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KS3 Mathematics

KS3 Mathematics. S7 Measures. S7 Measures. Contents. S7.2 Estimating measurements. S7.1 Converting units. S7.3 Reading scales. S7.4 Measuring angles. S7.5 Bearings. Metric units. Kilo-. The base unit for length is metre.

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KS3 Mathematics

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  1. KS3 Mathematics S7 Measures

  2. S7 Measures Contents S7.2 Estimating measurements S7.1 Converting units S7.3 Reading scales S7.4 Measuring angles S7.5 Bearings

  3. Metric units Kilo- The base unit for length is metre. The metric system of measurement is based on powers of ten and uses the following prefixes: meaning 1000 Centi- meaning one hundredth Milli- meaning one thousandth Micro- meaning one millionth These prefixes are then followed by a base unit. metre. The base unit for mass is gram. gram. The base unit for capacity is litre. litre.

  4. Metric units of length 1 kilometre (km) = Metric units used for length are kilometres, metres, centimetres and millimetres. 1000 metres (m) 1 metre (m) = 100 centimetres (cm) 1 metre (m) = 1000 millimetres (cm) 1 centimetre (cm) = 10 millimetres (cm)

  5. Metric units of length A race track measures 400 m. An athlete runs 2.6 km around the track. How many laps is this? 400 m = 0.4 km Number of laps = 2.6 ÷ 0.4 = 6.5 laps The following day the athlete completes 8 laps. How many km is this? 8 laps = 8 × 0.4 m = 3.2 km

  6. Metric units of mass 1 tonne = Metric units used for mass are tonnes, kilograms and grams and milligrams. 1000 kilograms (kg) 1 kilogram (kg) = 1000 grams (g) 1 gram (g) = 1000 milligrams (mg)

  7. Metric units of mass 60 tea bags weigh 150 g. How much would 2000 tea bags weigh in kg? We can solve this problem using a unitary method. 60 tea bags weigh 150 g So, 1 tea bag weighs (150 ÷ 6) g = 2.5 g Therefore, 2000 tea bags weigh (2.5 × 2000) g = 5000 g = 5 kg

  8. Metric units of capacity 1 litre (l) = Capacity is a measure of the amount of liquid that a 3-D object can hold. Metric units of capacity are litres (l), centilitres (cl) and millilitres (ml). 100 centilitres (cl) 1 litre (l) = 1000 millilitres (ml) 1 centilitre (cl) = 10 millilitres (ml)

  9. Metric units of capacity A bottle contains 750 ml of orange squash. The label says: Dilute with 4 parts water. How many of litres of drink can be made with one bottle? If the whole bottle was made up we would have 750 ml of squash + (4 × 750) ml of water = 750 ml of squash + 3000 ml of water = 3750 ml of drink = 3.75 l of drink

  10. Converting metric units To convert from a larger metric unit to a smaller one we need to _______ by 10, 100, or 1000. multiply Complete the following 34 cm = mm 340 0.0471 km = m 47.1 0.4 l = ml 400 0.3428 m = mm 342.8 7.3 kg = g 7300 23.51 g = mg 23 510 54.8 cl = ml 548 0.085 m = mm 850

  11. Converting metric units To convert from a smaller metric unit to a larger one we need to _______ by 10, 100, or 1000. divide Complete the following 920 mm = cm 92 65800 m = km 65.8 530 g = kg 0.53 526 mg = g 0.526 3460 ml = l 3.46 4539 cl = l 45.39 43.1 cm = m 0.431 87 kg = tonnes 0.087

  12. Converting metric units

  13. Imperial units of length 1 foot (ft) = Commonly used imperial units used for length include inches, feet, yards and miles. 12 inches (in) 1 yard = 3 feet (ft) 1 mile = 1760 yards Although these units can be difficult to convert between they are still in common use, for example, for road traffic signs and related measurements of speed.

  14. Imperial units of length 1 inch  We can convert between metric and imperial units of length using the following approximations: 2.5 cm 1 foot (or 12 inches)  30 cm 1 yard (or 3 feet)  just under 1 metre 5 miles  8 km (or 1 mile  1.6 km)

  15. Imperial units of length Paris 260 Calais 34 Dieppe 144 The following road sign was seen from the side of the motorway in France. What are the distances in miles? 8 km  5 miles 1 km  0.625 miles Distance to Paris  (264 × 0.625) miles = 165 miles Distance to Calais  (36 × 0.625) miles = 22.5 miles Distance to Dieppe  (144 × 0.625) miles = 90 miles

  16. Imperial units of mass 1 pound = Commonly used imperial units used for mass include ounces, pounds, and stone. 16 ounces 1 stone = 14 pounds Although these units can be difficult to convert between they are still in common use, for example, most people weigh themselves in stones.

  17. Imperial units of mass 1 ounce (oz)  We can convert between metric and imperial units of mass using the following approximations: 30 grams 1 pound  just under ½ kilogram (or 1 kilogram  2.2 pounds) 1 stone  just over 6 kg

  18. Imperial units of mass Which is cheaper: apples costing 53p per kilo or apples costing 25p per pound? 1 kilogram  2.2 pounds So, (2.2 × 25)p per pound 24p per pound  = 55p per pound The apples priced at 53p per kilo are cheaper.

  19. Imperial units of capacity 1 gallon = Commonly used imperial units used for capacity include fluid ounces, pints, and gallons. 8 pints 1 pint = 20 fluid ounces Although these units can be difficult to convert between they are still in common use, for example, beer and milk are still commonly measured in pints.

  20. Imperial units of capacity 1 gallon  We can convert between metric and imperial units of capacity using the following approximations: 4.5 litres 1 pint  just over ½ litre (or 1 litre  1.75 pints)

  21. Imperial units of capacity Therefore, 1 gallon of petrol costs  A litre of petrol costs 84.7 p. Approximately, how much would 1 gallon cost? 1 gallon  4.5 litres 4.5 × 84.7 p = 381.15 p = £381.15

  22. Imperial to metric conversions

  23. Spider diagram

  24. Units of area 1 cm 1 cm Area is measured in square units. Here is a square centimetre or 1 cm2. How many mm2 are there in a cm2? 1 cm × 1 cm = 1 cm2 = 10 mm 10 mm × 10 mm = 100 mm2 So, = 10 mm 1 cm2 = 100 mm2

  25. Units of area 1 m 1 m Area is measured in square units. Here is a square metre or 1 m2. How many cm2 are there in a m2? 1 m × 1 m = 1 m2 = 100 cm 100 cm × 100 cm = 10000 m2 10000 m2 So, = 100 cm 1 m2 = 10000 cm2

  26. Units of area 1 km2 = m2 We can use the following to convert between units of area. 1 000 000 1 hectare = 10 000 m2 1 m2 = cm2 10 000 1 m2 = mm2 1 000 000 1 cm2 = mm2 100

  27. Units of area A rectangular field measures 150 m by 250m. What is the area of the field in hectares? The area of the field is 150 m × 250 m = 37 500 m2 250 m 1 hectare = 100 m × 100 m = 10 000 m2 37 500 m2 = 3.75 hectares 150 m

  28. Units of volume 1 cm 1 cm 1 cm Volume is measured in cubic units. Here is a cubic centimetre or 1 cm3. How many mm3 are there in a cm2? = 10 mm 1 cm × 1 cm × 1 cm = 1 cm3 10 mm × 10 mm × 10 mm = 1000 mm3 = 10 mm 1 cm3 = 1000 mm3 So, = 10 mm

  29. Units of volume 1 m 1 m 1 m Volume is measured in cubic units. Here is a cubic metre or 1 m3. How many cm3 are there in a m2? = 100 cm 1 m × 1 m × 1 m = 1 m3 100 cm × 100 cm × 100 cm = 1 000 000 cm3 = 100 cm 1 m3 = 1 000 000 cm3 So, = 100 cm

  30. Units of volume 1 km3 = m2 We can use the following to convert between units of volume. 1 000 000 000 1 m3 = cm3 1 000 000 1 m3 = mm3 1 000 000 000 1 cm3 = mm3 1000

  31. Units of volume Dice are packed into boxes measuring 20 cm by 12 cm by 10 cm. If the dice are 2 cm cubes, how many of them fit into a box? The volume of the box = (20 × 12 × 10) cm3 = 2400 cm3 The volume of one dice = (2 × 2 × 2) cm3 = 8 cm3 Number of dice that fit in the box = 2400 ÷ 8 = 300 dice

  32. Volume and capacity 1 l = Capacity is a measure of the amount of liquid that a 3-D object can hold. A litre of water, for example, would fill a container measuring 10 cm by 10 cm by 10 cm (or 1000 cm3) 1000 cm3 1 ml = 1 cm3 1000 l = 1 m3

  33. Volume and capacity

  34. Volume and capacity Which holds more juice when full; a litre bottle or a carton measuring 6 cm by 10 cm by 20 cm? The volume of the carton is (6 × 10 × 20) cm3 = 1200 cm3 1 litre = 1000 cm3 The carton holds more juice.

  35. Converting units of area, volume and capacity 3 ha = m2 4000 m2 = ha 2.8 m3 = l 6 200 cm2 = m2 4.35 cm2 = mm2 9.6 cl = cm3 0.07 cm3 = mm3 38 000 cm3 = m3 0.72 l = cm3 5630 cm3 = l Complete the following 30 000 0.4 2800 0.62 435 96 70 0.038 720 5.630

  36. Units of time 1 minute (min) = Time does not use the metric system. Units of time include years, months, weeks, days, hours (h), minutes (min) and seconds (s). 60 seconds (s) 1 hour (h) = 60 minutes (min) 1 day = 24 hours (h) 1 week = 7 days 1 year = 365 days = 52 weeks 1 leap year = 366 days

  37. Units of time A machine takes 4 minutes and 10 seconds to make a toy car. How long would it take to make 18 toy cars? 4 minutes × 18 = 72 minutes 10 seconds × 18 = 180 seconds = 3 minutes 72 minutes + 3 minutes = 75 minutes = 1 hour 15 minutes

  38. S7 Measures Contents S7.1 Converting units S7.2 Estimating measurements S7.3 Reading scales S7.4 Measuring angles S7.5 Bearings

  39. Choosing units What units would you use to measure the following: The mass of a child Kilograms The length of a finger nail Millimetres The area of a field Hectares The mass of an ant Milligrams The distance between two cities Kilometres The capacity of a pool Litres The volume of a room Cubic metres The distance between two stars Light years

  40. Estimating measurements The height of a door is about 2 m. The mass of a large bag of sugar is 1 kg. A tea spoon holds 5 ml of liquid. Most adults between 1.5 and 1.8 m tall. A small car weighs about 1 tonne. The mass of a large bag of sugar is 1 kg. The area of a football pitch is 7500 m2. The capacity of a can of drink is 330ml. It takes about 20 minutes to walk one mile. When we estimate measurements we usually compare known measurements to find unknown measurements. Some useful measurements to know are:

  41. Estimating measurements

  42. S7 Measures Contents S7.1 Converting units S7.2 Estimating measurements S7.3 Reading scales S7.4 Measuring angles S7.5 Bearings

  43. Reading scales C A B 4 5 3 What numbers are the arrows pointing to on the following scale? 2.8 3.8 4.4 Each small division is worth 1 ÷ 5 = 0.2 A is pointing at 3.8 B is pointing at 4.4 C is pointing at 2.8

  44. Reading scales What numbers are the arrows pointing to on the following scale? 57.5 C C 72.5 B B A 65 70 80 60 Each small division is worth 10 ÷ 4 = 2.25 A is pointing at 65 B is pointing at 72.5 C is pointing at 57.5

  45. Reading scales What numbers are the arrows pointing to on the following scale? C 1.96 A 2.03 B 2.165 2.1 2.0 2.2 Each small division is worth 0.1 ÷ 10 = 0.01 A is pointing at 2.03 B is pointing at 2.165 C is pointing at 1.96

  46. Reading scales

  47. S7 Measures Contents S7.1 Converting units S7.2 Estimating measurements S7.4 Measuring angles S7.3 Reading scales S7.5 Bearings

  48. Measuring angles An angle is a measure of turn and is usually measured in degrees. A full turn measures 360°. 360°

  49. Measuring angles An angle is a measure of turn and is usually measured in degrees. A quarter turn measures 90°. It is called a right angle. 90° We label a right angle with a small square.

  50. Measuring angles An angle is a measure of turn and is usually measured in degrees. A half turn measures 180°. This is a straight line. 180°

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