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2-D 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 set up in any way for working on. This is done by entering the minimum and maximum value for the x and y axes, and the scale on the Grid Settings panel. 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 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.

triout

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

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

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	These options allow the user to save a file out so that they can work on it later.
Close	This closes the open file
Notes	This allows you to write notes about the activity you are undertaking, which can then be saved as part of Save process.
Print	This allows you to print a screenshot of the current screen or if you are in the notes area it print off the notes.

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