Top Tools for Learning 2017

Jane Hart, of the Centre for Learning and Performance Technologies, has published her annual list of Top Tools for Learning. Like last year, she has three sub-lists including Top 100 Tools for Education. Note that you can easily see the rankings for each sub-list using these rankings. Jane Hart’s analysis includes details of the contributors as well as her commentary on trends.

Looking at the Top 100 Tools for Education I see my favourites WordPress (Blogging and website tool) and Evernote (Personal information system) in there, these are also popular in all the lists.

Continuing to look at the Top 100 Tools for Education Excel is quite rightly highly placed. I regularly use Excel resources; just a few examples of some favourites:

Normal Trainer

Excel Files – Mike Hadden

Histograms

STEM Centre – Descriptive Statistics

See STEM Learning, part of the A Level (16+) Resources series.


A few more for investigation …
KahootKahoot (Classroom response tool) is very easy to use and free for teachers and students. In a few minutes I created a quiz on Directed Numbers … (not very exciting – just a test, very easy to create.) Kahoot qn

Another popular quizzing tool I know some of my colleague’s use is Quizlet.


Seeing Padlet (online discussion board) on the list reminded me of this very easy to use tool. I shall try this with Year 7!
Padlet equations


Unsplash – beautiful free photos to do anything you like with! Perhaps not surprising that this has moved rapidly up the lists!

marivi-pazos-229895
Photo by Marivi Pazos on Unsplash

Apart from illustrating Unsplash, I can have pictures of flowers to illustrate a mathematical connection! From Science News reading Fibonacci’s Missing Flowers we discover that the most common number of petals is five and whilst there are many flowers with the number of petals a Fibonacci number there are also flowers with four, six, seven or nine petals!


GrammaryI added a comma in a couple of places in this post thanks to Grammarly which has jumped up the Top 100 Tools list by 70 places. Very easy to use, Grammarly lets you check for 250 types of grammatical, spelling, and punctuation mistakes.

 

 


 

Formulae: A Level Mathematics

Looking at the Subject content for A Level Mathematics we see that Appendix A, pages 16-22 describes the mathematical notation for AS and A level qualifications in mathematics and further mathematics. Appendix B, pages 23-26 is on mathematical formulae and identities.
Formulae1
Checking individual examination board specifications shows us the formulae which will be provided in the examination; each looks very similar.

OCR (MEI) Formulae

OCR (MEI) Formulae

I think it is useful for students to be aware as they study the course which formulae they must know and which will be provided; though they should be very familiar with any provided formulae.

MEI Technology

MEI – Use of Technology

Teaching Calculus from the new specifications I see that the formula for Differentiation from first principles is provided which seems fair. Looking at MEI’s very helpful advice on Integrating Technology into your scheme of work we see some suggested resources for teaching differentiation, including this GeoGebra resource on First Principes. I like the way one can choose between numeric and algebraic.
GeoGebra first principles

MEI – Use of Technology, Differentiation

Staying with Calculus and technology, note that Desmos allows you to very easily see a function and its gradient function; note the requirement of the subject content that students should be able to sketch the gradient function for a given curve.
Differentiation
Desmos gradient function
A resource I found very useful for the matching a functions with their gradient functions comes from Underground Maths. I included Gradient Match which can be used interactively online in this post on introducing gradients at GCSE. Note that you can simplify the task by giving students the set of six functions and the six gradient functions separately.

 

 

 

 

gradient-match-underground-mathematics

Underground Mathematics – Gradient Match

 

 

 

MEI Ritangle Competition (& Technology!)

From MEI comes Ritangle, a competition for teams of students of A level Mathematics, Scottish Highers or the International Baccalaureate. This year’s Ritangle competition  launches Monday 2 October!

For the main competition, one question will be released daily for 21 consecutive weekdays, the first question will be released on 9th November 2017. I am looking forward to seeing the problems which I am sure will be of interest to many Mathematics students even if they are studying for alternative qualifications and cannot enter the competition.

Something which caught my eye is that Technology can help with some Ritangle questions which led me to some excellent Excel resources, which you can use whether or not you are participating in the competition.

Excel is a favourite for me – I use it in both my Mathematics teaching and in my Deputy Head role. Note from Nrich, we have many uses of Excel for Mathematical Investigation. I like this very clear illustration showing fraction multiplication.

Nrich Fractions multiplication

Excel Interactive Resource – Fraction Multiplication

For teaching sequences, Interactive Number patterns will be useful.

Quadratic Sequences

Nrich – Interactive Number Patterns 2

…and one of my favourites – Happy Numbers! (For the Excel spreadsheet – Nrich investigation)
Happy Numbers

Talking of technology, the Excel fractions resources here reminded me to try fractions with Graspable Math. Having tried Graspable Math on the Interactive whiteboard recently I can confirm it works perfectly.
Add Fractions

And finally, talking of Graspable Math, this led me recently to Dave Taylor’s excellent Increasingly Difficult Questions, a wonderful collection – and with an eye on the copying budget too!
Change the subject DT

Looking at the Graspable Math Teacher Resources, I see some of the Increasing Difficult Questions have been added to a canvas. Graspable Math lets you save your work so you can come back to it later or share it with others. Saving requires a google account. To share a file, use the share menu to get a link that gives others read access to a file. I decided I liked the idea of having a canvas ready for Simplifying Expressions, starting with IDQ-Simplifying Expressions 1, I opened it on my own canvas and adapted it slightly. I do like to keep all steps of the working displayed, so I have put the exercises on the left, creating a good space on the right.
Simplify Expressions IDQ

Tidying Up!

Tidy UpI have made several updates to the organisation of this blog recently, always attempting to make things easier to find!

This includes the creation of some new pages.

Lesson PlanningNote the Lesson Planning series which includes pages on Technology also some useful reading. Note the excellent post from Peps Mccrea, The 7 habits of highly effective lesson plans (on the Lesson Planning Reference page). Much food for thought here with the author’s emphasis quite rightly on learning and making the material memorable.

The post includes some rather thoughtful comments on sins of planning!

With Technology in mind I have the Tools & Calculators and Use of Technology pages and also a new series of GeoGebra pages. Note the wealth of resources available from MEI; MEI as a GeoGebra Institute provides us with many excellent classroom resources. The Calculators page includes instructions and examples on various calculators including the new Casio FX991EX-Classwiz.

MEI GeoGebra Institute

Quadratic Inequalities MEI

Shown here we have Quadratic Inequalities from the Higher Tier GCSE collection. This would also be useful for Advanced Level students.

For any teachers teaching the MEI A Level specification MEI have provided GeoGebra files of their large data sets.

MEI LDS

MEI Large Data Sets – GeoGebra

For more on Statistics data sets and teaching activities resources from the examination boards please see the Statistics page in the Advanced Level series. Edexcel have very useful guide to teaching Statistics including examples and calculator instructions.

Edexcel Guide

Edexcel Statistics Teaching Guide

 

Mathematical Songs

All checked and updated – many of these songs have gone down well for a considerable time. A more recent discovery was the One Direction quadratic formula song which makes my student smile (and sing a long!) (A reminder of GCSE Formulae)

The following songs have all gone down very well with students, particularly the Circle Song!

This on the Quadratic Formula makes my students smile – and they sing along! The One Direction Quadratic Formula song!

Or perhaps try these!
polygon-song

More favourites:

The Klein Four are a bit beyond school Mathematics you may appreciate this if you are studying a Mathematics degree!

….and of course, ‘Katie’s bad science’. I love this!
Original and re-edited version of Katie Melua’s song nine million bicycles proposed by Simon Singh and presented on Ted talks by Michael Shermer.

Mathematical Miscellany #16

A resource miscellany this week, a reminder of where to find excellent teaching resources provided by the examination boards and also from MEI.

MEI, AQA, Edexcel and OCR (also Eduqas, part of WJEC) provide excellent support for teachers. With GCSE and A Level subject content now the same for all the examination boards we have an excellent library of resources to use irrespective of the specification chosen for public examinations.

MEI have produced such a valuable collection for teachers with the latest addition to their work on Problem Solving. See their Problem Solving examples and solutions. As well as all the problems and solutions with very valuable suggestions and commentary, MEI have provided a guide to support teachers with the problem solving content of GCSE (14-16) and A Level (16-18).

At A level MEI’s Interactive Scheme of work includes a resource for each section of the course. See also, MEI on integrating technology into your scheme of work which includes many calculator, Desmos and GeoGebra tasks.

See also MEI Free Reources and a page added to the GeoGebra series on the MEI GeoGebra Institute.


AQA

TeachIt

TeachIt Maths

 


Edexcel

  • GCSE Teacher Support includes new content resources, a worksheet collection for Foundation and Higher, teaching low attainers and formulae posters.

    Edexcel Codebreaker

    Edexcel Worksheets

  • Teaching and Learning Materials includes an extensive collection from baseline tests for younger (KS3, age 11-14) students to demanding GCSE (age 14-16) Problem Solving questions. The Problem Solving questions with full mark schemes are excellent as are the Practice Papers and topic tests.
  • Signing up to the wonderful Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you useRegister for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number. In the GCE AS/A Level Mathematics cabinet you will find documents for GCE 2017 including baseline tests and unit tests, also Transiton materials for GCSE to A Level. More will be added to these collections.Edexcel Empoium

 


OCR


Statistics – The large data sets and more for Advanced Level Statistics from AQA, Edexcel, OCR and OCR (MEI) can be found on this page.
GeoGebra Regression


Eduqas is part of WJEC and offers Ofqual reformed qualifications to secondary schools and colleges. Eduqas has many very useful secondary and vocational resources for Mathematics. Note the series of resources for topics new to the GCSE specification.
Educas - Venn Diagrams


 

Graspable Math

Reading Jo Morgan’s latest Gems post led me to the very happy discovery of Graspable Math. Graspable Math offers a highly innovative interface for mathematical notation. You can read the Graspable Math story here.

You can learn a great deal about Graspable Math simply by experimenting, selecting Explore Algebra takes you to the interface which is intuitive; you can also find plenty of help and tutorials on the Learn section of the site, note the Gesture Library as well as the video tutorial collection.  There is a YouTube channel here.

Graspable Math is very easy to use, I decided I would solve an equation and wanted to show all the steps. I have used the method of selecting and holding the = sign to start as you can see illustrated in the video above; I was then able to enter an operation to apply to both sides of the equation.

equation to solve

equation to solve 2

We can also illustrate the solution graphically by inserting a graph to open a GeoGebra window.
equation & graph

Each expression has a circle at the end – simply drag that to the GeoGebra window. You will sometimes see more than one circle at the end of an expression, select to separate expressions hence showing all steps clearly.

I can see this becoming a regular part of lessons, a go to resource.

 

Mathematical Miscellany #15

From Colin Foster on Nrich we have Mathematical Etudes where he discusses lovely rich tasks and tedious exercises!

Colin Foster

Colin Foster – Mathematical Etudes

An important read as we begin another school year I feel, the more our students have to think about a task, the more they will learn. I agree with Colin liking the factors task, I have used this approach successfully in class too. In fact we can extend the task and look at finding numbers with varying numbers of factors.

Factors nzmaths

How many Factors – nzmaths

How Many Factors on nzmaths requires students to  find ways to group numbers, which numbers have only two factors and which have only three factors?

For more from Colin Foster his KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham.

Colin Foster - Instant Maths Ideas


From PhET Simulations one of my favourites is now available in HTML5 collection: Projectile Motion.

Projectiles
PhET Projectile Motion

I have included a page on PhET simulations in the Tools and Calculators series of pages, part of the Lesson Planning collection.


Educas has many very useful secondary and vocational resources for Maths. Note the series of resources for topics new to the GCSE specification.
Educas - Venn Diagrams


Dr Frost slideI have mentioned Dr Jamie Frost and his plans for the new A Level specifications. Dr Frost has been very busy producing a complete set of resources for Pure Mathematics 1, I do like the fact that Dr Frost has included extension questions for each chapter. These resources reference an Edexcel text but of course the content is common to all qualifications so all the explanations and worked examples for A Level. I have included a page for Dr Frost’s resources as part of the A Level series. Note the collection of extension questions mapped to the new specification.

Dr Frost has some brilliant ‘Just for your interest’ posters; see this for example on e. He has put the complete collection of these together. Follow Dr Frost on Twitter.


For more A Level (UK 16+) resources, Danielle Moosajee has a growing collection of A Level resources on her site PixiMaths, Check her KS5 Teaching Resources Index. The resources include very clear PowerPoints, associated questions and student self-assessments.


A consistently popular post on this blog is one on online whiteboards. All resources / links have been checked and I have removed resources which have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

doodle.ly

Doodle.ly



With UK examination results recently announced I have put links to the results statistics and grade boundaries on the Results 2017 page. Also included are some interesting links from Schools Week, see A-level results 2017: UK subject tables which compare results from 2014-2017. Also from Schools Week, on GCSEs – GCSE Subject Tables and “The 7 most interesting things we have learned”

An important read I feel on such Statistics from Cambridge Mathematics, Examining our own statistical literacy on results day. which makes such important points about the size of the dataset required for it to be explored in context.


And finally, here’s a great read from Shaun Allison on Getting off to the best start with a new class.


 

 

Lesson Planning

With the new school year fast approaching, I have reorganised some pages and resources in the never ending quest to make things easy to find! This is an ongoing project.

There are several additions to the Lesson Planning Pages.

Lesson Planning PagesA new series on Tools and Calculators includes for example GeoBoard Activities with GeoBoard resources.
Trangles on a 3x3 piboard

There are many excellent PhET simulations from The University of Colorado Boulder. Look at Trig Tour for example. Note that this is HTML5 so available across platforms.
Trig Tour

I do like to use resources in class that my students can use at home, so for example in the calculators and tools collections (see Calculators – Collections) under Equations – Linear and Quadratic, we have from Mathisfun this very clear and easy to use interactive illustrating the solution of linear equations.
balance-equations-mathisfun

You will also see on the same page this calculator from Math Warehouse which shows the solution to any quadratic equation with full working using the formula.

Quadratic Formula

Math Warehouse

The Problems and Activities page has had updates including the addition of Transum, a site I like a great deal as do many students. From Transum, we have the very wel known Maths Starter of the Day. Note that there is a complete index of starters including the topic of the starter. The Transum site is easy to navigate, there is a clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning. The example shown here is one of the Algebra Activities found on this page.

Transum

Transum – Algebra Activities

An essential part of every lesson is of course that we check that students are indeed learning, hence my reminder on Study Strategies on the Lesson Activities page.

retrieval-practice-learning-scientists

The Learning Scientists

Calculators

Calculator Pages

Calculating FinancesTime for a series of new calculator pages to make it easier to find information and resources on calculators. The pages in the series:

Some highlights from these pages…

The collection includes manuals from Casio and Texas and also some very clear guides from Dr Frost.

There are some excellent step by step instruction videos on using the Casio FX991EX calculator.

MEI have many tasks for older students using Casio Graphical Calculators (they also have tasks using GeoGebra and Desmos).

Normal
On the Mathematics for Students pages you can find everything from a game to help students understand order of operations to a Normal Distribution Calculator.