Transcript Geometry_GWest 2013

2013 MTANT
Bringing Geometry Alive!
Engage, explore and extend mathematics using the Australian
Curriculum content and the four proficiencies
 Gabrielle (Gay) West
[email protected]
MTANT 2013
Bringing Maths Alive! – 10 March
p 08 8944 9246
The Australian Curriculum: Mathematics
 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
MTANT 2013
Bringing Maths Alive! – 10 March (see Australian Curriculum folder)
Geometry
MTANT 2013
Let’s fly with 2D Shapes
MTANT 2013
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?
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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?
Angles wheels
Straws can be used
to measure angles
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
Let’s estimate, deduce
and check angle size
Angles
Hunting for shapes
using a circle and
elastic
Angles
0–360 0
Proving, visualising
and ‘seeing’ the
angle properties of a
circle
Angle estimation and
bearings
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
Let’s describe and write about our shapes.
Make creative designs
Describe 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?
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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?
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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?
The 4 Proficiencies: Make the shapes,
describe, compare, categorise and justify
Fluency:
Name this shape?
How many sides?
How many angles?
Problem Solving:
Make, manipulate, fold,
photograph, draw, label,
investigate to be able to
describe and explain.
Reasoning:
Understanding:
Tell me everything you can
about this shape .
Describe all the features of
a square.
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
Compare 2 shapes:
How are they the same?
How are they different?
Group these shapes into 2 or 3
categories and justify why?
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?
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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.
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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?
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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 . . .
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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 . . .
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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 . . .
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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)
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?
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
Compass points, bearings, grids and co-ordinates
MTANT 2013
Bringing Maths Alive! –Geometry10 March
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
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
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.
MTANT 2013
Bringing Maths Alive! – Geometry 10 March
Looking forward to hearing about some ideas
you tried in your classroom
Thanks for
participating!
MTANT 2013
Last little tuck to make it neat.