Mathematical Miscellany #55


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 @geogebra

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.

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, 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.