KS2: MATHS GEOMETRY
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The important thing
about mathematics
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is that it involves
abstraction and symbolism.
0003 10:00:23:22 10:00:27:23
These are the ingredients of
higher-order mental processes
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which is what we want
our children to develop.
0005 10:00:31:03 10:00:34:11
Every topic we teach
should aim to develop
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higher-order mental processes.
0007 10:00:37:07 10:00:41:23
Mathematics, above all other
subjects, makes this possible.
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We're at ScottsPrimary School
in snowy Hornchurch, Essex,
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to see maths teacher Gary Clapperton
teach a lesson on geometry
0010 10:00:51:19 10:00:53:04
to a Year 6 class.
0011 10:00:53:18 10:00:57:20
Scotts Primary is
an open-plan school of 210 pupils,
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10 per cent of whom
come from an ethnic background.
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My name's Gary Clapperton. I've been
teaching for about 36 years,
0014 10:01:08:06 10:01:11:03
but here at Scotts
I've been about 10 years.
0015 10:01:11:03 10:01:14:10
I went straight from school
to college, then into teaching,
0016 10:01:14:10 10:01:18:02
but I've done lots of other things
in my spare time.
0017 10:01:18:02 10:01:21:21
For about six years
I did some comedy writing
0018 10:01:21:21 10:01:25:05
for people like Russ Abbott,
Little and Large, "Spitting Image",
0019 10:01:25:05 10:01:27:01
that sort of thing.
0020 10:01:27:01 10:01:31:05
Richard Dunne first came to Scotts
about three years ago
0021 10:01:31:05 10:01:35:24
and explained his ideas to us,
to make maths make sense,
0022 10:01:35:24 10:01:38:08
and we've been using
his ideas since then.
0023 10:01:38:08 10:01:41:16
I think Richard's basic idea
is to make maths make sense.
0024 10:01:41:16 10:01:43:18
That's exactly what he does.
0025 10:01:43:18 10:01:46:09
Now we have ways of
teaching children maths
0026 10:01:46:09 10:01:51:00
that make sense to them,
therefore they find it much easier.
0027 10:01:51:24 10:01:55:16
In today's lesson we're looking at
explicit and implicit shapes,
0028 10:01:55:16 10:01:57:19
which is difficult to say
in the first place,
0029 10:01:57:19 10:01:59:15
even more difficult to teach.
0030 10:01:59:15 10:02:03:07
Then the children will be
gradually drawing those shapes.
0031 10:02:03:07 10:02:07:24
Because they're Year 6, the lesson
will involve some revision,
0032 10:02:07:24 10:02:11:21
but one thing I think they might
have trouble with is ratio.
0033 10:02:11:21 10:02:15:01
I'm hoping that my explanation
as we go through the lesson
0034 10:02:15:01 10:02:17:08
of how to draw the shapes
using ratio
0035 10:02:17:08 10:02:19:06
will help them.
0036 10:02:19:06 10:02:22:00
(narrator) Gary's involved
the children in taking photos
0037 10:02:22:00 10:02:23:19
of buildings around them.
0038 10:02:23:19 10:02:26:17
They'll be using these photos
in the lesson today.
0039 10:02:26:17 10:02:31:00
He's also made use of these images
on the interactive whiteboard.
0040 10:02:35:17 10:02:38:10
What do we call
the corners of shapes?
0041 10:02:39:14 10:02:41:12
- Jack.
- Vertices.
0042 10:02:41:12 10:02:45:04
Good. Good boy. Vertices.
But that's the plural.
0043 10:02:45:04 10:02:47:18
If we've got just one corner
in maths of a shape,
0044 10:02:47:18 10:02:49:07
what do we call it?
0045 10:02:49:07 10:02:51:07
- Stanislav.
- Vertex.
0046 10:02:51:07 10:02:52:17
Very good.
0047 10:02:52:17 10:02:55:20
So we've got the shape
with four vertices.
0048 10:02:55:20 10:02:57:24
But I'm going to label
these vertices.
0049 10:02:57:24 10:03:02:11
Remember, we must always label
with capital letters.
0050 10:03:02:11 10:03:06:19
It doesn't matter where we start. It
could be anywhere in the alphabet.
0051 10:03:06:19 10:03:09:06
In this case I'll label
the first one A,
0052 10:03:09:06 10:03:12:02
so it's A, B, C, D.
0053 10:03:12:02 10:03:16:21
So, this shape - ABCD -
what can you tell me about it?
0054 10:03:16:21 10:03:18:13
- Philip.
- A rectangle.
0055 10:03:18:13 10:03:22:21
Good. A rectangle.
What I want you to do on your photo
0056 10:03:22:21 10:03:27:14
is to draw the polygon
I've drawn on the board
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and label as I have labelled it,
0058 10:03:29:19 10:03:34:20
but then find some other
explicit polygons on the photo,
0059 10:03:34:20 10:03:37:07
draw them, and label them.
0060 10:03:37:07 10:03:41:09
I'll give you a few moments
to do that. Off you go.
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(narrator) By using
the children's photos,
0062 10:03:43:19 10:03:46:22
Gary hopes to raise their awareness
of the shapes around them
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and give the class a sense
of ownership of the lesson.
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Today Gary is supported by
teaching assistant Cathy Briggs,
0065 10:04:01:08 10:04:05:05
who'll be working one-to-one and
in small groups within the class.
0066 10:04:07:05 10:04:10:22
OK, Year 6. Stop there. Well done.
Put everything down.
0067 10:04:10:22 10:04:14:24
We want to see what shapes
you've found on your photo.
0068 10:04:14:24 10:04:18:10
Who would like to show us
on the whiteboard an explicit shape?
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Michael, show us your shape.
0070 10:04:31:07 10:04:33:19
Well done, Michael. Thank you.
0071 10:04:33:19 10:04:37:06
What can you tell us about
the shape Michael found?
0072 10:04:37:06 10:04:40:00
It's an explicit shape
because you can see it clearly.
0073 10:04:40:00 10:04:42:13
What can you tell us
about it, though?
0074 10:04:42:13 10:04:44:17
- Adam.
- It's a quadrilateral.
0075 10:04:44:17 10:04:48:12
Correct. It's a quadrilateral.
Anything else?
0076 10:04:48:12 10:04:50:24
- Holly.
- It has four right angles.
0077 10:04:50:24 10:04:55:13
Are you sure? Look closely.
How many right angles can you see?
0078 10:04:55:13 10:04:57:18
None.
0079 10:04:57:18 10:05:00:09
It's got no right angles, has it?
Never mind.
0080 10:05:00:09 10:05:03:02
What else can you tell us about it?
0081 10:05:03:02 10:05:04:02
Jacques.
0082 10:05:04:02 10:05:06:06
It has two pairs of parallel sides.
0083 10:05:06:06 10:05:08:15
Yes, it has two pairs
of parallel sides.
0084 10:05:08:15 10:05:10:24
Could we begin to give it a name?
0085 10:05:10:24 10:05:13:00
- James.
- It's a parallelogram.
0086 10:05:13:00 10:05:14:13
Good. It's a parallelogram.
0087 10:05:14:13 10:05:17:22
Who else wants to come out and
draw their shape on the whiteboard?
0088 10:05:17:22 10:05:19:22
Jack, come and draw yours.
0089 10:05:20:21 10:05:24:02
I've been using the interactive
whiteboard for three years.
0090 10:05:24:02 10:05:26:05
Like most people,
at first it was daunting,
0091 10:05:26:05 10:05:28:19
but I made the decision
from the very beginning
0092 10:05:28:19 10:05:32:24
to take my blackboard away, so I was
forced to use it from the start.
0093 10:05:32:24 10:05:37:07
I think if you start just using it
like a whiteboard or blackboard
0094 10:05:37:07 10:05:40:04
and then take it from there -
learn things as you go along.
0095 10:05:40:04 10:05:44:14
But I would never ever go back
to a time when I couldn't use it.
0096 10:05:44:14 10:05:47:21
What can you tell me
about Jack's shape?
0097 10:05:49:01 10:05:52:04
- Matthew.
- It's an isosceles triangle.
0098 10:05:52:04 10:05:54:24
Very good.
It's an isosceles triangle.
0099 10:05:54:24 10:05:59:00
Who thinks it's a right-angled
isosceles triangle?
0100 10:06:00:11 10:06:02:19
Good. It isn't.
Well done. Well spotted.
0101 10:06:02:19 10:06:05:23
So, if I get my ruler...
0102 10:06:05:23 10:06:08:11
And I'm going to draw
one side of the shape...
0103 10:06:08:11 10:06:12:03
It doesn't really matter
how long I make this side.
0104 10:06:12:03 10:06:15:20
A reasonable size -
not too big, not too small.
0105 10:06:15:20 10:06:18:14
Recapping how to draw
a regular mathematical shape
0106 10:06:18:14 10:06:22:05
leads Gary on to a neat way
of demonstrating ratio.
0107 10:06:22:05 10:06:25:17
This now must be
the same length as this side
0108 10:06:25:17 10:06:27:18
so I can draw it in.
0109 10:06:29:16 10:06:32:23
I now have drawn my explicit shape.
0110 10:06:32:23 10:06:38:13
And it doesn't really matter
what I do to this shape.
0111 10:06:38:13 10:06:43:24
If I move it around,
the angles are still right angles.
0112 10:06:43:24 10:06:47:13
The sides are still the same ratio.
0113 10:06:47:13 10:06:49:03
I can turn the shape...
0114 10:06:49:18 10:06:54:19
and it's still the same - same ratio
of sides, same right angles.
0115 10:06:54:19 10:06:56:10
I can even spin it round.
0116 10:06:57:16 10:07:02:22
Even though I'm a bit dizzy,
I can still see it's the same shape.
0117 10:07:02:22 10:07:06:06
I could even make it smaller.
0118 10:07:08:07 10:07:11:04
It's still got four right angles.
0119 10:07:11:04 10:07:15:00
It's still got this same ratio
of sides - one to two.
0120 10:07:15:00 10:07:18:07
If I make it bigger,
it's still the same.
0121 10:07:20:00 10:07:22:01
Still got four right angles.
0122 10:07:22:15 10:07:24:22
I'm going to label it
like I did before -
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A, B, C, D.
0124 10:07:30:01 10:07:31:18
Now you're going to have a go,
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so make sure you've got a piece
of plain paper in front of you,
0126 10:07:35:06 10:07:37:06
a pencil and ruler.
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You've got to first decide how long
that top edge is going to be.
0128 10:07:56:04 10:07:58:02
All done? Good.
0129 10:07:58:02 10:08:02:06
If I go back to the original photo,
0130 10:08:03:19 10:08:07:00
this house is out there somewhere.
0131 10:08:07:00 10:08:10:10
It's there in real life.
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And we call the actual house,
or even the photo of it,
0133 10:08:14:19 10:08:17:22
the real-life story.
0134 10:08:17:22 10:08:22:06
And on that house it does have
these explicit shapes
0135 10:08:22:06 10:08:24:10
which we can see.
0136 10:08:24:10 10:08:25:22
They're real.
0137 10:08:25:22 10:08:29:12
So we call any of these shapes
we can see
0138 10:08:29:12 10:08:31:18
the real story.
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However, once we start
drawing these shapes like this,
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and labelling them like this,
0141 10:08:41:09 10:08:44:12
it's no longer a window of a house.
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It's a rectangle - ABCD -
0143 10:08:47:11 10:08:50:10
or quadrilateral - ABCD.
0144 10:08:50:10 10:08:54:05
So this is called the maths story.
0145 10:08:54:05 10:08:59:15
Let's go back to the picture and
look at Jack's shape which he drew.
0146 10:08:59:15 10:09:04:11
Roughly what would you say
that angle is there?
0147 10:09:05:09 10:09:07:07
- Jacob.
- 100 degrees?
0148 10:09:07:07 10:09:11:13
100 degrees. So you think
it's more than 90 degrees?
0149 10:09:11:13 10:09:12:13
Yes.
0150 10:09:12:13 10:09:15:14
Who thinks
it's less than 90 degrees?
0151 10:09:15:14 10:09:18:13
What do you think is the size
of this angle then, Lauren?
0152 10:09:18:13 10:09:20:08
45 degrees.
0153 10:09:20:08 10:09:22:13
Who thinks 45 is too small?
0154 10:09:24:02 10:09:27:03
- What do you think, Greg?
- 80 degrees?
0155 10:09:27:03 10:09:30:02
Who agrees with Greg
it's about 80 degrees?
0156 10:09:30:02 10:09:33:11
So do I - only roughly,
about 80 degrees.
0157 10:09:33:11 10:09:37:21
(narrator) Gary's asked the class to
draw triangles on some plain paper,
0158 10:09:38:17 10:09:42:05
then to try and find some explicit
shapes in their photographs,
0159 10:09:42:05 10:09:45:11
making sure they understand
the explicit concept
0160 10:09:45:11 10:09:48:24
before moving on
to find implicit shapes.
0161 10:09:50:07 10:09:54:14
Who else would like to come out
and show us a shape they've found?
0162 10:09:54:14 10:09:57:17
Billy. Ah, I thought
this one was difficult.
0163 10:09:57:17 10:09:59:14
Here you are.
0164 10:10:00:17 10:10:02:14
Show us a shape.
0165 10:10:08:22 10:10:11:13
Good. Don't go away.
0166 10:10:11:13 10:10:14:02
Who agrees
it's a right-angled triangle?
0167 10:10:14:02 10:10:17:21
Who agrees it's an isosceles
right-angled triangle?
0168 10:10:17:21 10:10:21:02
Good. It isn't, is it?
Well done. What is it, then?
0169 10:10:22:09 10:10:25:00
- Dean.
- A right-angled scalene triangle.
0170 10:10:25:00 10:10:27:23
Who thinks it's
a right-angled scalene triangle?
0171 10:10:27:23 10:10:33:01
Good. We're going to
go on to implicit shapes.
0172 10:10:33:01 10:10:37:04
If I go back to
the very, very first shape I drew...
0173 10:10:38:03 10:10:43:11
If I draw a line
from corner to corner...
0174 10:10:47:12 10:10:51:24
I can now see that inside
that rectangle, hiding,
0175 10:10:51:24 10:10:54:18
were two triangles.
0176 10:10:54:18 10:10:56:14
Two implicit shapes.
0177 10:10:57:07 10:10:58:22
What you've got to do
0178 10:10:58:22 10:11:03:04
is see if you can find
any of these implicit shapes.
0179 10:11:03:04 10:11:07:01
The ones which are hidden,
they're hiding, difficult to find.
0180 10:11:08:00 10:11:11:16
Then have a go at drawing it
on your plain paper.
0181 10:11:11:16 10:11:13:23
That's an implicit shape...
explicit.
0182 10:11:16:04 10:11:20:17
That's what we want.
It's another trapezium.
0183 10:11:20:17 10:11:25:00
So, Stanislav, show me this
implicit shape you've drawn on here.
0184 10:11:25:00 10:11:26:04
There.
0185 10:11:26:04 10:11:29:08
- And what is it?
- A trapezium.
0186 10:11:29:08 10:11:34:12
Would it be better, though,
to maybe join the diagonals?
0187 10:11:34:12 10:11:37:01
This line here
you could put almost anywhere.
0188 10:11:37:01 10:11:40:03
You could do infinity along there,
couldn't you?
0189 10:11:40:03 10:11:42:12
Have a go at that.
0190 10:11:45:08 10:11:48:21
(narrator) It's coming to the end
of the lesson. Time for the plenary.
0191 10:11:48:21 10:11:51:10
So how many of them
will have understood
0192 10:11:51:10 10:11:54:07
the concepts of explicit
and implicit shapes,
0193 10:11:54:07 10:11:56:12
ratio and angle?
0194 10:11:56:12 10:12:00:05
Who did manage to find
one implicit shape?
0195 10:12:01:08 10:12:03:08
Let's just check, though.
0196 10:12:03:08 10:12:06:12
What is an explicit shape?
0197 10:12:06:12 10:12:08:21
- Hannah.
- A shape that stands out.
0198 10:12:08:21 10:12:13:02
Yes, a shape that stands out.
It's very clear, you cannot miss it.
0199 10:12:13:02 10:12:16:12
What is an implicit shape?
0200 10:12:16:12 10:12:19:23
- James.
- It's a shape...
0201 10:12:19:23 10:12:23:11
that's hard to see,
or doesn't stand out as much.
0202 10:12:23:11 10:12:26:02
Yes, it's hard to see,
it doesn't stand out so much.
0203 10:12:26:02 10:12:29:10
It's usually hidden
amongst the other shapes.
0204 10:12:29:10 10:12:35:12
When you're drawing shapes
from real life...
0205 10:12:35:12 10:12:39:03
and making them into a maths story,
0206 10:12:39:24 10:12:45:05
what do you have to think about
to draw them accurately?
0207 10:12:45:05 10:12:48:23
- The ratio of the sides.
- Good. The ratio of the sides.
0208 10:12:48:23 10:12:51:21
What else have you got to look at?
0209 10:12:51:21 10:12:53:08
Matthew.
0210 10:12:53:08 10:12:54:17
The angles.
0211 10:12:54:17 10:12:57:08
Yes, good.
You've got to estimate the angles.
0212 10:12:57:08 10:12:59:17
Well done, Year 6.
We're at the end of the lesson
0213 10:12:59:17 10:13:01:02
and you've done really well
0214 10:13:01:02 10:13:05:02
on what's actually
quite a difficult concept.
0215 10:13:07:07 10:13:09:21
My favourite bit
was drawing all the pictures.
0216 10:13:10:24 10:13:15:02
An explicit shape
is, like, showing out to you,
0217 10:13:15:02 10:13:18:01
but an implicit is harder to find.
0218 10:13:18:15 10:13:23:13
Maths story is talking about
the shapes that are in the picture.
0219 10:13:23:13 10:13:29:00
The real-life story
is the actual picture.
0220 10:13:29:00 10:13:31:20
(Gary) I was very pleased
with how the lesson went.
0221 10:13:31:20 10:13:35:19
I was worried at the beginning
about the ratio aspect.
0222 10:13:35:19 10:13:39:13
I think they took that on board very
well - much better than I thought.
0223 10:13:39:13 10:13:41:14
If I look back at
the learning objective,
0224 10:13:41:14 10:13:44:13
which was to identify
explicit and implicit shapes,
0225 10:13:44:13 10:13:48:20
I think on the whole
they did do that very well.
0226 10:13:55:00 10:13:57:15
Visiontext Subtitles:
Sarah Emery
0227 10:13:57:15 10:13:59:15