One of the most popular posts on this blog is Top >10 Mathematics Websites. It struck me that it might be useful to think about my top recommendations for students; once again using some categories as well as individual sites gives me the excuse to mention more than 10! So for your students:
Top >10 Mathematics Websites for Students
Back to the teachers!
I have mentioned TED-Ed before with its collection of Mathematics videos, note the feature now offered by TED-Ed to ‘find and flip’ which allows you to use a video and turn it into a lesson; see ‘Flip This Video’.
Looking at some videos, it struck me that something like Gaurav Tekriwal’s The magic of Vedic Math would be ideal to tinker with! (These ‘tricks’ can make ideal starters, I have linked to some further videos on this page on Number on Mathematics Starters.)
On the subject of videos and TED, have you heard Ken Robinson’s latest talk,
How to escape education’s death valley?
Scratch – from MIT
Scratch, from MIT is object-oriented programming language which is very easy to get started with as there is now a new release of the platform availble entirely in a browser; no program downloads are required. The interface is intuitive and easy to use; extensive help is available including a very clear Getting Started Guide and a set of Scratch Cards with clear instructions which will help you learn new Scratch code. Note the Scratch For Educators section.
As you can see from the sprite’s path the above program continues as follows:
Now that’s not a very efficient program! Scratch is a great way to learn programming as well as doing some Maths! We could look at external angles of polygons for example and show how to repeat a set of instructions.
Scratch – drawing an octagon
We could add some sound, change the pen colour or shade, learn about variables and generally have some fun!
Click the image then ‘See Inside’ at the top of the screen.
Try experimenting with this program which uses variables for the number of lines to draw and the angle to turn through. You will need to sign up to Scratch which is very easy and free.
It strikes me that Scratch could be used for many topics, bearings included.
Stephen Quinn’s dissertation is an investigation into using Scratch to teach KS3 Mathematics and has many ideas as well as useful information on Scratch.
The Mathematics of Pringles
WolframAlpha – hyperbolic paraboloid – click on the image for details
One day this week over our break time coffee, the Mathematics department was discussing the shape of a Pringle – as you do! I thought I’d look a little further into this and have it on good authority that a Pringle is a hyperbolic paraboloid. See Professor Benson Farb of the University of Chicago in the video posted on Freakonomics, The Math of Pringles.
Last week I mentioned various Statistics resources. A colleague and I used the Census at school site very successfully this week with our Year 8 classes. The students completed the Census at School 12/13 questionnaire on paper for homework then input their results in a computer room at school. The site worked very well indeed and the exercise led to some great observations and discussions by our students. We have now retrieved the data from the site for our two classes and can use that in our lessons this week. Working with data that they have generated themselves is certainly motivating and meaningful for our students. A mention must go to the excellent staff at Census at School who answered some queries of mine very helpfully and with extraordinary speed!
My class also look at and enjoyed the various Experiments at School (see the online experiments listed as 14-28), it is possible to generate data for the online experiments. We’ll investigate data from those experiments further this coming week.
I’m still using mini tests for my exam classes, I asked my Year 11 students to sketch the various graphs needed for our exam specification then went on to ask them to sketch some graphs and transformed graphs on the same diagram (see the KS4 resources).
Creating some worked solutions to exam papers for my students I wanted to annotate a graph of cos x (generated by the wonderful Desmos graphing calculator); now I normally use the Interactive Whiteboard software to do this but thought I’d try Skitch, a free app that allows you to annotate images with arrows, shapes, text, and more; annotations can be saved and shared. It is easy to use and I do like the look of the text!
Experiments at School: Database Interrogation Tool
This week I will be studying Statistics with both Year 8 (UK, age 12-13) and Year 12 (UK, age 16-17). This prompted me to revisit my Statistics and Probability Resources list and happily I was reminded of some of the excellent resources available. (This is one of many lists on the I’m Looking For……page).
To highlight a few sites from that list:
The Census at School site has an extensive collection of resources for students of all ages, try the true, false or sometimes true set of statements for older students, or perhaps clean up the dirty data with younger students. I rather like this starter and the KS3 and KS4 Statistics Statements. See also the CensusAtSchool International Project.
Try the Database Interrogation Tool from Experiments at school. Click on the logo to start, make any selections then on the Next arrow on the top right of the display to proceed. I like the way it is possible to choose variables and chart types; this could be useful for a class discussion on when it is appropriate to use various charts.
From the always excellent Standards Unit, we have ‘Mostly Statistics‘.
I have mentioned Hans Rosling’s excellent use of Gap Minder before. Note the links to a guide to the software and a page for teachers.
For more data sets, also for some very useful Excel files see Douglas Butler’s collection.
Another site I posted on some time ago is Mike Hadden’s excellent collection of resources which includes several Statistics resources.
For older students Jonny Griffiths has a wonderful collection of activities – Making Statistics Vital.
The Tools and Calculators section of the list includes virtual dice, also coins and dice simulations.
Some quotes end the list!
“Facts are stubborn things, but statistics are pliable.”
A collection of resources are available from Hwb (the all Wales Learning Platform, note this now includes all the material from the NGfL Wales website). Select Find and Use to explore the resources. The resources are also hosted on TES. (Note that the echalk resources such as the excellent transformations interactives are no longer free).
This on Developing Mathematical and Thinking Skills is authored by Melanie Blount. The resource can be used online or it is possible to download a zipped file. The concept cartoons would display very well on the interactive whiteboard and perhaps provide a useful starter activity.
Resources in this set I particularly like include Large Numbers and True Sometimes. Large numbers consists of a set of 20 questions (with the option to show answers) with big answers! With questions such as ‘How many mobile phones are in use in the world?’ this would make a very engaging lesson activity and would be ideal to use when teaching standard index form. The True Sometimes resource is a set of 10 statements; students must decide if the statements are always, sometimes or never true. (There are links to some Always / Sometimes / Never questions from other sources in the Rich Questions post.)
Last week, writing on revision I wrote about my use of ’mini tests’. I have used several this week with a variety of classes, with Year 12 I started with some basic calculus in one lesson and trigonometric equations in another. Watching them mark and correct their work confirmed my belief that these mini-tests are very useful; concepts and ideas we may think of as basics are not always as secure as they might be. I have started making a note of questions to ask them as I notice any misconceptions.
Coming up to examinations I often use a timed exam question as a starter which could be just a few minutes, I work out the marks per minute rate for the exam for timing.
I recently set a homework for my Year 11s to look at some specific topics and let them know they would have 35 minutes in class to answer exam questions. We then went through the questions straight away, they marked the paper and I collected their work to see how they did; I always tell my classes I am looking at their careful marking and corrections as much as their original answers. I was amused to see that one of my students had headed her paper ‘Mini-Mock’.
I have started a new page under resources for these mini-tests in case they are useful – just four there at the moment but more to come.
WolframAlpha – Handwritten!
- WolframAlpha: Handwritten style plot y=(x-2)(x-1)(x+3)
Reading the WolframAlpha community newsletter recently I was amused by their April fool on the introduction of the WolframAlpha Handwritten Knowledge Engine. It seems this has proved rather popular so what was originally intended for an April fool has now been made generally available. I really like the look of these diagrams, I suspect they will appeal to students and teachers, look at this number line for example.
WolframAlpha: handwritten style number line x=3
Craig Barton’s Collective memory resource – Angle Facts
This week it’s back to school after the Easter break and examination season is upon us. I need to help my students prepare; so, how to help them recall all the concepts and techniques they need for formal examinations? I have become convinced of the need for frequent recall; see this article on how highlighting is a waste of time – and note the conclusion to the Time article ‘ditch your highlighter and get busy with your flash cards’ and this from Science Daily on how short tests improved student retention on online courses (thanks to Earl Samuelson for pointing me in the direction of that article on Twitter).
Something I do regularly with all my classes is ask them some questions at the beginning or end of a lesson to see if they can recall recent (or not so recent!) work. See this file for an example: Mini-test example. The questions are short and can just be read out for students to write responses in their exercise books (making this a great starter – no IT or resources required). The questions in my example here are just recall type questions on a variety of topics but could of course be a series of questions on just one topic; questions requiring higher order thinking skills could also be used (see Rich Questions for ideas). I have added a new page to which I will add any mini-test resources.
I think this type of exercise is valuable at any time, not just at examination time and we should spend time regularly helping our students recall current or earlier work. A really useful source of questions which can be used this way are the mental tests from CIMT; these are included with their resources for Years 7, 8 and 9 and also for GCSE. For Key Stage 3 (ages 11-14) scroll down this page for the Year 7, Year 8 and Year 9 course material, the resources include mental tests as part of the teacher support material. On the GCSE page scroll down to the teacher support material and note the mental tests available for most units, see this on Formulae for example.
The Collective Memory resources on TES can make an excellent revision activity, students look at posters and then have to understand and recall that information. These can be used in a variety of ways which are fully described in the article. (A further set of resources is available here). Last year my GCSE students created several posters of their own which they found a very useful revision activity.
Some students find mind maps helpful to recall information, I have seen students create some excellent diagrams with Bubbl’us for example. For some more online revision tools including some to make flashcards the resources mentioned here may be helpful.
According to this story, told by Nathan Shaw Einstein said this. Now I am very pleased that I share my own ‘capture everything in such a way that you can find it again’ ideas with Albert Einstein! I have found some resources I really like recently – so the usual question – where to put them so I can find them again?
I mentioned in a recent post that I came across an outstanding resource on Combinatorics questions by Dr Jamie Frost thanks to the TES Mathematics forum; well Dr Frost has now made his excellent enrichment materials available on The Reimann Zeta Club. This clearly belongs on a list! So I added it to the Enrichment list (for lots of lists see the ‘I’m Looking For …‘ page. As well as adding this resource I checked the various links and also added the Brilliant website I have talked about recently.
Thinking about Enrichment, my own view is that this should be a natural part of the curriculum for all students and made me wonder where my Rich Tasks list ends and enrichment list starts (I solved the problem by adding the Rich tasks list to the Enrichment list!) A recent excellent addition to the Rich tasks list is Jonny Griffiths’ Carom-Maths -activities to bridge the gap between A Level and University.
Staying with the subject of Rich tasks, one of the entries on that list is the list of problems from the National Strategies site to develop mathematical processes and applications; those archives make me a little nervous – will they stay? I decided to create an Evernote shared notebook which lists those resources including links to to the problems on Nrich. Another recent addition to the Rich Tasks list is this excellent interactive from NGfL CYMRU to explore the Painted Cube problem (explained clearly here on Nrich)
I recently read this post by Don Steward and it struck me what a great starter ‘Sum and Product’ would make. I have so many links for starters they have a WordPress blog all to themselves and I have added the Sum and product problem Don describes to the Algebra page there; also new on Mathematics Starters and Plenaries is this link to MathsStarters.net which has a growing collection of starter activities (added to the Collections page); I particularly like the Bingo resources.
Working on an excellent project for TES recently (more on that later) I came across an excellent resource on fractions by Kaszal, the resource is an A5 worksheet consisting of 10 fraction calculations, some of which have mistakes and/or inefficient solutions. Students enjoy marking examples like this and it can lead to some excellent class discussions. I have added this to the Spot the Mistake page under Resources.
Douglas Butler’s comment on my post last week made me realise that I should include Autograph here, so a new Autograph page is now available under resources. (All resources on this site are free to use, I have included Autograph (for graphing, geometry, statistics and probability) here as although it is paid-for software, Autograph viewer and all the excellent resources available on line are completely free to use and do not require the Autograph software to be installed.
See also: Looking for things!
Google graph – click on the image.
A reminder that you can just type a function into Google and its graph will be returned!
Darth Vader on WolframAlpha – click on the image
WolframAlpha of course can show you some graphs of Easter eggs!
I noticed whilst using WolframAlpha today random suggestions of queries popping up that somebody out there thought I might enjoy (very worrying how right they are!). This popped up – I had not realised that typing for example Darth Vader curve into WolframAlpha would give me just that!
Looking for Easter ideas and resources I came across these Easter games on the excellent mathsticks.com site which has an extensive collection of resources for younger students ( a site I have recommended for younger students).
On the subject of Easter eggs I must return to this definition.
WolframAlpha – a little fun!
Desmos polar curve, click on the image to experiment.
My favourite graphing calculator as regular readers will know is the outstanding Desmos graphing calculator. Preparing some resources for my Further Mathematicians I realised that one can use a slider within a domain thus making it possible to show the curve being traced out, particularly useful for polar graphs but also for any curves. (There are some useful resources on polar curves here for students including some further Desmos pages).
Desmos quadratic, select the image to experiment.
Experimenting with a quadratic graph, I have plotted some points and can then draw the curve through these points.
Thanks to the TES Mathematics forum I came across an outstanding resource on Combinatorics questions by Dr Jamie Frost. The high quality here suggests it would be well worthwhile have a look at Dr Frost’s other resources! (Thank you Dr Frost!)
I have been interested in Astronomy since discovering Patrick Moore’s books in the library as a child so enjoyed Richard Byrne’s recent post on resources to help students understand the size of the universe, I particularly like 100,000 Stars, a visualization of the 100,000 stars closest to Earth. All those lovely big numbers in Astronomy are excellent for teaching Standard Form; I wrote some time ago on the excellent mathematics resources available from NASA, see this on Scientific notation for example.
Freerice is owned by and supports the World Food Programme. For every correct answer 10 grains of rice are donated through the World Food Programme. Users can answer questions in several categories including two on Maths, one on multiplication and one on basic Maths. It is possible to play at various levels, so choosing level 10 for example means that questions on fractions and directed numbers will be included. Students can sign up (under 14s need parents permission) or login easily with their Facebook account to track their totals and join and create groups. Teachers can now register a class, so this provides a way for teachers of much younger students to sign up their students.
Sporkle – you have 2 minutes to fill in the missing prime numbers!
Another site which includes a social aspect is Sporkle which has an extensive collection of timed quizzes in many subjects, many mathematics quizzes are available; I have linked to some here on Mathematics for Students. If you register you can create your own quizzes and give the link to friends. It is then possible to see how people get on with your quiz!
And last but certainly not least is a site which I came across recently which I think lives up to its name, Brilliant! Signing up to this site allows users to join an international community and get free weekly, personalised problems. Questions at various levels are available, including questions suitable for younger students.
Click the image to see this problem
This would be an excellent site for any students preparing for participation in Maths challenges, particularly by using Brilliant’s Techniques Trainer. Brilliant are currently developing a “Teacher Level” that has a wider range of problems that can be shared which would make it possible to share problems from a number of different levels with students. (Post with link to Brilliant for students).