Thursday, May 21, 2015

Investigating Triangles

For some reason, I woke up this morning thinking about triangles.  Particularly triangles with longest side 10 units.  I thought that Sketchpad might be an interesting way to construct said triangles and investigate relationships between the lengths of the other two sides.

You can see that I ended up with a tan triangle on the left and a plot relating the two remaining side lengths.  The following videos step you through the process of creating the sketch and using it to investigate some very interesting questions about the boundary of the region on the right, isosceles triangles, right triangles, and maximal areas.

In Ontario, students in the Grade 9 Applied Level are expected to do investigations like this, although they start with rectangles - which seems more complicated.  They are expected to investigate figures with maximal area as well as 3D shapes.

You can download the sketch, but it is more fun to create it yourself.  I have captured my investigation in case it helps in the 12 videos below.  If you find that you have trouble motivating yourself to watch 12 fascinating videos, you could just watch the last one to get a sense of where the investigation ends up.

(You can click on the title to get the video in a new tab)

Constructing the Triangle

Constructing the Point representing Side Lengths

Constructing the x and y segments

Tracing the Side Lengths

Investigating the Region of Possible Side Lengths

Investigating the Boundaries of the Region

Reasoning about the Equations of the Boundaries

Investigating Isosceles Triangles

Investigating More Isosceles Triangles

Investigating Right Triangles

Triangle in a Circle

Investigating Area

Friday, April 10, 2015

Two new Learning Tools available

The Ministry Digital Resources Development team is delighted to announce that two new apps, Money by Mathies and Notepad by Mathies, are now available at the App Store, the Google Play Store and for Desktop.  

Please visit to access them.  

There is also an email list that you can subscribe to if you would like to receive updates about new resources.  Visit or click the link at the top of the What’s New dialog inside .

The Money by Mathies app allows students to represent values using realistic coin and bill images provided by the Royal Canadian Mint and the Bank of Canada.

The Notepad by Mathies app allows annotations to be made on top of blank, lined, isometric or grid backgrounds.

photo 4Felicity.PNG

Supports, including wiki pages with sample screen shots, can be accessed using the i button in each app or from

American Politics Explained

I just think that this is so right-on and funny to boot!

Yoram Bauman is the world's only stand up economist.

Wednesday, January 21, 2015

The Rekenrek by mathies app

The team that I work with produces digital resources for Math which are catalogued at  This week we finally are able to add the Rekenrek for mathies app we developed for the App Store (iOS), the Google Play Store (Android) and desktop computers (Flash-enabled browsers).

The rekenrek is a powerful tool for helping students develop early number concepts.  It can be used to support the learning of addition and multiplication facts by helping students understand different ways these values can be constructed.  Information about how to use the app can be found by clicking on the i button within the app which provides a link to a wiki page with informative screenshots, links to PDF supports and two how-to videos.  It has been really rewarding working with primary educators to understand how learning tools can help students with skills like subitizing which as a secondary teacher I had no idea about.

One feature that is unique about our app is the annotation tool (accessed using the pencil icon) which allows students to draw on the stage and explain their thinking.  It is, in fact, a drawing app in its own right.  You could delete all the rekenrek rods and use it to draw on the screen.  We plan to add the annotation tool to all of our future apps.  One of the next ones under development is a notebook tool which is simply the annotation tool together with some stock backgrounds simulating a plain sheet of paper, grid paper and isometric dot paper.

The app was developed using Flash CS 6 and its export to iOS and Android AIR functionality.  This allows us to develop once and deploy in three versions.

It really has been a thrill to open up the official mobile stores and see our app there, ready for free download.  Please have a look, tell others and perhaps even provide a review.  If your students do something interesting, we would be happy to hear about it and, with their permission, even post their work to our wiki.

Thursday, September 25, 2014

Display issues with The Geometer's Sketchpad

There are 21 Sketchpad sketches contained within  You can find them by clicking the search icon at the top of the page, choosing "GSP Files" from the Search within drop down list, and clicking Display All.

These sketches were created in version 4 of The Geometer's Sketchpad™, which was the version licensed by the Ontario Ministry of Education at the time.  In the process of updating them to version 5, particularly to allow use with the Sketchpad Explorer iPad app, we noticed some discrepancies in how the sketches displayed on different machines.  Interestingly, most sketches worked just fine on my Windows machine, running at 96 pixels per inch (ppi), and on my iPad, running at 72 ppi, which is also the resolution for Macs generally.

The biggest discrepancy was between two Windows machines.  On one, the sketch looked like:

and on mine it displayed the right, honest way:

After a bit of frantic emailing to our always helpful Sketchpad gurus, we discovered that there is a system setting which was different.  Navigating to the Display settings in the Control Panel, we could tell that the first machine had set the size of all items to more than Smaller  (on a Windows 7 machine this is called 125% or 120 ppi).

You can also see the difference if you go to the System tab of Advanced Preferences in Sketchpad, which are found in the Edit menu after the Shift key is held down.

The Screen Resolution of 37.795 px/cm is equivalent to 96 ppi and should remain at that value on Windows machines, even if Reset All Preferences is clicked.  If the value is something different, it can be edited on this screen and once Sketchpad is restarted, the sketch will look like what everyone else sees.

We have been using Sketchpad for a long time and had not run into this before.  It makes us worry about distributing sketches that might look awful at ppi settings that we have no control over.

Zooming Integers:Place Value

I had the opportunity to tweak one of the Dynamic Number project's sketches yesterday. Zooming Integers provides an interesting display using an exploding or zooming number line.  In Ontario, we use spaces rather than commas to separate digit groups (see  Our Grade 6 curriculum includes millions and the sketch only goes up to 100 000.  I was able to copy the 100 000 page, change two parameters (with a little digging) and get a page that starts with a number line from 0 to 1 000 000.  Ontario benefits from having a provincial license for The Geometer's Sketchpad so that students can access this material.

You can access the tweaked sketch from here.

Wednesday, January 8, 2014

Using a StyleSheet in Actionscript 2 to display an iTunes img Correctly

There are times when a simple request turns into a flight down the rabbit hole. mathies and mathclips share an XML file with information about learning tools available to Ontario students.  A link to Sketchpad Explorer on the App store needed to be added.  On the mathies webpage, this was easily done with html like:

Sketchpad Explorer is available from the 
<a href=";uo=4" target="itunes_store">
<img src="" height="15px" width="61px" />
getting a result like:
where the image was unnecessarily copied from one created with to the local server.

In Flash, there were two issues:
  1. A phantom underline preceded the image as the result of a <u> tag surrounding the <a>...<img /> tags
  2. The topic list, a feature only of the mathclips tool tab,  appeared next to the image and not below it, despite <br /> tags.  This is due to Flash floating images.
The wrapping issue was solved using an idea from Panax and StyleSheets and the underline issue was solved by creating a blueNoUnderline class.

The StyleSheet is created in code as follows:
var myStyleSheet:TextField.StyleSheet = new TextField.StyleSheet();
myStyleSheet.setStyle("a", {color:'#0000FF', textDecoration:'underline'});
myStyleSheet.setStyle(".blueNoUnderline", {color:'#0000FF', textDecoration:'none'});
myStyleSheet.setStyle(".imageSpacer30", {fontSize:30});
The htmlText is massaged to wrap the <img /> tag inside a <p> tag (red text below).  The dummy paragraph suggested by Panax is added (green text below).  The blueNoUnderline class is added to the <a> tag to avoid a bit of underlined space (blue text below).
Sketchpad Explorer is available from the 
<a href='' target='itunes_store' class='blueNoUnderline'>
<img src='' width='61px' height='15px' />
<p class='imageSpacer30'></p>
<br />
<p><font size=\"10\">(Geometry, Measurement, Simulations)</font></p>
The necessity to precede the "blueNoUnderline" name with period in the setStyle was a late discovery as I did not see it any of the examples I looked at.  For a while, I was convinced that StyleSheets read from .css files were the only ones that worked.