Shape, Space & Measures

CPD Course 04/05Nigel Davies

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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

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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.

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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..

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Everyday ⇨ Mathematical Everyday ⇨ Mathematical

Round

Fatter

Corner

Circular

Wider

Vertex

⇨

⇨

⇨

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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 …)

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… 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.

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Identifying 2D shapesIdentifying 2D shapesThis shape is rising above the top edge of the board.

What might the shape be?

ATM

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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.

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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.

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Key Stage 2Key Stage 2Work should include :

… handling & constructing shapes

… using a variety of construction materials

… exploring simple nets of solids

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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.

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A visualisation activityA visualisation activity

Imagine a square-based pyramid, made out of plasticine, in the air in front of you …

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Possible visualisationsPossible visualisations

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Sorting quadrilateralsSorting quadrilateralsParallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium

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Sorting quadrilateralsSorting quadrilateralsParallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium

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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.

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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.

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Mathematical Mirror LinesMathematical Mirror Lines

Older children will need to know that a ‘mathematical mirror’ is double-sided, reflecting both ways.

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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.

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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

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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

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Combining transformations

Combining transformations

In Key Stage 2, children will learn to recognise simple combinations of the various types of transformation.

Measures

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MeasuresMeasures

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 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.

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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.

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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.

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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?

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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.

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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.

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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?

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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

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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

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Possible resourcesPossible resources

Teaching Measures

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Resources (contd.)Resources (contd.)

Measuring Cylinder

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Resources (contd.)Resources (contd.)

Sorting 2D shapes

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Resources (contd.)Resources (contd.)

2go

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MSW LogoMSW Logo

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“Primary Games” Volume 2“Primary Games” Volume 2

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Shape GameShape Game

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Maths Pack 3Maths Pack 3