# Tidying Up!

A break is always a good time for tidying up and reorganising things!

Continuing the Use of Technology series of pages, the PhET Simulations, Standards Unit Software and Wolfram Alpha pages have been added to the series.

Added to the GeoGebra series is a new page, GeoGebra Resources-Edexcel so all the resources for GCSE and A level Maths and Further Maths are available in one place.

A recent addition to the top menu includes Updates where updates to popular posts are noted. A further new page added today is Popular Posts and Links, just a small number of currently popular posts and/or files. I see that the file of legacy coursework tasks from Edexcel has proved very popular this year as has The Workers of Zen.

# Graspable Math

The User Guide.

Recently published – a really clear user guide for Graspable Math.

I was delighted to see the announcement of the new user guide recently.

This can be downloaded from the Learn section of Graspable Math where you will see the Canvas User Guide. Together with the tutorial videos and Gesture Library resources there are excellent resources for learning Graspable Math.

All instructions are very clear in this 47 page document – everything you ever wanted to know how to do! Check the list of contents:

I checked how to insert a video and it struck me that you can insert a video on a canvas, watch it and try out the feature on the canvas. Try solving an equation on this canvas.

As a teacher, remember you can create a free Teacher account. Check out the Activity Bank with some great activities which will help you and your students learn Graspable Math.

I wrote recently about Graspable Math in this post which has proved very popular – where you will find more examples, including a couple of problems from Don Steward.

Remember that the Learn Section has Tutorial Videos, a Common Gestures Overview, and an Interactive Gesture library where you can watch then try gestures as well as the user guide. Look at this video on Scrubbing Numbers – a lovely feature enabling you to generate many examples.

# Mathematical Miscellany #44

From Ross Blair on MATHSgrader comes a complete set of Interactive assessments to complement the Maths Genie homeschool program. The resources are provided in three tiers, Tier A roughly accords with grades 1-2. Tier B with grades 3-5 and Tier C is 6-9. Check the menus for Teachers and Pupils for easy site navigation.

For A Level Owen (Owen134866 on TES) has a library of Mathematics teaching resources, these are really clearly structured with step by step examples. Recently added, is A-level Core Pure Mathematics Year 2/A2 for the second year of Further Mathematics. These resources have been added to the Teaching Resources page for Further Mathematics. This Calculus content is part of the core Pure Mathematics specification common to all examining boards. For more on Further Calculus in Further Mathematics, see my post here.

Also note for Further Mathematics, Jack Brown who has created thousands of videos covering the complete A Level specification has been very busy with his Further Maths collection of teaching videos and exam paper walkthroughs;  the easiest way to navigate the videos is through his website, TLMaths.com. A recent addition to the exam paper walkthroughs is the specimen paper for OCR MEI Modelling with Algorithms.

My post on Graspable Math proved popular last week and included a canvas of the problems from one of Dave Taylor’s wonderful Increasingly Difficult Question sets. I decided I liked the idea of having a canvas ready for his 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.

Taking a canvas and adapting can help you learn to use the interface if you are unfamiliar with it. Using this One Incorrect canvas by Eric Weitnauer which is based on Don Steward’s one incorrect simplification I made a copy of Eric’s canvas and created one for the first problem from Don Steward’s blog post, discovering along the way that if you enter text for a web link, then Graspable Math inserts that as a link.

For a clear example of this feature in action, have a look at this video.

By Colleen Young

# Graspable Math

A revisit to 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, 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.

To experiment with the interface select Explore algebra online.

Graspable Math is easy to use, I decided I would solve an equation and wanted to show all the steps. To start, go to a blank canvas and choose Insert / Math Expression, 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.

An alternative to the above is to use the settings menu; choose Dragging to apply the inverse operation to both sides.

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

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.

The scrubbing feature is very useful, drag up or down on a number to change its value; the change will propagate through the rest of the working.

A great example of the use of the scrubbing feature can be found on this canvas created by Graspable Math for this lovely problem, Create a System of Two Equations by Daniel Luevanos on Open Middle, accessible for students yet such a great task for mathematical thinking. We could discuss inequalities here as well as simultaneous equations.

Graspable Maths have provided a ‘cheat sheet‘ providing a handy summary of how to use the interface.

Graspable Math took one of Dave Taylor’s wonderful Increasingly Difficult Question sets and created a canvas of the problems.

We now have Graspable Math Activities, Graspable Math have a free version and optional subscription (watch for information from Graspable Math on this, but teachers can be reassured that they can continue to use Graspable Math with their students). You can use the Activity Bank to learn how to use Graspable Math. Select Graspable Math Gesture Tutorial and you can watch demonstrations and try the features for yourself. This seems a really good way to learn to use the interface.

It is possible to insert a video onto a canvas, so you could inset a video and then follow the instructions on the canvas. Try this on solving equations.

Graspable Math – One Incorrect

A lovely way to practice – use this One Incorrect canvas by Eric Weitnauer which is based on Don Steward’s one incorrect simplification.

Also a good way to learn to use Graspable Math – save a canvas and adapt it, I made a copy of Eric’s canvas and created one for the first problem from Don Steward’s blog post, discovering along the way that if you enter text for a web link, then Graspable Math inserts that as a link.

For a clear example of this feature in action, have a look at this video.

# 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.

Excel Interactive Resource – Fraction Multiplication

For teaching sequences, Interactive Number patterns will be useful.

Nrich – Interactive Number Patterns 2

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

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.

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!

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.