Geometry and Measurement: Transformation
Level 1
AO1: Communicate and record the results of translations, refl ections, and rotations on plane shapes. This means students will physically carry out translations, reflections, and rotations on shapes and discuss what patterns they see. Translations are shifts of a shape along a line, for example repeating a potato print across the top border of a page. Reflections are images of a shape as though it is reflected in a mirror. Rotations are turns, so when an object is turned about a point, either inside or outside of itself, the image is a rotation of the original shape. At level one rotations can be described as fractions of a full turn, for example half and quarter turns.
Level 2
AO1: Predict and communicate the results of translations, reflections, and
rotations on plane shapes.
This means students will experience physically moving shapes so that they can predict the
location and orientation of the shape after it has been translated, reflected or rotated, e.g.
draw/show what this shape will look like if I give it a half turn about its centre.
Students should be able to identify how many mirror lines a shape has that maps it onto itself,
e.g. a square has four mirror lines. Translations are images of a shape as it is shifted along a
line, e.g. 
... Reflections are
images of a shape as it is reflected in a mirror (sometimes called a flip), e.g. 
Note that the line may outside the object or within it. Rotations are images of a shape as it is turned about a point outside or within it,
e.g. 
.
Level 3
AO1: Describe the transformations (refl ection, rotation, translation, or enlargement) that have mapped one object onto another. This means students will explore describe transformations. “Transformation” is a generic term used to describe actions on shapes that result in some form of pattern, usually symmetric. A reflection is the image of a shape as seen through a mirror line either inside or outside the shape, sometimes called a “flip”. A rotation is the image of the shape turned about a point either inside or outside the shape. A translation is the image of a shift of the shape along a line, and an enlargement is the image of the shape made bigger or smaller by some scale factor. At Level Three students should be able to compare the image of a shape with the original and describe the transformation. This can include a sequence of two transformations. For example:
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A' is the image of A |
B' is the image of B |
C' is the image of C |
Level 4
AO1: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
This means students will know invariant properties are those features of a figure that do not change as it is reflected, rotated, translated or enlarged.
Under rotation lengths, areas, angles do not change but orientation does.
Under reflection lengths, areas and angles do not change but orientation does.
Under translation lengths, areas, angles and orientation do not change.
Under enlargement angles and orientation do not change but lengths and areas do.
At Level Four students should be able to use the above invariant properties to create symmetrical patterns such as tessellations, logos and friezes, and to create enlarged copies of graphics.
Level 5
AO1: Define and use transformations and describe the invariant properties of figures and objects under these transformations. Further detail on this Achievement Objective will be added shortly.
AO2: Apply trigonometric ratios and Pythagoras’ theorem in two dimensions. Further detail on this Achievement Objective will be added shortly.
Level 6
AO1: Compare and apply single and multiple transformations.
This means students will be able to draw, with the assistance of technology where available, the results of transformations acting successively on a figure, for example, frieze patterns. The transformations involved are reflection, rotation, translation and enlargement. They should recognise when combinations of transformations give the same or a different result, for example, reflection then translation has the same result as translation then reflection (glide reflections), and acknowledge this in describing which transformations result in a figure being mapped onto a given image. Students should also connect the result of translations and reflections on lines and parabolas with the similarities and differences in their equations, for example, the image of y = x2 + 3 reflected in the x-axis is y = - (x2 + 3) or y = - x2- 3.
AO2: Analyse symmetrical patterns by the transformations used to create them.
This means students will apply their knowledge of variant and invariant properties under these translations in explaining how they determined which translations were involved in a given mapping. This includes attendance to equality of lengths and angles, and order (direction). For example, students should describe how the following frieze pattern may have been created from the arrow element... (possibilities include)
