed and comment on any patterns they notice. Also included in the first Newsletter item is the excellent Primitives application by Alec McEachran, I included this myself with some resources for looking at Prime Factors in an earlier post.

It’s a small world! I see the second item is on Craig Barton’s Web Whizz video on Teachmathematics. You can see all Craig’s videos here on TES Resources.

On WolframAlpha, if you query on a word you can see a word frequency history, see this on Mathematics for example (the history is based on a Google books sample of one million books). An opportunity for some cross curricular work perhaps?

WolframAlpha is still free to check working for as many queries as you want making it very useful for students but now step by step solutions are limited to three a day unless you sign up to WolframAlpha Pro, so choose your three carefully! The new style step by step solutions are clearly presented – see this integration by parts for example:

(See this page for WolframAlpha examples showing the syntax for many different queries. I have added a couple of new slideshows for older students recently, on Set Theory & Logic and Differential Equations).

I mentioned Numberplay from The New York Times in a recent post but it’s worth another mention, they have some excellent articles. (Note this is included on the Reading page).

Finally, still on the subject of reading, I enjoyed Andrew Old’s post on ‘What Ofsted Say They Want’. Just what is good teaching all about? This is so sensible!

For UK teachers I hope you enjoyed half term last week or like me are looking forward to a week off this coming week!

By Colleen Young Posted in Number

Some resources used in my classes….

Below I have given details of some resources I am currently using with my classes or have recommend to my students so they can explore examples further themselves.

Year 12 (age 16-17)
I want to talk about quadratic inequalities this week so I thought I’d use the Desmos graphing calculator to draw some pictures! Click on the image for the Desmos page and select ‘projector ‘ mode for display on the interactive whiteboard. Last week a student in this class asked where she could find some additional resources on polynomial division.
Note: I use the Desmos calculator so much I have decided it deserves a page of  its own here (under Resources).

Year 13 (age 17-18)
Some students in a Further Maths class asked for some Polar coordinates resources to support their studies – so a post for them on my blog for students – these resources would also work well on the interactive whiteboard for use in class. As regular readers know I am a great fan of WolframAlpha and use it with all my classes (WolframAlpha now have a paid for service but it is still completely free to use to check answers for an unlimited number of queries, the free use limits step by step solutions to 3 a day). One of this class showed me that he has the WolframAlpha app on his phone.

Year 11 (age 15-16)

My Year 11 group are studying the AQA Level 2 Certificate in Further Mathematics (a course I am very much enjoying teaching) as well as completing their GCSE course this year. We have been studying calculus and I have found the Desmos graphing calculator very useful to illustrate problems we have been solving. This class have mock examinations coming up and I wanted to recommend some additional resources for them (we have various texts and the AQA support is excellent but the more the better and there is currently no textbook for the course); one site with some very useful resources for some parts of the course such as introductory Calculus is David Smith’s ‘The Maths Teacher.’ 

Year 8 (age 12-13)

I have a Year 8 class this year, none of whom I have taught before, we have been looking at surface area and volume. Math Open Ref has a rather nice animation which helps when looking at the surface area of a cylinder. (More on John Page’s Math Open Ref). I will also use this site when we look at constructions soon. Most had not seen WolframAlpha before so were quite impressed at how easy it is to check working! There are slideshows available for students showing the syntax for a selection of examples on my blog for students.

Negative Numbers – Resources

Sometimes resources for younger students can be useful for lower secondary age students, see for example Mark Robinson’s Numberlines  from the old Ambleside Primary School site which includes an option to display a number line from -5 to 5.

For another excellent number line resource see J Barrett’s Numberline Jump Maker on I often recommend that students sketch a number line to help with addition and subtraction problems and very clear resources like these can really help. Teacher Resources on Line includes a Big Number Line under Basic Materials for display on a classroom wall

Games can be an excellent way to practise with negative numbers see for example games such as Connect 3 from Nrich and Tic Tac Go, a Wisweb applet.

Further resources include exercises from Trinity School in Nottingham (under Number) and Interactive Resources from CIMT (see unit 3, 3.3 on Negative Numbers and Unit 15, 15.1 and 15.2 for operations with negative numbers in the tutorials section).

There are many excellent resources on TES, the resource collections includes a section on Topic Specials which includes 10 of my favourite resources on Negative Numbers.

Desmos Calculator Examples

Direct link to presentation on Slideshare. Download this pdf file: Assessment – Desmos illustrations – all pages link to a Desmos graph.

My Year 12 (age 16-17) students have been studying coordinate geometry recently. I have been advising them whilst they are studying this topic that it can be very helpful to see good diagrams. I created the above slideshow to provide them with diagrams for a set of questions assigned to them and also to show them examples of the syntax to use for the excellent Desmos graphing calculator. Clicking the image on each slide takes you to a Desmos page with the graphs.

Registering with Desmos (free) gives you the ability to create, save and share pages (Facebook, Twitter or permalink).

Several students have said how much this has helped them.

For further examples see this post.

By Colleen Young Posted in Desmos