Statistics with Desmos

Desmos now provides several functions for computing statistical properties from lists of data.

It is also possible to perform basic statistical tests, count combinations and permutations, and work with distributions. The supported functions can be found on page 11 of the Desmos User Guide. Part of the Learn Desmos series, you can see many functions demonstrated in this series of graphs.

Also very helpful is this Desmos article, from which we see that the Normal, Poisson and Binomial distributions are all supported.

With a requirement for Advanced Level being the use of technology to explore data, the Desmos statistical functions will provide a very valuable addition to our lesson toolbox.

In this article on Data Visualisations, we see that boxplot, dotplot and histogram functions are available.

Boxplots – Desmos Activity Builder

This activity builder includes excellent tasks for students to explore boxplots.

Bob Lochel has uploaded this helpful video illustrating the use of these functions.

For Valentine’s Day …

An annual update, ideas and resources for Valentine’s Day …

From @OCR_Maths, we could try this puzzle.

OCR often share some great maths puzzles, look out for them.

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The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  

For Valentine’s day we have an appropriate article from Maths Careers, did you know that 6 is a kissing number?! And for your Further Mathematicians, What is the equation for a heart?

 

 

 

Also from Maths Careers, see this post with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….

Note the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white space at the end – the picture here has been made using strips 10 cells long.

 

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For an alternative source of Valentine’s cards, we can turn to NASA! Take your pick from this post or these fabulous NASA images. (And don’t forget that NASA provides us with many Mathematics resources.)

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Here’s a Valentine logic starter from Transum.

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This Valentine Relay from Chris Smith is excellent as are 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.

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From Maths4Everyone, try this Valentine’s Day Maths Treasure Hunt. Students have to work out the costs of gifts, meals and other outings for Valentine’s Day.

You can find a whole collection of Treasure Hunts from Maths4Everyone here.

Also on TES resources, from a favourite TES author of mine, Andy Lutwyche, you will find this Valentine’s card Area and Perimeter problem.
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From the MEI Archives, the February 2015 edition of the MEI Monthly Maths Magazine includes some connections between maths and Valentine’s Day. On page 7 note the article “A Happy Ending” which includes references to some Numberphile videos, Professor Ron Graham discusses the Happy Ending Problem and from Dr Emily Riehl, The Stable Marriage Problem. We also have a great Parametric Heart spreadsheet from Think Maths.

This edition of the magazine includes some lovely activities which link paper folding and proof.

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From Perton Maths Department, try these Valentine puzzles.

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

and from the WolframAlpha archives, Computing Valentine’s Day.

Factorisation of Quadratic Expressions

When factorising quadratic expressions I always encourage students to check coefficients first, if the coefficient of x² and the constant are prime for example they clearly do not need elaborate methods.

Some students have difficulty with the splitting the middle term method; if one must have a recipe to follow – try the box method.

Working on Quadratic Grids from Underground Mathematics will help students develop and understand the method.

For instructions on the method:

Quadratic Factorisation Box method (pdf file)

Perhaps even simpler is Lyszkowski’s method which avoids the manipulation required by conventional methods.

Lyszkowski’s method

I came across the method through Colin Foster’s wonderful Mathematical Etudes site. To quote Colin Foster:

Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.

Note the Etudes by topic at the foot of the page; Number, Algebra, Geometry, Probability & Statistics are available. Looking at Algebra for example, under Solving Equations we see Connected Quadratics which is where I found Lyszkowski’s method of factorising quadratics.

Comparing the two methods with an example:

We could have a look at the general case for the box method :

and for Lyszkowski’s method:

Try this excellent lesson plan of  Colin Foster’s on Quadratic Equations. I really like the starting activity in this lesson which should promote a deeper understanding of factorising quadratic expressions.

 

Mathematical Miscellany #25

Have a look at the latest newsletter from Simon Job’s MathsLinks, Don’t just write the date this year – write it as a number sentence using the digits of the date in order.

A brilliant resource shared on MathsLinks here – Dynamic Calculus, a collection of interactive learning objects for teaching calculus. This is an HTML version, there is no reliance on the Java version of GeoGebra and no use of Flash.

Or try Errors in Measurement, a very clear GeoGebra resource.

Subscribe to the newsletter and/or follow @mathslinks on Twitter or Facebook for regular updates – highly recommended.

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I do like the ClassWiz calculator and have been collecting some useful videos from the excellent Calculator Guide on this page, many of which I have shown students in class. Checking some ClassWiz resources from the Calculator Guide, a happy discovery, Learning Mathematics with Classwiz, a free ebook by Barry Kissane; all you ever wanted to know about the calculator with exercises, activities and notes for teachers.

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MEI (thank you) alerted me to this poster – 100 jobs in STEM! This poster and many other careers resources are available from Tomorrow’s Engineers. Looking at the UK Statutory Careers Guidance we see that schools should link curriculum learning to careers. We have the brilliant Maths Careers site to help us here.

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Look at all the events available through The Advanced Mathematics Support Programme (AMSP); the events include free online courses for teachers in state-funded schools and colleges in England.

AMSP On Demand Professional Development

Use the Event format dropdown menu for event types, one type is On Demand Professional Development; teachers can access the materials at any time over a period of up to one year. I have signed up to ‘Preparing your students for the MAT and the TMUA’ course myself; the materials I have looked at to date are excellent. In each unit short videos guide teachers through the ideas of the topic along with practice materials, triggers for reflection and suggestions for further study. Forums are provided for teachers to interact and collaborate with others studying the same material and all the forums are monitored by an expert tutor who will respond to queries.

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A reminder that the AMSP Problem Solving Competition closes 1st February and is for any students in Years 7 to 11. Can your students solve a vexing vexillology problem? Full details are available on the AMSP competition page.

 

Multiple Choice Questions

I have been updating posts on Multiple Choice Questions to make sure all links are working correctly and any outdated resources removed.

The posts Multiple Choice Questions and Multiple Choice for older students can be found on this new page, Multiple Choice Questions under Problems and Activities.

There are many excellent sources of questions in these posts, Don Steward for example, who has so many outstanding resources on his Median blog, includes some multiple choice quizzes.

Don Steward – Rearrangement Steps

See this on rearrangement for example. Note that Don has a collection of practice and quiz questions which includes multiple choice quizzes.

A recent happy discovery is the excellent multiple choice questions from the American Mathematics Competitions (AMC). There are several competitions which increase in difficulty by student age. Detailed Problems and solutions are available, I do like this problem, a good one to use when teaching Systematic Listing Strategies perhaps.

Phil Bruce – Multiple Choice Starter Questions

On TES resources, author pbrucemaths has a brilliant collection of clearly indexed multiple choice starter questions, Phil Bruce has aimed to cover every objective on the GCSE syllabus.

Colin Billet – GCSE Multiple Choice Questions

Also on TES, Colin Billet has created multiple choice questions from old GCSE papers, one set is for the higher tier and another for foundation.