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.

Edexcel GCSE GeoGebra Resources

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:

User Guide – 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

Some updates this week…

mathsgrader Interactive Assessments

mathsgrader interactive example

MATHSgrader Wk1 Assessment Tier C

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.

 

One Incorrect - Don Stward - first problemTaking 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.

Note formulas on the menu.
Graspable Math Formulae

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

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.
Explore algebra online
Learn Videos

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.

equation to solve

Graspabale Math - Solve Equation

Settings
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.
Graspable Math - GeoGebra

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.Create a system of two equations

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.

Sim Eq Opn Middle Problem 1

Cheat Sheet
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.
IDQ Changing the Subject

Graspable Math Gesture TutorialWe 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.

One Incorrect

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.

One Incorrect - Don Stward - first problemAlso 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.

Median - Don Steward

Note formulas on the menu.
Graspable Math Formulae

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

See also Graspable Math – The User Guide.

For Valentine’s Day…

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?!

careers-heartsAlso, 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!….
valentine-mobius-hearts
use-to-create-mobius-heartsNote 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. See Valentine’s Day for the Desmos details.

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.


Save your money on cards and send your loved ones (or anybody!) a math-o-gram!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
valentine-design

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people, you could even use the Desmos API …

NASA Valentines
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.)

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

I Love YOU


For those in school this week try some Valentine class activities. Transum Valentine Puzzle
Here’s a Valentine logic starter from Transum.

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.

valentine-relay