Angles and shapes Summer 2, week 4 Miss Churchs email: - - PowerPoint PPT Presentation

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Angles and shapes Summer 2, week 4 Miss Churchs email: - - PowerPoint PPT Presentation

Oct 27, 2023 169 likes •988 views

Angles and shapes Summer 2, week 4 Miss Churchs email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherlands email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moores email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need

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SLIDE 1

Angles and shapes Summer 2, week 4

Miss Church’s email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherland’s email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moore’s email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need to email Miss Church OR Miss Sutherland, do not send it to both 

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SLIDE 2

Hi all , happy Monday! This is your final 7 weeks of primary school maths! So we will use this time to consolidate and go over things to ensure you are as confident as possible when going into secondary school. This week we will be recapping angles within polygons (shapes)

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SLIDE 3

2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72

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SLIDE 4

7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144

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SLIDE 5

L.O. To compare the perimeters and areas of different squares and rectangles.

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SLIDE 6

What is the difference between the perimeter and area of a shape?

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SLIDE 7

What is the difference between the perimeter and area of a shape? The perimeter is the total length of the sides (like the fence to a garden). The area is in the INSIDE part (the garden)

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SLIDE 8

How do we work out the perimeter and the area of a rectangle or square?

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SLIDE 9

How do we work out the perimeter and the area of a rectangle or square? To find the perimeter we add up the lengths of all 4 sides. To find the area we multiply the length and width together. The answer is always in ___²

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SLIDE 10

Find the perimeter of these rectangles and squares.

12cm 6cm 0.5m 80cm 7cm 3m

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SLIDE 11

Find the perimeter of these rectangles and squares.

Perimeter= 36cm Perimeter= 260cm Or 2.6m Perimeter= 28cm 12cm 12cm 6cm 0.5m 80cm 7cm 3m

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SLIDE 12

Find the area of these rectangles and squares.

12cm 7cm 12cm 0.25m 8cm 4m

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SLIDE 13

Find the area of these rectangles and squares.

Area= 12 x 7 Area = 84cm² Area= 300cm² Or 3m² Area= 8x8 Area= 64cm² 16m² 12cm 7cm 12cm 0.25m 8cm 4m

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SLIDE 14

A rectangle has an area of 36cm. What could the lengths of its sides be?

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SLIDE 15

Possible answers for the rectangles are: 1 and 36 2 and 18 3 and 12 4 and 9 72 and 0.5 10 and 3.6

We couldn’t have 6 and 6 because that would make a square, and we have been asked for a rectangle

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SLIDE 16

Possible answers for the rectangles are: 1 and 36. 2 and 18 3 and 12 4 and 9 72 and 0.5 10 and 3.6

Do you think all these rectangles will have the same perimeter? Work them out and see.

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SLIDE 17

Possible answers for the rectangles are: 1 and 36 P= 74cm² 2 and 18 P=40cm² 3 and 12 P=30cm² 4 and 9 P= 26cm² 72 and 0.5 P= 145cm² 10 and 3.6 P= 27.2cm²

What do you notice?

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SLIDE 18

L.O. To compare the perimeters and areas of different squares and rectangles.

Your task today is quite investigative. Go back to the school’s website and download Monday’s work.

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SLIDE 19

Remember to email your work over to us so we can see how you’re getting on 

Year 6 Miss Church, Miss Moore and Miss Sutherland

echurch@kingsavenue.lambeth.sch.uk

ksutherland@kingsavenue.lambeth.sch.uk

amoore@kingsavenue.lambeth.sch.uk

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SLIDE 20

Angles and shapes Summer 2, week 4 Tuesday

Miss Church’s email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherland’s email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moore’s email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need to email Miss Church OR Miss Sutherland, do not send it to both 

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SLIDE 21

2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72

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7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144

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SLIDE 23

L.O. To revise how the find the area and perimeter of parallelograms and triangles.

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SLIDE 24

Recap: how do I find the area and perimeter of a parallelogram and a triangle?

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Recap: how do I find the area and perimeter of a parallelogram and a triangle? Perimeter is the same for both- just add up the lengths of the 3 or 4 sides. Area= parallelograms is l x w (like rectangles or squares) triangles is ½ x b x h (because a triangle is HALF the area of a rectangle or square)

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SLIDE 26

Perimeters and areas:

Find the perimeters and areas of these parallelograms

14cm 8cm 20cm 0.5m 11m 6m

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SLIDE 27

Perimeters and areas:

Find the perimeters and areas of these parallelograms

Perimeter= 44cm Area= 112cm ² Perimeter= 140cm Area= 1,000cm² Or 10m² Perimeter= 34m Area= 66m² 14cm 8cm 20cm 0.5m 11m 6m

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SLIDE 28

Perimeters and areas:

Have a look at the example below on how to find the perimeter of the triangle- look closely as it requires some different lengths to the height

12cm 7cm 11cm Perimeter= 12cm + 11cm+ 11cm= 34cm Area= ½ x 12 x 7 = ½ x 84 = 42cm²

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SLIDE 29

Perimeters and areas:

Find the perimeters and areas of these triangles

8cm 5cm 3m 5m 8cm 9cm 6cm 7m 10cm

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SLIDE 30

Perimeters and areas:

Find the perimeters and areas of these triangles

P= 20cm A= 20cm² P= 17m A=7.5m² P= 27cm A= 36cm² 8cm 5cm 3m 5m 8cm 9cm 6cm 7m 10cm

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SLIDE 31

L.O. To revise how the find the area and perimeter of parallelograms and triangles.

Today we will be investigating and looking at parallelograms and triangles. Please go back to the school’s website and download today’s work.

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SLIDE 32

Remember to email your work over to us so we can see how you’re getting on 

Year 6 Miss Church, Miss Moore and Miss Sutherland

echurch@kingsavenue.lambeth.sch.uk

ksutherland@kingsavenue.lambeth.sch.uk

amoore@kingsavenue.lambeth.sch.uk

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SLIDE 33

Angles and shapes Summer 2, week 4 Wednesday

Miss Church’s email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherland’s email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moore’s email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need to email Miss Church OR Miss Sutherland, do not send it to both 

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SLIDE 34

2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72

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SLIDE 35

7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144

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SLIDE 36

Remember that Wednesday is a recap day on Arithmetic bits. This week we will do another Arithmetic test to ensure we are remembering these key skills that will help you in Secondary School. Please go back to the School’s website and download Wednesday’s work. 

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SLIDE 37

Remember to email your work over to us so we can see how you’re getting on 

Year 6 Miss Church, Miss Moore and Miss Sutherland

echurch@kingsavenue.lambeth.sch.uk

ksutherland@kingsavenue.lambeth.sch.uk

amoore@kingsavenue.lambeth.sch.uk

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SLIDE 38

Angles and shapes Summer 2, week 4 Thursday

Miss Church’s email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherland’s email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moore’s email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need to email Miss Church OR Miss Sutherland, do not send it to both 

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SLIDE 39

2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72

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SLIDE 40

7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144

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SLIDE 41

L.O. To find the total sum of angles in regular polygons

Recap: what do we mean by regular polygons?

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SLIDE 42

L.O. To find the total sum of angles in regular polygons Recap: what do we mean by regular polygons? A polygon is a shape that has more than 3 straight sides. Regular means that all sides and angles are equal

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SLIDE 43

Today, we will be working out the interior angles of some polygons. We will NOT need a protractor. We will NOT have any angles given to us. We will simply use what we know about other shapes.

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SLIDE 44

Firstly, lets recap some of our polygons…

Heptagon Hexagon Pentagon Octagon

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SLIDE 45

Firstly, lets recap some of our polygons…

Heptagon (7) Hexagon (6) Pentagon (5) Octagon (8)

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These are regular polygons and these are irregular polygons

Irregular pentagon (5) Irregular Octagon (8)

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SLIDE 47

Today we will be focusing on regular polygons, and finding out the total sum of Interior angles in ANY POLYGON, whether it be 5 sides, 20 sides or 102 sides! If you can, print out the following polygons so you can draw on them. If you can’t, draw them on some paper as big as you

  • can. Try and get them as regular as possible- it will

still work even if it isn’t 100% accurate.

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SLIDE 48
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SLIDE 49
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SLIDE 50
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SLIDE 51
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SLIDE 52

Let’s recap first. What is the total sum of angles in a triangle? What is the total sum of angles in a rectangle or ANY quadrilateral?

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SLIDE 53

What is the total sum of angles in a triangle? 180 What is the total sum of angles in a rectangle or ANY quadrilateral? 360 What is the relationship between 180 and 360?

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SLIDE 54

What is the total sum of angles in a triangle? 180 What is the total sum of angles in a rectangle or ANY quadrilateral? 360 What is the relationship between 180 and 360? 180 is half of 360. So in theory, 2 triangles should fit inside 1 quadrilateral…. Yes?

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SLIDE 55
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SLIDE 56

I can cut all these quadrilaterals into 2 triangles. This PROVES that these quads Have a total sum of 360º

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SLIDE 57

OK, now back to our other polygons. Let’s all start with the Pentagon (5 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. REMEMBER: YOU GO FROM THE SAME POINT EACH TIME!

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SLIDE 58

OK, now back to our other polygons. Let’s all start with the Pentagon (5 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get.

1 3 2

I have 3 triangles this time. So 3x180= 540º The sum of the interior angles Of a Pentagon= 540º

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SLIDE 59

OK, now back to our other polygons. Now do the same for the Hexagon (6 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. REMEMBER: YOU GO FROM THE SAME POINT EACH TIME!

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SLIDE 60

OK, now back to our other polygons. Let’s all start with the Hexagon (6 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. I have 4 triangles this time. So 4x180= 720º The sum of the interior angles Of a Hexagon= 720º

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SLIDE 61

OK, now back to our other polygons. Now do the same for the Heptagon (7 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. REMEMBER: YOU GO FROM THE SAME POINT EACH TIME!

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SLIDE 62

OK, now back to our other polygons. Now do the same for the Heptagon (7 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. I have 5 triangles this time. So 5x180= 900º The sum of the interior angles Of a Heptagon= 900º

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SLIDE 63

OK, now back to our other polygons. Now do the same for the Octagon (8 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. REMEMBER: YOU GO FROM THE SAME POINT EACH TIME!

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SLIDE 64

OK, now back to our other polygons. Now do the same for the Octagon (8 sides) Start at ONE POINT . All lines will be going from this one point. Using a ruler, join this point to other points opposite. I have done one below to show you. See how many triangles you get. I have 6 triangles this time. So 6x180= 1080º The sum of the interior angles Of a Octagon= 1080º

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SLIDE 65

So how can we use this to find out the total sum of interior angles in a 35-sided shape 102-sided shape 97-sided shape? Let’s put what we know into a total and see if you can see any patterns:

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SLIDE 66

Let’s put what we know into a total and see if you can see any patterns: Shape Number of sides Number of triangles Quadrilateral 4 2 Pentagon 5 3 Hexagon 6 4 Heptagon 7 5 Octagon 8 6

What do you notice about the relationship between the number of sides, and the number of triangles?

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SLIDE 67

Let’s put what we know into a total and see if you can see any patterns: Shape Number of sides Number of triangles Quadrilateral 4 2

  • 2

Pentagon 5 3

  • 2

Hexagon 6 4

  • 2

Heptagon 7 5

  • 2

Octagon 8 6

  • 2

You ALWAYS have two less triangles than sides. Can we use this to write a formula? Have a go. Think about what we did to the number of triangles.

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SLIDE 68

Shape Number of sides Number of triangles Quadrilateral 4 2

  • 2

Pentagon 5 3

  • 2

Hexagon 6 4

  • 2

Heptagon 7 5

  • 2

Octagon 8 6

  • 2

The formula looks a little something like this: (Number of sides – 2) x 180 ^^^ can we shorten this part

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SLIDE 69

Shape Number of sides Number of triangles Quadrilateral 4 2

  • 2

Pentagon 5 3

  • 2

Hexagon 6 4

  • 2

Heptagon 7 5

  • 2

Octagon 8 6

  • 2

The formula looks a little something like this: (Number of sides – 2) x 180 ^^^ can we shorten this part

(N-2) x 180

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SLIDE 70

Using the above formula, you can now work out the total sum of these shapes. Give it a go! 35-sided shape 102-sided shape 97-sided shape

(N-2) x 180

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SLIDE 71

Using the above formula, you can now work out the total sum of these shapes. Give it a go! 35-sided shape= 33x180= 5,940º 102-sided shape= 100 x 180= 18,000º 97-sided shape= 95 x 180=17,100º

(N-2) x 180

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SLIDE 72

Remember to email your work over to us so we can see how you’re getting on 

Year 6 Miss Church, Miss Moore and Miss Sutherland

echurch@kingsavenue.lambeth.sch.uk

ksutherland@kingsavenue.lambeth.sch.uk

amoore@kingsavenue.lambeth.sch.uk

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SLIDE 73

Angles and shapes Summer 2, week 4 Friday

Miss Church’s email: echurch@kingsavenue.lambeth.sch.uk Miss Sutherland’s email: ksutherland@kingsavenue.lambeth.sch.uk Miss Moore’s email: amoore@kingsavenue.lambeth.sch.uk If you are in 6CS, you only need to email Miss Church OR Miss Sutherland, do not send it to both 

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SLIDE 74

2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72

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SLIDE 75

7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144

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SLIDE 76

L.O. To revise all angle knowledge and apply my skills to problem-solving activities.

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SLIDE 77

Below are some types of angles that we have looked at within year 6. Remind yourself of what these angles add up.

Right angle

Straight line

Full turn

Angles in a quadrilateral

Angles in a triangle

Vertically opposite angles are…

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SLIDE 78

Below are some types of angles that we have looked at within year 6. Remind yourself of what these angles add up.

 Right angle= 90º  Straight line= 180º  Full turn= 360º  Angles in a quadrilateral= 360º  Angles in a triangle= 180º  Vertically opposite angles are the SAME

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SLIDE 79

Today, you will be using all your skills about angles to

find missing ones within shapes. There are a variety

  • f different activities that you can try- all of them

use your angles knowledge. (some may also use your knowledge from yesterday).

If you do task 1,2 or 3, then you must do 2 of them

MINIMUM

If you do task 4 and beyond, you only do 1 of them

MINIMUM.

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SLIDE 80

Remember to email your work over to us so we can see how you’re getting on 

Year 6 Miss Church, Miss Moore and Miss Sutherland

echurch@kingsavenue.lambeth.sch.uk

ksutherland@kingsavenue.lambeth.sch.uk

amoore@kingsavenue.lambeth.sch.uk