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Measurement

Grade 5/6

Term 3 2012

Sunshine Harvester P.S

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Topics

• Length• Perimeter• Area• Surface Area• Mass• Volume and Capacity• Angle• Time• Temperature• Pythagoras Theorem

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Length

• The distance from one point to another.• What do we measure length in;

–Millimetres (mm) –Centimetres (cm)–Metres (m)–Kilometres (km)

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km m cm mm

x1000

÷10

x10x100

÷100÷1000

Converting Lengths

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Perimeter

• The distance around the outside of a shape.

E.g. What is the perimeter of this shape?

P = 6 + 8 + 8 P = 22 cm 8cm

6cm

8cm

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Perimeter of Circles• Outside of a circle is called

the circumference.• To measure the

circumference we use the equation;

c = π x diameter• The diameter is a straight

line going through the middle of a circle from one side to another.

Pi = 3.14

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• We can also measure circumference by using the radius of a circle.

• The radius is a straight line from the middle of a circle to the edge of one side.

• If we use the radius, the equation we use is;

c = 2 x π x r

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Area• Area is the inside space of a 2 dimensional

shape..

• Our unit of measure is always squared ² Area = length x width (a = l x w)

E.g. what is the area of the following shape;

4m

8m

A = l x wA = 8 x 4A = 32m ²

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• Triangle: area = ½ x base x height

a = ½ x b x h

• Parallelogram: area = base x height

a = b x h

• Trapezium: area = ½ x (side a + side b) x height

a = ½(a + b) x h a

b

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• Circle (with diameter): area = π x radius squared

a = π x r²

• Circle (with radius): area = π x (diameter ÷ 2)

a = π x (d ÷ 2)

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Surface Area & Nets• Surface Area is the

total area of all the faces of a solid shape.

• A Net is a 2D representation of a 3D shape that can be folded to form the 3D shape that it represents.

5

5

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Rectangular Prism= 2(l x w) + 2(w x h) + 2(l x h)

Height

LengthWidth

SA = 2(l x w) + 2(w x h) + 2(l x h) = 2(5 x 8) + 2(5 x 4 ) + 2(8 x 4) = 2(40) + 2(20) + 2(32) = 80 + 40 + 64 = 184 cm²

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Cylinder = 2πr x (radius + height)

4 4

7

SA = 2πr x (r + h) = 2π x 4 x (4 + 7) = 2π x 4 x (11) = 276.32 cm²

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Mass

• The weight of an object.• What do we measure mass in;

–Milligrams (mg)–Grams (g)–Kilograms (kg)–Tonnes (t)

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t kg g mg

x1000

÷10

x10x100

÷100÷1000

Converting Mass

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Volume & Capacity• Volume is the amount of space a 3-

dimensional object occupies.• Capacity is the amount or number that can

be held by an object.• It is measured in cubes ³

For rectangular prisms:V = l x w x he.g. V = l x w x h = 5 x 3 x 3 = 45m³

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For cylinders:V = π x r² x he.g. V = π x r² x h = π x 3² x 10 = 282.6 cm³

For triangular prisms:V = (1/2 x b x h) x hV = (1/2 x b x h) x h = (1/2 x 19 x 24) x 24 = 5472 cm³

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Angles• Are measured in degrees.

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• Angles that add up to 90 degrees (right angle) are called complementary angles

Complementary Angles

23

x

X = 90 – 23 = 67°

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Supplementary Angles• Angles that add up to 180 degrees (straight

angle) are called supplementary angles

X = 180 – 139 = 41°

x

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• Vertically Opposite angles are the same; they are equal.

Vertically Opposite Angles

x = 180 – 35 = 145°y = 180 – 145 = 35°

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Types of and Angles in Triangles.

All angles in any triangles add up to 180 degrees!

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Angles in Quadrilaterals.

All angles in quadrilaterals add up to 360 degrees!

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Angles in Circles.

All angles in circles add up to 360 degrees!

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120°

130°

x°

Example:

x = 360 – 130 - 120 = 110°

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Time

• What do we measure time in:–Seconds–Minutes–Hours–Days–Weeks–Months

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Time Conversions60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

2 weeks = 1 fortnight

12 months = 1 year

365 days = 1 year

366 days = 1 leap year

52 weeks & 1 day = 1 year

52 weeks & 2 days = I leap year

10 years = 1 decade

100 years = 1 century

1000 years = 1 millennium

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Types of Time

• am – ante-meridian• pm – post meridian

• 12 hour time

• 24 hour time

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Temperature

• Temperature is measure in degrees Celsius °

• A thermometer is the tool use to measure temperature.

http://www.weatherwizkids.com/weather-temperature.htm

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Pythagoras Theorem

• Pythagoras' theorem describes how the lengths of sides in a right angled triangle are related to each other.

• If you have a right angled triangle and make a square on each of the sides then the biggest square has the same area as the other two squares put together.

• Pythagoras' theorem expresses it like this:

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

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c² = a² + b²c² = 3² + 4²c² = 9 + 16c² = 25

This gives us the size of the square on the hypotenuse side. To find the size of the line, we square root our answer;

c = √c²c = √25c = 5

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Backtracking• If you know the lengths of two sides of a right

angled triangle, then Pythagoras' theorem allows you to find the length of the other side. Remember, it only works on right angled triangles.