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Shape, Space & Measures
CPD Course 04/05Nigel Davies
April 18, 2023 2
Shape & SpaceShape & SpaceActivities 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
April 18, 2023 3
Developing understandingDeveloping 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.
April 18, 2023 4
VocabularyVocabulary
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..
April 18, 2023 5
Everyday ⇨ Mathematical Everyday ⇨ Mathematical
Round
Fatter
Corner
Circular
Wider
Vertex
⇨
⇨
⇨
April 18, 2023 6
ProgressionProgression
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 …)
April 18, 2023 7
… continued… 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.
April 18, 2023 8
Identifying 2D shapesIdentifying 2D shapesThis shape is rising above the top edge of the board.
What might the shape be?
ATM
April 18, 2023 9
Identifying 3D shapesIdentifying 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.
April 18, 2023 10
3D ⇨ 2D3D ⇨ 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.
April 18, 2023 11
Key Stage 2Key Stage 2Work should include :
… handling & constructing shapes
… using a variety of construction materials
… exploring simple nets of solids
April 18, 2023 12
Some activitiesSome 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.
April 18, 2023 13
A visualisation activityA visualisation activity
Imagine a square-based pyramid, made out of plasticine, in the air in front of you …
April 18, 2023 14
Possible visualisationsPossible visualisations
April 18, 2023 15
Sorting quadrilateralsSorting quadrilateralsParallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium
April 18, 2023 16
Sorting quadrilateralsSorting quadrilateralsParallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium
April 18, 2023 17
Position, direction & movement
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.
April 18, 2023 18
ReflectionReflectionChildren 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.
April 18, 2023 19
Mathematical Mirror LinesMathematical Mirror Lines
Older children will need to know that a ‘mathematical mirror’ is double-sided, reflecting both ways.
April 18, 2023 20
RotationRotationChildren 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.
April 18, 2023 21
Describing rotationDescribing 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
April 18, 2023 22
TranslationTranslationSliding 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
April 18, 2023 23
Combining transformations
Combining transformations
In Key Stage 2, children will learn to recognise simple combinations of the various types of transformation.
Measures
April 18, 2023 25
MeasuresMeasures
Children need both the practical experiences of estimating, comparing & measuring and the knowledge & skills to
understand & use instruments calibrated in various standard measures.
April 18, 2023 26
Striking a balanceStriking a balanceChildren 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.
April 18, 2023 27
ProgressionProgressionDeveloping 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.
April 18, 2023 28
Direct comparisonDirect comparisonMeasure 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.
April 18, 2023 29
Comparing & orderingComparing & orderingTask 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?
April 18, 2023 30
Comparing & orderingComparing & orderingTask 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.
April 18, 2023 31
Measuring using unitsMeasuring using unitsUsing 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.
•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.
April 18, 2023 32
Standard unitsStandard unitsList 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?
April 18, 2023 33
Measuring instrumentsMeasuring instrumentssmall 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
April 18, 2023 34
Direct or Indirect?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. AS 4.9 – 4.12
April 18, 2023 35
Possible resourcesPossible resources
Teaching Measures
April 18, 2023 36
Resources (contd.)Resources (contd.)
Measuring Cylinder
April 18, 2023 37
Resources (contd.)Resources (contd.)
Sorting 2D shapes
April 18, 2023 38
Resources (contd.)Resources (contd.)
2go
April 18, 2023 39
MSW LogoMSW Logo
April 18, 2023 40
“Primary Games” Volume 2“Primary Games” Volume 2
April 18, 2023 41
Shape GameShape Game
April 18, 2023 42
Maths Pack 3Maths Pack 3