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Scheme of work – Cambridge IGCSE® Mathematics (US) 0444
Unit 5: Transformations and vectors (Core)
Recommended prior knowledge
Unit 4 transformations, Unit 7 (7.1)
Context
This is the second unit of five geometry units. So long as Unit 4 and Unit 7 (7.1) have been taught this can be taught at any time. Unit 5.6 can also be used for
revision of Unit 4 transformations so a gap between the two units is desirable. Students who are following the extended syllabus will move through this faster but
need to have all these skills in place before working on the extended units, or applying them in other areas of mathematics.
Outline
Vector notation is introduced. All transformations are looked at in the Cartesian plane and the effect of the transformation on the objects by looking at the
coordinates of both the object and the image. Within the suggested teaching activities ideas are listed to identify and remediate misconceptions and to pull learning
through to the required standard. The learning resources give both teaching ideas, summaries of the skills and investigative problems to develop the problem solving
skills and a depth of understanding of the mathematics, through exploration and discussion.
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
5.1
Vector Notation:
directed line segment
uuur
AB ;
x
component form  
y 
General guidance
Define a vector.
http://nrich.maths.org/4890
CCSS:
N-VM1
Teaching activities
Set up two points on a horizontal line on a coordinate grid and ask students
how they would describe moving from one to the other and challenge them to
find a way of accounting for the left right and right left separately hinting at the
number line for guidance. Do the same for up and down movements. Then
two points on a diagonal. Refine the coding to vector notation.
Past Paper 13 June 2011 Q8
(syllabus 0580)
Set up a set of 10 cards with a vector on each. All cards are visible. Students
are given a start point but choose a finish point on a grid. Player 1 has to pick
a vector cards from the set that will translate the start point as close to the
finish as possible. (it doesn’t matter if they don’t select the best card). They
plot on the grid to prove they have achieved it. Meanwhile the other player
picks a card from the same set and sends the end point of the first plot as far
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Syllabus ref
5.6
CCSS:
G-CO2
G-CO3
G-CO4
G-CO5
G-SRT1
Learning objectives
Transformations on
the Cartesian plane:
Translation, reflection,
rotation, enlargement
(dilation)
Description of a
translation using
column vectors
Suggested teaching activities
away from the finish point as they can manage. Players alternate using one
card at a time. Each player plots in different colours. Once a card is used it is
set aside so both players can see it and of course check the other has plotted
correctly. Player one wins if they are at the finish point or closer to it after their
final plot, than the point player 2 has reached. Player 2 wins if it is the other
way around. (Player 2 has no choice about their final move so player 1 can
still win if cards are chosen strategically).
Finally ask all the class to work out the vector from the start point to the final
end point of the game. Class should discover they all have the same vector (a
check for the accuracy of plotting) and discuss why.
Notes and exemplars
Representing and describing transformations.
General guidance
Transformations can be made or described – standard short questions.
Ensure students realise which of the transformations produces a congruent
image and which produce an image that is only similar to the object.
Learning resources
http://nrich.maths.org/5457
www.counton.org/resources/ks3framewor
k/pdfs/transformations.pdf page 205
Past Paper 31 June 2011 Q7
(syllabus 0580)
Teaching activities
Students look at the effect on coordinates of all the transformations by
constructing sets of each and recording the object and image coordinates and
discussing patterns.
On page 205 of the framework document there is a grid of L shapes and an
activity that can be used for the transformations that produce congruent
outcomes.
This is an opportunity to revise understandings of transformations.
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