Engage, explore and extend mathematics using the Australian Curriculum content and the four proficiencies

Gabrielle (Gay) West gabrielle.west@nt.gov.au p 08 8944 9246

2013 MTANTBringing Geometry Alive!

Bringing Maths Alive! – 10 March

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The strands, sub-strands, content descriptions and elaborations describe ‘what’ is to be taught

The four proficiencies describe ‘how’ it should be taught

Achievement Standards describe and the work samples show the core skills and understandings

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The Australian Curriculum: Mathematics

Bringing Maths Alive! – 10 March (see Australian Curriculum folder)

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Geometry

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Let’s fly with 2D Shapes

Bringing Maths Alive! – Geometry 10 March

Folding Shapes

A4 coloured paper can be folded to make many 2 D shapes with no measuring or cutting Follow the diagrams See if you can make the shapes Try these folds with A3 and A5 paper and all the A series paper [Note A series paper was invented in 1922 in

Germany.]

Start with an A series sheet

This is called a square fold.What is this shape?

One more fold. Let’s turn this around

Look familiar?

Can you name this shape?

What can you tell me about this special 2D shape (quadrilateral)?

Turn it around and look at the sides and angles . . . What about lines of symmetry? Tell me about the diagonals. Do they intersect? Do they bisect?

Describe this. Will it tessellate? What shapes can you make with 1, 2, 3, or more of these kites? What are the functions of this shape, in real life?

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Angles wheels Let’s estimate, deduce and check angle size

Bringing Maths Alive! – Geometry 10 March

Straws can be used to measure angles

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Angles

Hunting for shapes using a circle and elastic

Proving, visualising and ‘seeing’ the angle properties of a circle

Angle estimation and bearings

Angles

0–360 0

Bringing Maths Alive! – Geometry 10 March

Let’s describe and write about our shapes.

Make creative designsDescribe and write about our

shapes.

Let’s try another shape

Square fold again.

Fold it up along the edge.

What about this shape?

Can you name this shape?

What can you tell me about this shape? Turn it around. Look at the sides and angles . . . What about lines of symmetry? Will it tessellate? What shapes can you make with 1, 2, 3, or more

of these shapes? Compare it to the kite – how are they the same,

how are they different? Where do you see this shape in the

environment?

Let’s try a new fold

A hot dog fold – right down the middle

Fold the left bottom corner up to the centre

Now the top left corner edge comes down.

Check this out!

What is special about this shape?

What can you tell me about this shape? Look at the sides and angles . . . What about lines of symmetry? Will it tessellate? Why is it called regular? What shapes can you make with 1, 2, 3, or more of

these shapes? Where do you see this regular shape?

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The 4 Proficiencies: Make the shapes, describe, compare,

categorise and justify Fluency:

Name this shape?

How many sides?

How many angles?

Understanding:

Tell me everything you can about this shape .

Describe all the features of a square.

Problem Solving:

Make, manipulate, fold, photograph, draw, label, investigate to be able to describe and explain.

Reasoning:

Compare 2 shapes:

How are they the same?

How are they different?

Group these shapes into 2 or 3 categories and justify why?

Bringing Maths Alive! – Geometry 10 March

Third shape coming up!

Remember the name of this fold?

Fold it up to the line.

Tuck in the corner.

Turn it around.

What do you see?

What can you tell me about this special triangle? Look at the sides and angles . . . What about lines of symmetry? Fold it in half and investigate the new shape. Will it tessellate? What shapes can you make with 1, 2, 3, or more of

these shapes? Compare this triangle to the previous triangle. How

are they the same? How are they different?

Fourth shape

Here we go again!

You’re getting good at this

Fold the bottom up and unfold.

You’ve seen this shape before.

This is a very common shape.

What can you tell me about this shape? Look at the sides and angles . . . Why is it a regular shape? What about lines of symmetry? Draw in the diagonals. Why are they special? Can you fold it in interesting ways? What shapes can you make with 1, 2, 3, or more of

these shapes? Functions of this shape? Where do you see this shapes in everyday life?

Landscape view

Fold in half, fold in half again.

Use the centre line and first fold line

Do the same to the top

Fold the right corner edge up

Fold the left top corner edge down

This is an interesting shape

What is special about this shape?

What does this shape remind you of? What can you tell me about this shape? Look at the sides and opposite angles . . . Explain what ‘parallel’ means. What about lines of symmetry? These diagonals will be interesting, tell me about

them. Will it tessellate? What shapes can you make with 1, 2, 3, or more of

these shapes? Have you seen this in the world around you?

Are you ready?

Hamburger fold, then in half again

Left corner up to the crease.

Right corner up to the crease.

Top left corner down along the edge.

Top right corner down to the edge.

Turn this around…

This shape looks familiar . . .

What can you tell me about this shape? Look at the sides and angles . . . What about lines of symmetry? Will it tessellate? What shapes can you make with 1, 2, 3, or

more of these shapes? Compare this shape to a square and a

parallelogram and a square? How is it the same? How is it different?

Let’s start off the same again.

Hamburger fold, then in half again

Left and right bottom corners up to the crease.

Top left corner down along the edge..

Top right corner down along the edge.

Fold in the side tip to the centre.

Fold in the other side tip to the centre.

Turn it over and what do you have?

That was tricky . . .

What can you tell me about this shape? Look at the sides and angles . . . What about lines of symmetry? How many diagonals does it have? Is this related to the number of sides and angles? Will it tessellate? What shapes can you make with 1, 2, 3, or more

of these shapes? Have you ever seen this shape before?

Here we go again!

Now for something completely different!

Bottom left corner up to top right corner.

Fold in half.

That was easy . . .

What can you tell me about this shape? How is this shape different to the others we have

made? Look at the sides and angles . . . What about lines of symmetry? Will it tessellate with other shapes? What shapes can you make with 1, 2, 3, or more

of these shapes?

Fold the right side in to line up with centre fold.

Same with the other side.

Turn it around and what do we have?

That was easy . . .

What can you tell me about this shape? Look at the sides and angles . . . What about lines of symmetry? Will it tessellate with other shapes? What shapes can you make with 1, 2, 3, or more

of these shapes?

Look at all the shapes you can make!

How many more shapes can make?

Try folding all the shapes in half joining some different shapes overlapping the shapes using larger paper A3 using smaller paper A5, A6 etc (Record your investigations and have fun!)

Reference: Geopaperpolygons by Cal Irons et al (Origo Publishers)

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Deductive geometry and design Open questions:

My shape has 6 sides. What could it look like?

How can we find out about the angles?

Open question:

Tell me everything you can about this shape / design?

Bringing Maths Alive! – Geometry 10 March

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Compass points, bearings, grids and co-ordinates

Bringing Maths Alive! –Geometry10 March

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Construct, investigate and explore ominoes

Use tiles, blocks, card, grid tea towels and grid paper

Dominoes, trominoes, tetrominoes, pentominoes and nets of a cube:

- manipulate: flip, slide and turn or

- transform: reflect, translate, and rotate

Symmetry, perimeter, area and tessellation understandings

Visualisation of shapes and

objects

Bringing Maths Alive! – Geometry 10 March

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Construct, investigate and explore 3D objects

Construct 3D objects

Use toothpicks, plasticine, play dough, lollies

Similar open questions as with 2D shapes.

Look at cross-sections – visualise then check. [Plasticine and fishing line and real objects]

Measure and draw real 3D objects – think about the best scale to use.

Bringing Maths Alive! – Geometry 10 March

Looking forward to hearing about some ideas you tried in your classroom

Thanks for participating!

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Last little tuck to make it neat.