q38 transformations notes - cloud object storage | store … · 2015-07-15 · 3 $...
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Teaching notes Key question / task
Describe the single transformation that maps triangle A onto each of the triangles B to J in turn.
Resources: • Question sheet, including tables; • Tracing paper if needed.
Reasoning: questions to discuss and explore • What is the least information needed to define each type of
transformation (translation, reflection, rotation, enlargement)? • What type of transformation leaves a shape unchanged? (Identity) • What type of enlargement leaves a shape unchanged? • Is it possible to define a reflection that leaves a shape unchanged? • In what way does the description of the original transformation
change for the inverse of translation, reflection, rotation or enlargement?
Consolidation • Discuss the difference between translation, reflection, rotation and
enlargement by comparing the image with the original shape; • Find the equations of horizontal and vertical lines, e.g. y = 3, x = -‐4; • Recognise lines with the formula y = x or y = -‐x.
Possible extensions • Discuss the effects of an enlargement with a negative scale factor; • Discuss the possibility of combining 2 (or more) transformations
to create the same effect as one single transformation, e.g. reflection in the line y = x then rotation through 180° around (0, 0) corresponds to a single reflection in the line y = -‐x.
Stimulus question 38 Transformations
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Commentary / notes: Here we have a choice of 2 activities:
• Describing the 9 transformations in full; • Describing the 9 transformations and also describing the inverse transformation fully for each.
Learners should be very familiar with implementing transformations (given the original shape and a description of the transformation), but they often lack confidence in defining transformations from one shape to another (given the original shape and its image). Encourage learners to use appropriate vocabulary. Key vocabulary: (0, 0) is the origin; a transformation maps a shape onto another; the new shape is called the image. Discuss which information is necessary in order to define a translation, reflection, rotation or enlargement, i.e.
• For a translation, use vector notation to indicate the horizontal and vertical distances moved; • For a reflection, the mirror line must be shown (be this a straight line equation or one of the axes); • For a rotation, give (the co-‐ordinates of) the centre of rotation, angle and direction (clockwise or anticlockwise) – note that there
is no need to give the direction for a rotation through 180° (or 0° or 360°), • For an enlargement, give the scale factor and the centre of enlargement (unless the position of the image is unimportant, in which
case the scale factor will be sufficient). Often, more than one correct answer will be possible, e.g. a clockwise rotation through 90° is the same as an anticlockwise rotation through 270°.
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GCSE Subject Content: Note that underlined type indicates Intermediate level and bold type indicates Higher level
Foundation Intermediate Higher Transformations, including:
• Reflection • Rotation through 90°, 180°, 270°. Clockwise and anticlockwise rotations; centre of rotation
• Enlargements with positive, fractional and negative scale factors • Translation; description of translations using column vectors
Learner Outcomes and Assessment (to aid comment-‐only marking) Reasoning strand – Learners are able to:
Assessment guidance – Can learners:
• Select appropriate mathematics and techniques to use; • Explain results and procedures precisely using
appropriate mathematical language; • Note what further information is needed and choose
which information is most appropriate.
• Recognise a translation? • Describe a translation accurately? • Recognise a reflection? • Describe a reflection accurately? • Recognise a rotation? • Describe a rotation accurately? • Recognise an enlargement? • Describe an enlargement accurately
Number strand – Learners are able to:
• Describe translation and use vectors; • Describe reflection in horizontal and vertical lines; • Describe rotations and discover the centre of rotation; • Discover the centre of an enlargement; describe an
enlargement.