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Programme Of Study For Key Stage 3 Mathematics

These are the Transum resources related to the statement: "Pupils should be taught to identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids"

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
- Construct a congruent triangle Construction (with compass and straight edge) of a triangle congruent to a given triangle.
- Transformations Draw transformations online and have them instantly checked. Includes reflections, translations, rotations and enlargements.

Click on a topic below for suggested lesson starters, resources and activities from Transum.

- Enlargements When areas and volumes are enlarged the results are far from intuitive. Doubling the dimensions of a rectangle produces a similar shape with four times the volume! Doubling the dimensions of a cuboid produces a similar shape with eight times the volume! The activities provided are intended to give pupils experiences of dealing with enlargements so that they better understand the concept and are able to produce diagrams, make models and answer questions on this subject. Once positive scale factors have been mastered the notion of fractional and negative scale factors await discovery!
- Transformations A transformation in mathematics is an operation performed on a shape (or points) which changes the view of that shape (or points). This topic includes four transformations namely reflection, translation, rotations and enlargement. A reflection can best be described as the mirror image of a shape in a given line (which acts as the mirror). After reflection the shape remains the same size but the orientation is the mirror image of the original. The transformation known as a translation can be thought of as a movement or shift in position. The size and orientation of the shape remains the same but the position on the plane changes. A rotation can be described as turning. This transformation is defined by the angle of turning and the centre of rotation (the point which does not move during the turning). Finally enlargement is the term we use when a shape increases in size but maintains the same shape. The shape after enlargement is defines as being similar to the shape before enlargement. His use of the word similar has a precise mathematical meaning. All of the angles in the enlarged shape are the same as the angles in the original shape and the lengths of the sides are in the same proportion. An enlargement is defines by the scale factor of the enlargement and the centre of enlargement. We use the term enlargement even if the shape becomes smaller (a scale factor between minus one and one). A negative scale factor will produce an enlarged mirror image of the original shape.