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The Create Tab
The Auto Tab
Examples of Using the Tool
Features of the Tool
Keyboard Shortcuts
PDF Supports

In the Set Tool sets of objects can be generated randomly or designed by the user. Sort and classify objects. Create patterns. Represent, compose and decompose whole numbers, tenths, and fractions. Explore experimental probability.

Take a screenshot of your work to share with your teacher or add to a portfolio.
You can insert pictures into the Tool using theimportPicture.PNGbutton.

The Set Tool allows for up to four attributes to be considered:
  1. Shape: Star, Circle, and Gingerbread
  2. Size: Small, Medium and Large
  3. Colour: Green, Yellow, Blue and Pink
  4. Face: Shown and Hidden

The Create Tab - User Generated Sets

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Nine cloner shapes representing all the possible shapes and sizes are presented in the first section of the panel.
Drag any of them from the panel to the workspace.

Use the multiplier to quickly create 1, 2, 5 or 10 copies of a shape.
The nine shapes have faces shown and are randomly coloured.

Click on any colour swatch to change all shapes in the tab to that colour. Click on the random colour wheel button (the one with the question mark) to make the colour of any dropped shape random.

Make the shapes either have a face or not have a face or have a random face.

Drag a ten frame into the workspace from the third section of the panel.
Use the radio buttons to choose between solid (ten frames) and dashed (frame of tenths) division lines.

You can also change an individual cloner by clicking on it and selecting the desired colour and face.
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If you use dashed internal divisions in a frame, it is called a frame of tenths - the full frame representing a whole in that case.
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The Auto Tab - Randomly Generated Sets

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Click the left or right arrows to decrease or increase the number of objects on the workspace.
Enter a number directly in the text field to change the number of objects on the workspace.
Click the New button in the first section of the panel to create a random set using the allowed attributes from the second section.

Click on the shape icons to restrict which shapes will be used to create random new objects.

Click on the colour squares to restrict which colours will be used to create random new objects.

Click on the size circles to restrict which sizes will be used to create random new objects.

Click on the face squares to restrict whether new objects can have faces or not.

Notice that you can drag ten frames to the workspace from the auto tab as well.
Use the radio buttons to choose between solid (ten frames) and dashed (frame of tenths) division lines.


Examples Using The Set Tool

1. Students might be asked to create sets of a certain size, like 10. They can use the Scramble Position button, which we liken to kicking the desk leg, to work on Conservation of Quantity; 10 stays 10!
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2. Simple patterns can be created and extended.
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3. Operations can be modelled.
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The multiplier allows multiple shapes to be dragged onto the workspace in one action. Here, the multiplier was set to 10, and in two drags 20 gingerbreads are placed in the workspace. Next, the multiplier was set to 5, and five more were added. Two were selected and deleted, using the recycle bin, leaving 23. The annotation tool is used and the take-away meaning of subtraction illustrated. The three groups of 5 that are left are counted to get the difference. Notice how anchors of 5 and 10 help solve this problem.

4. Young students are often asked to sort sets by attribute. The auto tab allows for random sets to be created quickly. Here, 24 objects are created automatically and the student has sorted them by colour.
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This student’s sort is a pictograph on its head!
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The Count button can be used as a check, which is especially useful when the
student has created the set themselves.

5. Later, students might use a Venn Diagram to sort based on two attributes. The Venn Diagram is created using the oval and text box annotation tools accessed from the pencil icon.
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Here a student creates 20 random shapes and then classifies them by the two attributes: blue and star, dragging them to their proper position in the Venn Diagram. The ten frame is useful for organizing and counting the 14 objects that are neither blue nor stars. Students will get a feeling for variability as they compare their results to other students and realize that although the colours are equally likely to occur; they do not often occur equally. Here we would expect 6 or 7 stars (20 divided by 3 possible shapes) with each colour represented 1 or 2 times (4 colours evenly distributed among the 6 or 7 stars). Instead we get four stars, none of which are yellow or pink.

A grade 12 student could calculate some of the theoretical probabilities. For example, the probability that an object is placed outside the rings is 3423=12. This means that you would expect to have only 10 objects outside - which is consistent with the observation that both blues and stars are underrepresented in this sample (4 blues compared to 5 expected, 4 stars compared to 6.67 expected).

6. Feeling Blue
Students might be asked to explore how much the number of blue shapes differs from the expected. Even choosing a set as small as 12 objects is interesting. There are four colours, so each would be expected to show up 3 times. If students create random sets of 12 will they ever observe a set that is missing a colour? Will they ever get all twelve objects to be the same colour?

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Imagine the following investigation: a student opens up the Set Tool and then the auto tab. She types 12 for the number of objects and presses enter. Twelve random objects are displayed. She then presses the Auto Arrange button to line them up.

She makes note of the number of them that are blue and then selects all the objects by drawing a marquee rectangle around them.
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This makes the Copy button appear as well as the Configure Selected Shapes button. Pressing on the latter button opens a dialog that allows changes to the attributes of the selected objects.
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You can change the attribute to a specific value - like star, yellow, medium and faceless - or use the ? buttons to randomly set the attribute. The student clicks on the random Colour button repeatedly, continuing to make note of the number of blue objects in the set.
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She records the results using the annotation tool and considers questions like:
  1. Are each of the possible values equally likely? If not, which number of blue objects would you expect to occur most frequently?
  2. How does your tally chart compare to others in your class? Does it make sense to combine them into one big tally chart?
  3. Do you think it is equally likely to have 0 blue objects as it is to have 6?
  4. What percentage of sets have 3 or fewer blues?

7. Students could be asked to create and count all the object possibilities.

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To create the above, one of each of the nine cloners is dragged into the workspace maintaining the 3 by 3 array. This group is then selected and coloured green using the Configure Selected Shapes Button.
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It is then copied to create the yellow, blue and pink possibilities. Then the whole lot is copied, positioned and the smile wiped off their faces.

Students in later grades might calculate the total number of possibilities using 3 x 3 x 4 x 2. This construction allows students to see the 3 times 3 to start, then the multiplication by 4 as the colours are considered, and then the doubling when facedness is addressed. The eight copies of 9 elements form a 6 by 12 array which is decomposed into friendly numbers in order to determine the product. The annotation tools help to make the thinking visible.


Features of the Tool



Annotation Tool

Make notes or highlight various features of your representation. More details.

Insert Image Button

You can insert images into the tool. More details.



Step backward or forward through your actions with the tool.
This feature is not only useful for backtracking when a misstep is made, it enables a student to demonstrate their work from the start to the finish. They press Undo until they are at the start of their solution and then press Redo repeatedly, explaining each step.


Delete all your work and return the tool to its starting state.


Access a link to this wiki, a feedback form as well as copyright details and version number.


Change background colour.
Restore the tool to its default settings.


(in the work space)
Click to clear the entire work space.
Alternatively, drag items to the recycle bin to remove them.

Object Size

Increase / decrease object sizes.


Make a copy of the selected objects.

Configure Selected Shapes

Press this button to bring up a panel that will allow you to change the selected objects. You can choose specific colours, sizes and whether to show a face. It is also possible to randomize any attribute using the randomize buttons.

Auto Arrange

Line up all objects along the top of the workspace.

Scramble Position

Randomly distribute all objects within the workspace.

Object Count

Check to see how many objects are in the workspace.

Other Functionality


Multiple Select

Draw a marquee around an object, or group of objects to select it.

Click an object to add to or remove from selection.

Selected objects can be moved, copied or recycled as a group


Keyboard Shortcuts

On the desktop version of this tool, all of the standard Keyboard Shortcuts have been implemented as well as the special movement keyboard shortcuts.

PDF Supports

mathies Set Learning Tool Tip Sheet

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