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Measurement

Measurement. Note 1 : Measurement Systems. In NZ the measurement system used is the metric system. The units relate directly to each other. metre. m. gram. g. litre. L. °C. degrees celsius. s/min. seconds/minutes. square metres. m². ha. hectares. m³. cubic metres.

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Measurement

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  1. Measurement

  2. Note 1 : Measurement Systems In NZ the measurement system used is the metric system. The units relate directly to each other.

  3. metre m gram g litre L °C degrees celsius s/min seconds/minutes square metres m² ha hectares m³ cubic metres

  4. To change within a unit from one prefix to another prefix, we either multiply or divide by a power of 10. smaller to larger unit divide by a power of 10 larger to smaller unit multiply by a power of 10 Examples: convert the following 5.76m to cm 489mL to L 3789600cm to km

  5. Homework Book Page 159-160

  6. STARTERS Convert the following: 59mL to L 4200kg to tonne 11m465mm to cm A dairy stores milk in 5 litre containers. How many 350mL milkshakes can be made from one of these containers?

  7. Note 2: Derived Units Derived units show comparisons between two related measures. For example, speed is a measure of how much distance changes over time. The units for speed are m/s or km/h. Distance Speed Time

  8. Examples: A cyclist travels at a steady speed of 24km/h for 40 minutes. How far did the cyclist travel? 40 minutes = 2/3hour Distance = speed x time = 24 x 2/3 = 16 km

  9. Changing from one speed unit to another Note: 1km = 1000m 1 hour = 3600sec Examples: Change 45km/h into m/s 45km/h = 45 x 1000m/h = 45000m/h = 45000m/3600s = 12.5 m/s

  10. Examples: Change 74m/s into km/h 74m/s = 3600x74m/h = 266400m/h = 266.4km/h

  11. Homework Book Page 162-163

  12. STARTERS Convert the following: 19m/s to km/h A truck travels at an average speed of 75km/h for a distance of 300km. What time does the journey take? A Boeing 747 has a cruising speed of 910km/h. Change this into m/s?

  13. The perimeter is the distance around the outside of a shape.Start at one corner and work around the shape calculating any missing sides. Note 3: Perimeter 5 cm 6 cm 5 cm 2 cm Perimeter = 5cm + 3cm + 6cm + 2cm + 11cm + 5cm = 32cm

  14. Homework Book Page 164 - 166

  15. STARTERS Calculate the perimeter of The plan shows an L-shaped paddock. Calculate the total cost of fencing it at $24/m

  16. The perimeter of a circle is called the circumference. The formula for the circumference is: C = πd or C = 2πr where d = diameter r = radius. Note 4: Circumference Example: Find the circumference of C = 2πr = 2 x π x 8cm = 50.3cm (1dp)

  17. If a sector has an angle at the centre equal to x, then the arc length is x/360 of the circumference. Example: Find the perimeter of the sector Angle of sector = 360° - 120 ° = 240 ° Arc Length = x/360 x2πr = 240/360 x 2 x π x 6m = 25.1m (1dp) Perimeter = 2 x 6m + 25.1m = 37.1m

  18. Homework Book Page 167 - 169

  19. STARTERS Calculate the perimeter of Paul goes for a short cycle ride. Each wheel on his bike has a radius of 27cm. His distance counter tells him the wheel has rotated 650 times. Find how far he has travelled in metres.

  20. Note 5: Area Area is measured in square units.

  21. Examples converting units:

  22. Examples of converting units 5.6cm2 to mm2 Big Small x 5.6cm2 = 5.6 x 100 = 560mm2 396000cm2 to m2 Small Big ÷ 396000cm2 = 396000÷10000 = 39.6m2

  23. 8m 15m 10m 17m 17m 7m 9m 12m Examples: Calculate the area of these shapes Area = ½  base  height = ½  17  10 = 85 m2 ½  12  7 = 42 m2

  24. Radius = 7 ÷ 2 = 3.5 cm Area = x/360x π x r² = 180/360 x π x 3.5² = 19.2 m² (1dp) Area = ½ (sum of bases) x height = ½(9 + 12) x 7 = 73.5 m² (1dp)

  25. Homework Book Page 170 – 171

  26. STARTERS Find the area of A chocolate bar is wrapped in a rectangular piece of foil measuring 10cm by 15cm. Calculate the area of the piece of foil. How many pieces could be cut out from a larger sheet of foil measuring 120cm by 75cm?

  27. Note 6: Compound Area • Compound shapes are made up of more than one mathematical shape. • To find the area of a compound shape, find the areas of each individual shapes and either add or subtract as you need to.

  28. Examples: find the area of Area splits into a rectangle and a triangle Area = Area rectangle + area triangle = b  h + ½ b  h = 4  5 + ½  4  2 = 24cm2

  29. Area splits into a rectangle with another rectangle taken away Area = area big rectangle – area small rectangle = b  h - b  h = 6  4 – 3  2 = 18m2

  30. Homework Book Page 172 – 174

  31. STARTERS Find the area of Trapezium = 750 Rectangle = 1000 Half Circle = 628.3 Area = 750 + 1000 - 628.3 = 1121.7 cm2

  32. Note 7: Finding missing parts of shapes To find missing sides of shapes, rearrange the formulas. Example 1: The area of the triangle is 135m2. Calculate the height of the triangle. Area = ½  base  height 135 = ½  18  x 135 = 9x x = 15m

  33. Example 2: Calculate the radius of a circle with an area of 65cm2. Area = π r2 65 = π r2 r2 = 65/π r = √65/π = 4.5 cm

  34. EXERCISES: Each of these shapes has an area of 60cm2. Calculate the lengths marked x. 10cm 15cm 2.5cm √60 =7.7cm

  35. EXERCISES: Calculate the radii of these circles with the given areas. 18.7 cm 3.87 m 1.38 cm 0.798 km

  36. EXERCISES: A circle has an area of 39.47m2. Calculate: • Radius • Diameter • circumference 3.55 m 7.09 m 22.27 m

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