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2D Shapes User Guide

This 2-D Shape Creation tool has been developed as an easy to use software environment in which teachers and learners can create, explore and transform simple two dimensional shapes on a coordinate grid.

The environment will support a range of thinking skills which underpin rich mathematical activities and will help students to:

Understand and use mathematical notation

for example labeling vertices of shapes so that we can describe angle

Develop a need for mathematical conventions

for example when a shape is rotated a positive angle will result in an anti-clockwise transformation.

Make and test conjectures

for example what happens to the area of a shape when it is enlarged

Develop a fascination with mathematics

for example how many different shapes might have an area of 12 square units

Use mathematics in context

for example positive and negative numbers

Explore independently the relationships within and between properties of shapes.

One of the distinct advantages that the software offers is the explicit connections that students can make across a range of topics. For example, linking coordinate work to the geometrical properties of 2-D shapes and then exploring different transformations of these shapes.

Creating and exploring 2-D shapes

When you launch the tool, the grid will take the default setting of -10 to 10 on both axes. The grid can be adjusted by selecting the Grid Settings panel and entering the minimum and maximum value for the x and y axes, and the scale.. You also choose the number of decimal places within which you will be working. (Note: The decimal place specified here will determine the level of accuracy for the data calculated for each shape in the Shape properties pane) At this stage you will want to consider the most appropriate numbers and whether you are working within the range of positive and/or negative numbers (or both) and whether you will be expecting decimal measurements for side lengths, areas and perimeters later on in the activity.

So, setting these values…
…would give this set of axes.
With a co-ordinate grid created, to draw a shape on the screen, you first need to choose the shape from the add shape menu. For example, if you select Triangle, you will see the following screen.
The three co-ordinate pairs define the position of the vertices of the triangle on the grid. The values shown above would give the following screen.

The coordinates need to be entered in a clockwise (or anti-clockwise order) to produce a closed shape. The values can be amended after the shape has been produced on the screen. If the coordinates of the vertices are entered in an anti-clockwise order, the interior angles of the shape are measured.

If you then select the triangle and access the shape properties panel, the data in the Shape Properties Pane will automatically fill, as can be seen in the diagram below. All of the measurements (angles, sides, areas, perimeters and lengths) can be hidden and revealed. The shape can be renamed by editing the Name text.

Each of the 2-D objects available to explore with the 2-D Shapes tool is defined as follows:

2-D Object	Defined by:	Example
Quadrilateral	The four coordinates of the quadrilateral’s vertices. A quadrilateral will have angle measurements, side lengths, an area and a perimeter.
Circle	The first pair of coordinates represent the centre of the circle, the second pair defines a point on the circumference of the circle. A circle will have a perimeter and an area.
Triangle	The three coordinates of the triangle’s vertices. A triangle will have angle measurements, side lengths, an area and a perimeter.
Line	The equation of the line can be labeled by changing its Name.
Arc	The coordinates of three points that lie on the arc. An arc will have a length.
Ray	The coordinates of the beginning of the ray, followed by the coordinates of any point the ray will pass through.
Segment	The coordinates of the two points that define the end of the segment. A segment will have a length.
Vector	A vector will have a magnitude (length).

Transforming shapes

The transformation features of the 2-D Shape Creation tool will allow any object to be transformed by a translation, rotation, reflection and enlargement.

Each of the transformations is defined as follows:

Transformation	Defined by:	Example
Translate
Rotate	A rotation is defined by a centre of rotation and a positive or negative angle of rotation.
Reflect	A line of reflection is defined by the pair of coordinates that it passes through.
Enlarge	An enlargement is defined by the coordinates of the centre of enlargement and the scale factor. Scale factors can be positive or negative integers or decimals. Up to three characters can be used.

File Menu

The file menu contains the options to save and open previous work and also to import shapes from previous work.

File Menu Option	Description
Open	This option allows the user to select work that they have already saved out and continue to work on it.
Save/Save As	These options allows the user to save a file out so that they can work on it later. Save will update the opened saved file and Save as will save to a brand new file.
Recently Opened	This displays a list of recently opened saved files.
Import Shape	This allows the user to import shapes from a saved file without altering the current state of the workspace (i.e., grid settings will remain unchanged and any 2D shapes that have been created will remain). A workspace can be occupied by either a new exercise or by an open file.
Delete	This deletes the current saved file.
Close	This closes the open file