Transcript Document

Shape, Space & Measures
CPD Course 04/05
Nigel Davies
Shape & Space
Activities 1, 2, 3 & 4 :
Sit back to back with your partner.
Look at the picture.
Don’t let your partner see the picture
Tell your partner how to :
build the model/make the picture using tiles/draw the
picture
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Developing understanding
… through practical exploration of shapes, positions,
directions & movement.
… through use of everyday language to identify & describe
shapes & their properties, & to describe positions, directions
& movement.
… through increasingly precise use of mathematical
language.
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Vocabulary
Young children might say “bigger” when they mean taller,
wider, thicker or heavier.
When they talk about a ‘round’ shape, do they mean a circle
or a sphere?
Building up correct vocabulary is vital..
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Everyday ⇨ Mathematical
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Round
⇨
Circular
Fatter
⇨
Wider
Corner
⇨
Vertex
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Progression
Reception :
Use language such as circle or bigger to describe the shape &
size of solids & flat shapes.
Use everyday words to describe position.
Year 1 :
Use everyday language to describe features of familiar 3D &
2D shapes (the shapes of flat faces, the number of corners or
sides …)
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… continued
Year 2 :
Use the mathematical names for common 3D & 2D shapes &
describe some of their features.
Use mathematical vocabulary to describe position, direction
& movement.
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Identifying 2D shapes
This shape is rising above the top edge of the board.
What might the shape be?
ATM
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Identifying 3D shapes
Collect a range of 3D shapes & put them in a bag.
Without looking, the pupil feels the objects individually &
considers which of their properties they will use to sort the
objects.
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3D ⇨ 2D
Help pupils to interpret 2D
representations of 3D objects
by making sense of
photographs & diagrams.
For example, use
construction kits to
build models shown in
drawings or photos.
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Key Stage 2
Work should include :
… handling & constructing shapes
… using a variety of construction materials
… exploring simple nets of solids
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Some activities
Include shape work in starters
… revise relevant vocabulary & properties of shapes.
Estimate & check angle sizes.
Predict the results of paper-folding & cutting.
Do ‘visualisation’ activities.
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A visualisation activity
Imagine a square-based pyramid, made out of plasticine,
in the air in front of you …
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Possible visualisations
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Sorting quadrilaterals
Parallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium
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Sorting quadrilaterals
Parallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium
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Position, direction & movement
By Year 2, children are expected to be able to use
mathematical vocabulary to describe position, direction &
movement.
To do this, they need practical opportunities to explore
reflection, rotation & translation.
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Reflection
Children need to understand that when an object is reflected
in a flat mirror, its reflection is …
… the same size & shape as the original shape (congruent)
… ‘back to front’
… the same distance ‘behind’ the mirror as the original shape
is in front.
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Mathematical Mirror Lines
Older children will need to know that a ‘mathematical
mirror’ is double-sided, reflecting both ways.
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Rotation
Children need to understand that when an object is rotated …
… its shape & size remain the same
… only its position changes
… the shape rotates around a centre of rotation – this is the
only point that does not change position.
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Describing rotation
Children need to state the centre of rotation, the angle of
rotation & whether the rotation is clockwise or anticlockwise.
90o
About this point
Anticlockwise
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Translation
Sliding a shape along a straight line, with every point moving
the same distance in a parallel direction.
… the image is congruent to the original
… the orientation remains the same
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Combining transformations
In Key Stage 2, children will learn to recognise simple
combinations of the various types of transformation.
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Measures
Measures
Children need both the practical experiences of estimating,
comparing & measuring and the knowledge & skills to
understand & use instruments calibrated in various standard
measures.
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Striking a balance
Children who can hold a ruler or tape measure, but who have
no idea how long a metre is or what a metre is used for are
unlikely to be able to measure confidently.
Similarly, children who have plenty of practical experience in
laying metre sticks end to end along a hall but who have
never converted metres to centimetres will be disadvantaged
in many contexts.
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Progression
Developing concepts
Comparing 2 objects directly, side by side, no measuring or
counting.
Comparing more than 2 objects, ordering 3 or more objects.
Using lots of the same uniform unit, progressing to using one
unit repeatedly.
Using standard units.
Using measuring instruments calibrated in standard units.
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Direct comparison
Measure
Activity
Potential problems
Length
Holding a paintbrush & pencil
alongside each other to see
which is longer.
Not lining up the objects from the
same baseline.
Looking at a characteristic other
than length.
Time
Using 2 ‘wind-up’ toys & seeing
which runs for longer.
Focusing on factors other than
time.
Weight
Comparing weight of one object
with another using a balance.
Focusing on size, not weight.
Capacity
Tipping water from one mug into
another.
Not realising that when the 2nd
mug fills to the brim & runs over
that it holds less than the 1st
mug.
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Comparing & ordering
Task 1 :
You have 5 parcels & you want to put them in order of weight
You have only one balance. What is the best way to do it?
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Comparing & ordering
Task 2 :
You have 5 batteries A, B, C, D & E. They all last for different times.
Which of the following statements must be false if all the others are true?
D lasts longer than C & less long than B
All the batteries last longer than A
B lasts longer than E
C lasts longer than B & D
C lasts less long than E
E lasts longer than exactly two of the batteries.
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Measuring using units
Using lots of the chosen unit to
establish that measuring requires
counting all the units.
•Measure own height using play people.
•Pour from
a full jug of water into a
number of identical yogurt pots.
Using one uniform or standard unit to
establish that you do not need the
actual number of physical units.
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•Measure the length of
a table using
one 10cm rod again & again.
•Measure how much a doll’s teacup
holds using one 5ml spoon.
•Use a sand timer repeatedly to time
how long it takes to change for P.E.
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Standard units
List the standard units you would use to measure the
following. Which ones would you introduce in KS1?
Length
Capacity
Weight
Time
Temperature
How can we make these units concrete or visible?
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Measuring instruments
small ruler
metre stick
trundle wheel
callipers
tape measure
kitchen scales
hanging spring balance
bathroom scales
lever balance and weights
litre jug
measuring jug calibrated in 100 ml divisions
5 ml medicine spoon
stop watch
3 minute/1 minute sand timers
digital clock
analogue clock
metronome
pendulum
sundial
thermometer
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Direct or Indirect?
Direct comparison to compare objects :
A. Comparing two things.
B. Ordering more than two things.
Indirect comparison using units :
C. Using a uniform non-standard unit that can be handled.
D. Using a standard unit that can be handled.
E. Using a measuring instrument.
F. Making & calibrating own measuring device.
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AS 4.9 – 4.12
Possible resources
Teaching Measures
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Resources (contd.)
Measuring
Cylinder
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Resources (contd.)
Sorting 2D
shapes
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Resources (contd.)
2go
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MSW Logo
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“Primary Games” Volume 2
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Shape Game
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Maths Pack 3
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