GCSE Maths Lesson 9 Finishing Geometry for the time being

GCSE Maths Lesson 9 Finishing Geometry for the time being
Units and Measure, including compound measures

Card match Lesson 3 Activity 1.docx

What are we doing today? By the end of today’s lesson you will be able to: derive and use the sum of angles in a triangle answer questions using: sum of exterior angles of a polygon = 360° general iterative processes (iteration – a process of repeating)

Homework follows

Card Activity – Angles 0605cardsortangles.doc
Answers: 68°, 248°, 20°, 75°, 57°, 65°, 58°, 134°, 111°, 130°, 70°, 110°

Q – What is angle o?

Q – What are angles a and b?

What are angles m and n?

Activity – Dinky King!

Lines of symmetry - Regular Polygons
Equilateral Triangle Square Regular Pentagon Regular polygons have lines of symmetry equal to the number of sides/angles that they possess. Regular Regular Hexagon Regular Octagon

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. Order 1

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2 3 2 1 Order 3

Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 1 Order 2 3 3 4 2 1 2 1 Order 4 Order 3

Rotational Symmetry Have a look at the following shapes…

order 4 Eg1. A square It fits on itself 4 times
back order 4 We say that a square has…

order 1 Eg2. A heart shape It fits on itself only once
back order 1 We say that a heart has…

What is the order of rotational symmetry?
answer

How can you PROVE that the angles in a triangle add up to 180°?

Look at your answers to Dinky King – they also prove that the angles of a triangle add up to 180°

How can you PROVE that the angles in a quadrilateral add up to 360°?

Draw any quadrilateral. Draw a diagonal on your quadrilateral.
b Draw any quadrilateral. Draw a diagonal on your quadrilateral. Label the angles in one of your triangles a, b, c The sum of the angles in the first triangle is 180° so: a + b + c = 180 Label the angles in the other triangle d, e, f The sum of the angles in the second triangle is 180° so: d + e + f = 180 a f c d

= the sum of the angles in ANY quadrilateral = 360° e b + e b a a f f
c c + d d So the angles in your quadrilateral are: a, b + e, f, and c + d So therefore: the sum of the angles in a quadrilateral = a + b + e + f + c + d Which rearranged: the sum of the angles in a quadrilateral = a + b + c + d + e + f Substituting a + b + c = 180 and d + e + f = 180 (from 4 and 6) the sum of the angles in a quadrilateral = the sum of the angles in ANY quadrilateral = 360°

Interior and exterior angles of polygons
This is Mr Red! (click on him)

Edexcel polygon exam questions

What are we doing today? By the end of today’s lesson you will be able to: derive and use the sum of angles in a triangle answer questions using: sum of exterior angles of a polygon = 360° general iterative processes (iteration – a process of repeating)

General iterative processes

Activities & worksheets

Website of the week Help is at hand

What are we going to do now?
Change freely between related standard units (eg time, length, area, volume / capacity, mass) and compound units Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

Give out conversion card
Metric measurement Give out conversion card

Metric Conversions - LENGTH
Functional Skills Mathematics - Measurements Metric Conversions - LENGTH Examples: Convert 3m to cm 3 x 100 = 300cm Convert 5.7km to m 5.7 x 1000 = 5700m Convert 3.6km to cm 3.6 x 1000 = 3600m 3600 x 100 = cm x 1000 x 100 x 10 km m cm mm ÷ 1000 ÷ 100 ÷ 10

Metric Conversions – WEIGHT/MASS
Examples: Convert 5g to mg 5 x 1000 = 5000mg Convert 2.9kg to g 2.9 x 1000 = 2900m Convert 7.6 tonnes to mg 7.6 x 1000 = 7600Kg 7600 x 1000 = g x 1000 = mg x 1000 x 1000 x 1000 g mg Tonne kg ÷ 1000 ÷ 1000 ÷ 1000

Metric Conversions - CAPACITY
Examples: Convert 9l to cl 9 x 100 = 900cl Convert 90ml to cl 90 ÷ 10 = 9cl Convert 15300ml to l 15300 ÷ 10 = 1530cl 1530 ÷ 100 = 15.3l x 100 x 10 ml l cl ÷ 100 ÷ 10

Tarsia puzzle

Or Metric units cross number

What might we buy in here?

6 inch or foot-long subs

How would you order a pizza from here?

Dominoes uses imperial units too!
Pizza sizes: Small - 9.5” Medium ” Large ”

Metric to Imperial Conversions
You need to be able to use the following conversions: Metric Imperial 8km 5 miles 2.5cm 1 inch 4.5 litres 1 gallon 1 kg 2.2 pounds

Length Conversions of World Records
1 inch = 2.5 cm 1 metre = 3.3 feet

This mans nose is 8.8cm, convert this to inches.

The diameter of this bubble is 20.3 inches, convert this to cm.

This woman’s legs are 132cm, convert this to inches.

This man’s mouth is 6.8 inches, convert this to cm.

This snake is 7.3 m, convert this to feet.

This woman’s waist is 15.2 inches, convert it to cm

Answers Nose Bubble Legs Mouth Snake Waist 8.8cm or 3.52 inches

Homework - metric and imperial measures sheet

What are we going to do now?
Change freely between related standard units (eg time, length, area, volume / capacity, mass) and compound units Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate

Converting km/h to m/s And converting m/s to km/h

Converting km/h to m/s

Converting m/s to km/h

Your Turn Convert 100km/h to m/s Convert 6km/h to m/s
Convert 450m/s to km/h. Convert 705m/s to km/h.

= Metric Conversions cm3 mm3 VOLUME = 1000mm3 VOLUME = 1cm3 x 1000
÷ 1000

= Metric Conversions m3 cm3 VOLUME = 100000cm3 VOLUME = 1m3 x 100000
÷

Perimeter, area and volume

What do you know already?
Can you position the cards in the correct places to show how you would work out the perimeter, area or volume of each shape?

What are perimeter and area?
Perimeter is the length around the outside of a shape. Area is the space inside a shape.

Example The rectangle has a perimeter of: 5 + 3 + 5 + 3 = 16cm
The rectangle has a area of: 5 + 5 + 5 = 15cm² Take note of the units! 5 × 3 = 15cm²

Find the perimeter and area of this rectangle:
20cm 24cm²

The formulae to remember:
Rectangle: Area = length × width 𝐴=𝑙𝑤 Triangle: Area = base × height ÷ 2 𝐴= 1 2 𝑏ℎ Remember that the height is at right angles to the base!

Two examples: Example 1 Example 2
Find the area and perimeter of this rectangle: Area = 8 × 6 Area = 48cm² Perimeter = Perimeter = 28cm Find the area of this triangle: Area = 5 × 12 ÷ 2 Area = 60cm² ÷ 2 Area = 30cm² 13cm 6cm 5cm 8cm 12cm

Have a go at some: Answer: Area = 88cm² Answer: 35cm² Perimeter = 38cm
Question 1 Question 2 Find the area of this triangle: Find the perimeter and area of this rectangle: 11cm 8cm 7cm 10cm Answer: Area = 88cm² Perimeter = 38cm Answer: 35cm²

The formulae: Parallelogram: Area = base × vertical height 𝐴=𝑏ℎ Trapezium: Area = (Half the sum of parallel sides) × height 𝐴= 𝑎+𝑏 2 ×ℎ

Two examples Example 1 Example 2
Find the area of this parallelogram: Area = 7 × 5 Area = 35cm² Find the area of this trapezium: Area = ×5 Area = 30cm² 4cm 5cm 6cm 5cm 7cm 8cm

Have a go at a couple of questions:
Find the area of this parallelogram: Find the area of this trapezium: 12cm 9cm 10cm 8cm 7cm 11cm Answer: 96cm² Answer: 70cm²

Area – Working Backwards
Now you can find the area of shapes, can you find a length having been given the area?

Formulae Reminder: Rectangle: 𝐴=𝑙𝑤 Triangle: 𝐴= 1 2 𝑏ℎ Parallelogram: 𝐴=𝑏ℎ Trapezium: 𝐴= 𝑎+𝑏 2 ×ℎ

Find the missing lengths:
None of these are drawn to scale ?cm 6cm Area = 48cm² 7cm Area = 21cm² 8cm ?cm 6cm 8cm ?cm 5cm Area = 32cm² Area = 28cm² 9cm Height = ? 4cm Height = 4cm

How to calculate the volume of a cuboid:
A cuboid is a prism, which means that it has the same cross-section all the way through. Find the area of the cross-section then multiply by the length. Volume = Height × Width × Length 𝑉=ℎ𝑤𝑙 This is how you calculate the volume of all prisms.

Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³
An example: Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ 3cm 4cm 5cm Take note of the units!

Another example, working backwards:
Find the height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm Volume = 280cm³ 7cm 10cm

Two questions to have a go at:
Find the volume of this cuboid: The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³) 8cm 6cm 0.5m 5cm 0.5m 1m Answer: 240cm³ Answer: 0.2m or 20cm

What is a prism? A prism is a 3D shape that has the same cross-section all the way through. For example: Triangular Prism Hexagonal Prism Cylinder

Calculating the volume of a prism:
Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length

Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
Two examples Example 1 Example 2 Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³ If the volume of this prism is 360cm³ and it is 9cm long, what is the area of the cross-section? Area of cross-section = 360 ÷ 9 Area of cross-section = 40cm² 3cm 8cm

Find the volume of this triangular prism:
A couple of questions: Question 1 Question 2 Find the volume of this triangular prism: A circular pond contains 18,850 litres of water. It has a diameter of 4m. How deep is the pond if it is a cylinder? (1 litre = 1000cm³) 9cm 12cm 8cm Answer: 432cm³ Answer: 1.5m or 150cm

Perimeter, area and volume - Homework

What is the value of x? 6

The area of this shape is 20cm2.
What is the length, b ? 4cm b cm 5

What is the perimeter of this shape?
2.5cm 2.5cm 2 cm 7

What is the volume of this shape?
4

2 The perimeter of this shape is 7cm. What is the missing length x?
x cm

What is the area of this shape?
12

What is the surface area of this shape?
18

What is the value of y? 23

The area of this square is 100cm2.
What is the length of each side? 10

1 The perimeter of this rectangle is 18cm What is the value of y? y cm

What is the length, b ? 13 10cm b cm

11 The perimeter of this rectangle is 28cm What is the value of y? 3cm

6cm 4cm 6cm 9

14

19 9.5cm

16

17 8.5cm

3cm What is the area of this shape? 4cm 20 Clue

21 The perimeter of this shape is 71cm. What is the missing length x?
x cm

22 7cm 4cm

What is the perimeter? 24

Two-way tables and frequency trees.

How could we display the information below in an easier format
How could we display the information below in an easier format? A school chess club has 70 members of which 40 are boys. Students play in competitions on a regular basis. Last month, 13 girls and 11 boys played in competitions. 2 of 4 AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

A two way table might be helpful….
Played in competition last month Did not play in competition last month Boys 11 29 40 Girls 13 17 30 24 46 70 What other methods might we use to display the information? 3 of 4 AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

11 40 Boys 29 70 13 Girls 30 17 Use a frequency tree
Played in competition 11 40 Boys Didn’t play in competition 29 70 Played in competition 13 Girls 30 17 Didn’t play in competition 4 of 4 Copyright © 2015 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

In Year 6 at a local primary school there are 120 students
In Year 6 at a local primary school there are 120 students. The ratio of boys to girls is 9:6. The girls were twice as likely to own a mobile phone as they were to not own a mobile phone. The ratio of boys who own a mobile phone to those who don’t own a mobile phone is 5:3 2 of 3 AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

45 72 Boys 27 120 32 Girls 48 16 Use a frequency tree
Owns a mobile phone 45 72 Boys Doesn’t own a mobile phone 27 120 Owns a mobile phone 32 Girls 48 Doesn’t own a mobile phone 16 3 of 3 Copyright © 2015 AQA and its licensors. All rights reserved. AQA Education (AQA) is a registered charity (number ) and a company limited by guarantee registered in England and Wales (number ). Our registered address is AQA, Devas Street, Manchester M15 6EX.

What did we do last time? 1.

Last bit of probability for now - tree diagrams

TREE DIAGRAMS First coin Second coin H H T H T T

Imagine choosing a ball from this bag and then replacing it
Imagine choosing a ball from this bag and then replacing it. If you did this three times, what's the probability that you would pick at least one green ball? What’s the best method to use to answer this question? What if you didn't replace the ball each time?

Replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

Not replacing it - if you did this three times, what's the probability that you would pick at least one green ball?

Two cards are drawn from a pack with replacement
13 52 39 A spade Not a spade 1st card 2nd card

Two cards are drawn from a pack without replacement
13 52 39 A spade Not a spade 1st card 2nd card

Exam question 11

Looking back at targets
Do you understand that the sum of the probabilities of all possible mutually exclusive outcomes is 1? Do you understand the difference between theoretical and experimental probability? Can you calculate probability using a tree diagram?

Probability revision quiz HIGHER
In teams of 3 work together to answer all the questions

Finding probabilities 1 (words)
5 points 10 points 15 points P(roll an odd number on a dice) is P(it will rain tomorrow) is P(baby born is a girl) is P(being younger tomorrow) is P(win lottery) is P(sun rising tomorrow) is

Finding probabilities 2 (fractions)
5 points (dice) 10 points (cards) 15 points P(red prime)= P(black)= P(4)= P(even)= P(red picture card)= P(less than 5) =

Finding probabilities 3 (OR rule)
5 points (dice) 10 points (cards) 15 points P(prime or square)= P(6 or 7)= P(4 or 5)= P(2, 3 or 4)= P(red 3 or black queen)= P(2 or 3) =

Finding probabilities 4 (2 events)
5 points (2 dice) 10 points 15 points P(2 numbers the same)= P(5 or 6)= P( 7 )= P(13)= P(less than 4) = P(even) = You have 1 minute to list all the outcomes of 2 dice before the questions come up.

Finding probabilities 5 (biased dice)
1 2 3 4 5 6 0.2 0.1 0.05 x 0.15 5 points 10 points 15 point P(not 4)= P(6)= P(2)= P(1 or 3)= P(not 2)= P(odd) =

Finding probabilities 6 (tree diagrams)
Copy down this information: The probability it rains on a Monday is 0.3 The probability it rains on Tuesday is 0.25 5 points 20 points 30 points P( it rains on both days) Draw a tree diagrams to show all outcomes P( it does not rain on Monday)= P(It does not rain on Tuesday)=

Bonus question (40 points)
Based on the following tree diagram what is the probability I pick 2 different colours?

Relative frequency in a graph

PLENARY Who wants to be a millionaire? millionaire_probability.ppt

Need to do recurring decimals

GCSE Maths Lesson 9 Finishing Geometry for the time being

Similar presentations

Presentation on theme: "GCSE Maths Lesson 9 Finishing Geometry for the time being"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

GCSE Maths Lesson 9 Finishing Geometry for the time being

Similar presentations

Presentation on theme: "GCSE Maths Lesson 9 Finishing Geometry for the time being"— Presentation transcript:

Similar presentations

About project

Feedback