# year 9 measurement. unit plan length length length perimeter perimeter perimeter area area volume...

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• Slide 1
• Year 9 Measurement
• Slide 2
• Unit Plan Length Length Length Perimeter Perimeter Perimeter Area Area Volume Volume Capacity Capacity Project Project
• Slide 3
• Length How Long is a Piece of String???
• Slide 4
• The Metre (m) The metre (m) is the base unit for length in the metric system. Originally the metre was thought to be one ten-millionth of the distance from the north pole to the equator through Paris, France.
• Slide 5
• The Metre (m) From the metre, other units of length were devised to measure smaller and larger distances. Millimetres (mm), Centimetres (cm) and Kilometres (km)
• Slide 6
• Estimations Worksheet
• Slide 7
• Conversion Rules
• Slide 8
• Lesson Summary 3 things that I learned today 3 things that I learned today 2 things that I enjoyed 2 things that I enjoyed 1 thing that I want to learn about 1 thing that I want to learn about
• Slide 9
• Conversions Worksheet
• Slide 10
• Perimeter
• Slide 11
• The Perimeter We say that a soccer field has a boundary line that is marked out along the playing perimeter. However, in mathematics we use the word perimeter when we are talking about the distance around a figure.
• Slide 12
• Find the Perimeter of These
• Slide 13
• And These
• Slide 14
• Can you work out the Formula? Square: Square: Rectangle Rectangle
• Slide 15
• Try These Ones
• Slide 16
• Applied Questions
• Slide 17
• Circumference Around we go
• Slide 18
• Circumference The circumference of a circle is the perimeter or length around the circle.
• Slide 19
• Investigation You will need: Some Cylinders Soft drink cans, Toilet roll, Piece of pipe
• Slide 20
• Investigation What to do: Step 1 Measure the diameter, of one object as shown. The distance between the two marks is the diameter of your object.
• Slide 21
• Investigation What to do: Step 2 Mark a point on the circumference of your object and then roll it for one complete revolution as shown. The distance between the two marks is the circumference of your object.
• Slide 22
• Investigation What to do: Step 3 Copy the table below and fill it in for your objects. ObjectCircumferencediameterCircumferencediameter 1. 2. 3.
• Slide 23
• The Life of Pi () It has been known for thousands of years that whenever the circumference is divided by the diameter the answer is always the same. You should have found this in the previous investigation (allowing for slight inaccuracies in measurements).
• Slide 24
• The Life of Pi () The actual value for: Circumference diameter for any circle lies between 3.14 and 3.15 This value is symbolised by the Greek letter (pi).
• Slide 25
• The Life of Pi () So, for any circle, Circumference = diameter In other words, Circumference = diameter or C = d.
• Slide 26
• Circumference Since the diameter is twice the length of the radius, we can also write: Circumference = 2 radius or C = 2 r diameter radius
• Slide 27
• Pi The exact value for cannot be written down because it is a non-terminating (does not stop) and non-recurring (does not repeat) decimal. The value of , correct to 36 decimal places is: = 3.141 592 653 589 793 238 462 643 383 279 502 884
• Slide 28
• Pi
• Slide 29
• Passage 1 Kings 7:15-24 The Message (MSG) 15 -22 First he cast two pillars in bronze, each 8.2m tall and 5.5m in circumference. He then cast two capitals in bronze to set on the pillars; each capital was 2.3m high and flared at the top in the shape of a lily. The Message (MSG) 15 -22 First he cast two pillars in bronze, each 8.2m tall and 5.5m in circumference. He then cast two capitals in bronze to set on the pillars; each capital was 2.3m high and flared at the top in the shape of a lily. 22 -24 When the pillars were finished, Hiram's next project was to make the Sea an immense round basin of cast metal 4.6m in diameter, 2.3m tall, and 13.8m in circumference. The Message (MSG) Copyright 1993, 1994, 1995, 1996, 2000, 2001, 2002 by Eugene H. Peterson 22 -24 When the pillars were finished, Hiram's next project was to make the Sea an immense round basin of cast metal 4.6m in diameter, 2.3m tall, and 13.8m in circumference. The Message (MSG) Copyright 1993, 1994, 1995, 1996, 2000, 2001, 2002 by Eugene H. PetersonEugene H. PetersonEugene H. Peterson
• Slide 30
• Try These Questions
• Slide 31
• Try These Questions A cylindrical water tower has a base diameter of 7 m. What is the circumference of the base? A circular flower bed has a radius of 2.5 m. What is the perimeter of the edge of the bed?
• Slide 32
• Try These Questions A bicycle wheel has radius 40 cm. Find the circumference of the wheel. How many kilometres would be travelled if the wheel rotates 10 000 times? How many times does the wheel rotate if the bike is ridden 10 km?
• Slide 33
• An Investigation Which fits better Which fits better A round peg in a square hole, or A round peg in a square hole, or A Square peg in a round hole? A Square peg in a round hole?
• Slide 34
• Try These Questions Find the perimeter of the door:
• Slide 35
• Try These Questions Find the perimeter of these shapes:
• Slide 36
• Practical Uses of Perimeter Sunshine Run how far do you actually run? Sunshine Run how far do you actually run? The Octagon how far is it to walk around the Octagon? The Octagon how far is it to walk around the Octagon?
• Slide 37
• Area Area is the amount of surface within a two-dimensional shape.
• Slide 38
• At Home Around the home, there are many surfaces such as driveways, paths, floors, ceilings and walls. All such surfaces have boundaries, that is, they are enclosed within a two-dimensional (2-D) shape. Information on cans of paint and bags of fertiliser refer to the area they can cover. Similarly, garden sprinklers cover a certain area of lawn.
• Slide 39
• Some Measures 1 square millimetre (mm 2 ) 1 square centimetre (cm 2 ) 1 square metre (m 2 ) 1 hectare (ha)
• Slide 40
• Try these questions.. What unit would you use? What unit would you use? What unit would you use? What unit would you use?
• Slide 41
• Another Measure 1 km 2 is one kilometre square which is 1 km 2 is one kilometre square which is 1000m 1000m 1000m 1000m Population Density is one measure that uses km 2. Population Density is one measure that uses km 2. Population Density Population Density It measures how densely populated countries are by: It measures how densely populated countries are by: Counting the number of people in the country Counting the number of people in the country Measuring the land area and then dividing Measuring the land area and then dividingPopulation Land Area
• Slide 42
• Population Density It measures how densely populated countries are by: It measures how densely populated countries are by: Counting the number of people in the country Counting the number of people in the country Measuring the land area and then dividing Measuring the land area and then dividingPopulation Land Area
• Slide 43
• Our Octagon Can you work out the area inside the Octagon? Can you work out the area inside the Octagon? How many people can we fit inside? How many people can we fit inside?
• Slide 44
• North Island vs South Island Which one would you prefer to live in? Which one would you prefer to live in? Which is more crowded or has highest population density? Which is more crowded or has highest population density?
• Slide 45
• North Island vs South Island 3 148 400 people live in the 3 148 400 people live in the North Island North Island It is 113 729 km. It is 113 729 km. Therefore the number of people per km or the population density is: Therefore the number of people per km or the population density is: 3 148 400 = 27.7 people per km 113 729
• Slide 46
• North Island vs South Island 1 008 400 people live in the 1 008 400 people live in the South Island It is 151 215 km. It is 151 215 km. Therefore the number of people per km or the population density is: Therefore the number of people per km or the population density is: 1 008 400 = 6.7 people per km !!! 151 215
• Slide 47
• Now you try! Have a go at some area questions Have a go at some area questions Page 289, questions 3 & 5 Page 289, questions 3 & 5 Page 293, question 9, 10 & 11 Page 293, question 9, 10 & 11 Sheet (ask Mrs Holman or Mr Porter) Sheet (ask Mrs Holman or Mr Porter)
• Slide 48
• Triangles Investigation Make a box make sure the corners have 90 o angles. Make a box make sure the corners have 90 o angles.
• Slide 49
• Triangles Investigation Put a dot anywhere along the top side o