Mathematical Miscellany #55

Featuring:

In Mathematical Miscellany #54 I featured two excellent resources from Curriculum for Wales; a third is now available, “The Foundations of Algebra” is suitable for progression step 3 of the new #CurriculumForWales (age 11). The workbook contains chapters on patterns, commutativity, distributivity & associativity.

Foundations of Algebra – Curriculum for Wales

I do like the above exercise which as the Teacher’s Guide acknowledges is based on Don Steward’s work, directed number arithmetic speed up and Chris McGrane’s Alternative representation of integers. A further useful resource for such an exercise is Jonathan Hall’s Directed Number MCQ Generator on MathsBot with which you can generate all the addition and subtraction multiple-choice questions you want; choose between Counters on or off.

Foundations of Algebra – Teacher’s Guide

As with the other two resources, a very comprehensive teacher’s guide is also available. You can see the contents here, this resource with its carefully chosen and varied activities and exercises will help students with the foundations of Algebra.


PhET Sims

On the subject of negative numbers, from PhET simulations we have another excellent resource in their latest addition to the Mathematics collection. To use the number line as a model for ordering real numbers and also to illustrate operations with negative numbers we can use the excellent, Number Line: Distance. Also available are Number Line: Integers, and Number Line: Operations. All are excellent for students to explore.

This resource has been added to my post on Negative Numbers which looks at some resources to develop understanding of operations with positive and negative integers and exercises for practice.


A popular post on this blog is on Venn Diagrams, first written in 2016 this has recently been checked and updated with some new resources including always excellent resources from Amanda Austin on Dr Austin Maths. Included in her Probability resources you will find an excellent section on Set Notation and Venns.

Dr Austin Maths

GeoGebra retweeted this from Javier Cayetano Rod

…the translation:

“Adding some leaves to the stem of a flower can be the perfect excuse to talk about translations and turns in space @debora_pereiro . Added to the flower generator in @geogebrahttps://geogebra.org/m/duqthjva

Which in turn led me to this amazing GeoGebra collection, Flowers 3D, Author: Deborah Pereiro Carbajo.

Have look at Flowers from Curves, simply brilliant!

Flowers from curves – Deborah Pereiro Carbajo

Explore the collection – you could be a while!

Complete Maths has made Robert Smith’s session “Web Autograph, a First Look” freely available


Highlight equivalence – Math Whiteboard

I wrote earlier this year on the excellent Math Whiteboard. This is completely free to use; If you create a whiteboard you can then get a link for that whiteboard which you can share. When I have created a whiteboard I then save a second copy so I can always return to the original.

With an individual subscription ( currently $15 for a year) it is possible to access all the features of Fluid Math including as an authoring tool for creating Math Whiteboard activities. It is also possible to save your activities.

A new feature is available – the ability to create answer boxes to check for correct answers. You can see examples using this feature here.

Math Whiteboard

Math Whiteboard

For easy reference, pages on Math Whiteboard have been added to the Use of Technology series which is available from the top menu.

Math Whiteboard is a Collaborative Whiteboard designed specifically for Mathematics Teaching and Learning. With a very attractive interface and underlying powerful Computer Algebra System, this is an outstanding (completely free) resource for Mathematics Educators.

I was very fortunate to have a demonstration of this incredible resource from Donald Carey, one of the creators of this tool; there is no doubt that he and his team are passionate about Mathematics and the learning and teaching of Mathematics.

Select Create or join a whiteboard now.

Next, select the new whiteboard button …

You can scroll through the ‘getting started with math whiteboard’ section to get an overview of the wonderful functionality of this resource.

I have created a new series of pages on Math Whiteboard in my Use of Technology series so this will be easy to find from the top menu tabs. I will be adding further pages as I explore this more, but it’s certainly something I will be using! (Not to be confused with Maths White Board, another fantastic resource with an extensive question bank ready for use which has also been added to the series.)

Using a whiteboard you can have everything in one place, multiple representations.
We could insert a text box with instructions for students, you could insert a video in the text box. You can also paste an image as you can see in an example below, where I included an image from Don Steward’s Median. This example uses a feature I really like, Highlight equivalence.

Math Whiteboard – Highlight equivalence feature

You can see many examples of whiteboards, scroll down the homepage to see these.

Writing Mathematics Online

August 2018I have written various posts on the available tools online for writing Mathematics and this is a topic which remains consistently popular. Time for yet another revisit and update as new possibilities are now available – all resources / links here have been checked. I have removed resources where blogs / twitter have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

Something I use a lot. I should explain my requirements – I want tools to communicate Mathematics online, for example I may wish to provide some model solutions or answer students’ questions. Writing mathematics can be a pain (and yes I know about LaTeX). Note that there are various possibilities – sometimes just a static picture is required, sometimes you may want to display how to solve a problem in stages, or perhaps you require a collaborative space. You will also need to consider if you want the examples to be permanent or whether you just want a collaborative space for discussion. A graphics tablet is essential.

My favourite method for illustrating Mathematics online (and in fact the one I use most often) when I just need a series of static displays is to turn an interactive whiteboard flipchart (or a PowerPoint) into a pdf file; the pdf file can then be sent to students or uploaded to whatever virtual learning environment or online storage your school uses. If you do not have access to interactive whiteboard software there are alternatives, one could use Windows Paint for example; there are also various free online tools available; see some of the resources below.

flipchart to pdf example

flipchart to pdf example

For sharing resources, it is possible to upload a PowerPoint or pdf file to Slideshare. There are many examples on this blog of my SlideShare slideshows – see this for example

I should mention that I find Slideshare excellent – I use the free version which offers me everything I need – it works every time – I use it a lot!
I created the PowerPoint for the slideshow above by writing on the interactive whiteboard software using my graphics tablet and taking a picture of each page using the Windows snipping tool (it’s in Accessories) – this takes seconds – the snipping tool is something I use every day! (Alternatively I could have saved the interactive whiteboard flipchart as a pdf).

There are as always several options:

Whiteboard.fi
For a free online whiteboard tool for teachers and classrooms try Whiteboard.fi. You can read about the features here and follow News and Updates. It is currently possible to lock the classroom once a class has started, preventing new students joining and coming soon the teacher will be able to pause student whiteboards, disabling their drawing functionality until a teacher wishes to enable it again. For Maths teachers we see coming soon we will be able to insert equations.

Whiteboard fi Diagnostic Questions - White Rose AlgebraThe ability to insert an image is excellent, given that each student can only see their own board and the teacher’s it strikes me that Diagnostic Questions could be so useful here. Display the question, have students put their answers on their boards and the teacher will be able to see the responses of all the students. The image featured above is from the White Rose Maths Collection which features quizzes for each topic unit for their Years 1 to 8 maths mastery schemes of work. Remember there are numerous collections including GCSE questions from the examination boards and a collection of problems adapted from the UKMT Mathematical Challenges.

Screencastomatic

Screencastomatic

If you wish to record a screencast of the moving pen / step by step solution variety and save your work, Screencast-o-matic is an excellent option. It is very easy to use to capture the screen and your recording can then be uploaded to YouTube if you wish.

Illustrating how to simplify an algebraic fraction : simplify-algebraic-fraction

Screencast-o-matic offers everything I want in this category. It is very easy to use indeed – I can write very smoothly whilst recording.

Further resources offering various solutions for writing Mathematics online:

Twiddla

Twiddla

For a collaborative board, try twiddla which seems excellent for collaboration – voice as well if you want. Twiddla offers some very sophisticated features including the ability to use mathematical formulae and upload files and images. Use of the board with all it’s features is free but you cannot save any of your work (possible with a subscription). This would be good for working online with a group of students.

Microsoft whiteboard

Microsoft Whiteboard

From Microsoft, comes their free whiteboard app. To use Microsoft Whiteboard on Windows 10, you must sign in with a free Microsoft account or an Office 365 account (work or school). Full instructions are provided on the help page.

Writing RepeaterFinally – your students may find this amusing – the Writing Repeater from ICT Games – write something and play it back – now this is a lovely tool for little ones learning to write but I’m sure we can think of some uses!

Handwriting recognition, LaTex and more!

A consistently popular post on this blog is that on online whiteboards. If I want to communicate mathematics online to answer a student query for example I find it quicker to use a graphics tablet and an online whiteboard.

I do keep an eye on various LaTex generators, one that has come to my attention is MyScript. In this demonstration, handwriting is turned into LaTex (one line at a time). The handwriting recognition is impressive and I found it easy using my graphics tablet to enter expressions accurately; see the quadratic formula below for example.

MyScript

So you scribble an expression and it get turned into LaTex for you – it works:

MyScript

MyScript

But I must confess I was just as excited to note that immediately see a graph where appropriate, powered by my favourite Desmos graphing calculator.

..and finally, if you wish to be distracted by some more fun applications there are some other great demonstrations from MyScript. Try Web Shape for example and turn your sketches into vectorized shapes. This should work well on the interactive whiteboard.

improve your scribbles!

Improve your scribbles!

 

Online Whiteboards & Feedback

One of the most popular posts on this blog is the one on online whiteboards which I keep updated. Note with Screenr now retired as you will see in the updated post, Screencastomatic will allow you to achieve the same result as seen here – easily create a screencast and upload to YouTube.

This was part of some feedback on a homework task (Tethered Goat – see nrich version here).
The video has been uploaded to our class wiki (I use Wikispaces).


The wiki page includes advice on the features of  a great solution, some questions for reflection and some images of student work.