1. Measurement AS 1.3 3 credits

2. Metric System Length is measured in metres Capacity is measured in litres Weight in grams c means one hundredth - 100 cm in 1 metre m means one thousandth – 1000mm in 1 metre k means 1000 - 1000g in 1 kg Convert 300 g to kg30 cm to m 2000mm to m5kg to g 300cm to mm2000mg to kg 0.3kg 0.3 m 2m 5000g 3000mm 0.002kg

3. Perimeter The perimeter is the outside edge of a shape. For a – Polygon, you add the lengths of the sides – Circle, it is 2πr, the circumference Examples. Find the perimeter of 6cm 3cm 2cm 3cm 2cm 4cm 5cm 4 cm Watch all measurements are in the same unit!!!! 6+6+3+3 =18 cm 4+4+5= 13 cm 2+2+4+4+3= 15 cm 2 π x 5 = 31.4 cm

4. Find the perimeter of 4m 6m 5m 22cm 28m 56cm 36cm 25.2m 100cm 23.1m 15.7m 37.7m

5. 36cm 40cm 17cm 30 mm 24 m 32 mm 35.8 mm 34cm 26 m 32 m

6. Find the Perimeter 837 m 17.2 m 11.6 km 14.8 cm

7. Circumference of a Circle or E.g. Calculate the circumference of these circles 3cm 64mm 9.42cm (2dp) 402.12mm (2dp)

8. Find the perimeter 24cm 32cm 20 m 40m

9. h b h b a Area Rectangle – Area = b x h Parallelogram – Area = b x h Triangle – Area = ½ b x h Trapezium – Area = ½(a + b) x h Circle – Area = π r 2 h b r3cm h b 4cm 6cm 3cm 8cm 6 cm 8cm A = 4x6 =24cm 2 A = 3 x 8 = 24cm 2 A = ½6x8 = 24cm 2 A = ½(3+6)x2 = ½(9)x2 = ½ x 18 = 9cm 2 A = π 3 2 = 9 π = 28.26cm 2 3cm 6cm 2 cm

10. 42.25cm 2 54 mm 2 30 cm 2 35 m 2 90 cm 2 42 m 2

11. Revision centre diameter radius chord circumference arc segment sector

12. 56.52 cm 254.34 cm 2 37.68 cm 113.04 cm 2

13. Find the area 40cm 2 60cm 2 12m 2 40mm 2 5mm

14. 56 cm 2 70cm 2

15. 117 cm 2 187 m 2 84.36 mm 2 100 mm 2

16. 26cm 42cm 2 5.6m 1.96m 2 503mm 94.2cm 216cm 3 12000cm 3

17. Composite Shapes To find the area of a compound shape, break it into pieces and find the area of each part

18. 4cm 12cm 248 cm 2 200 cm 2 48 cm 2 144 cm 2 80 cm 2 244 cm 2 1cm 3 cm 2 1cm 2 4cm 2 8cm 2

19. Try these find the light shaded area 13cm 2 8cm 2 16cm 2 10.2cm 2

20. 1.7 m 2 6.8 m 2 yes

21. More compound shapes 36 96

22. 52 62.8

23. 53.94cm 2 5.46 cm 2 Shaded Area 53.94 – 5.46 = 48.48cm 2 28 cm 2 78cm 2 Shaded Area = 78 – 28 = 50 cm 2

24. 52.5 m 2 6.75 m 2 200 m 32000 + 59600 = 91600m 2

25. Circles! Find the Area 167.4 m 2 4.15 cm 2 18.10 m 2 227.2 cm 2 8.73 m 2

26. Surface area To find the surface area, you find the areas of all the sides of a shape and add them up Rectangular Prism – You have two sides with Area = h x b – two with sides Area = b x l – two with sides Area = h x l Surface Area = 2 x (4 x 8) + 2x (8 x 5) + 2 x (4 x 5) = 184m 2 b h l 8m 4m 5m

27. Try these 4m 3m 8m 5m 6m 10m 12m 5m 4m 10m 5m 4m 2 (8x4)+2(3x4) +2(8x3) = 136m 2 120+100+60=280 m 2 40+120+96 = 256m 2 40 + 80 + 100 = 220m 2

28. Sphere surface area = 4πr 2

29. Surface Area of a Cylinder 25cm 15 cm To find the surface area of a cylinder we find the area of the circular top and bottom, and then we find the area of the curved surface area. If we were to flatten it out, it would be a rectangle. Area of circular top and bottom: Curved Surface Area: Surface Area:

30. 301.6cm 2 603.2cm 2 2789.7cm 2 318.9cm 2

31. Try these: Ex 7.7 pg 110 54 cm² 350cm² 396cm² 1740cm²

32. Do Now: A circular stage has an 8m diameter and a height of 30cm. Find the surface area of the stage. Area of Circle (top) Area of curved face: Total Surface Area: (1dp)

33. Volume 5m 2m 3m 4m 5m 3m 4cm 2cm V = 5 x 2 x 3 = 10 x 3 = 30 m 3 V = π x 2 2 x 4 = 12.57 x 4 = 50.27 cm 3 V = ½ x 4 x 3 x 5 = 6 x 5 = 30 m 3

34. Find the volume, given the area of the face 300 m 3 315.2 m 3 600 m 3 40.6 m 3

35. Find the Volume of these prisms 720 m 3 324 m 3 768 m 3 480 m 3 525 m 3

36. More Volumes… Volume of a Pyramid Volume of a Cone Volume of a Sphere These formulas are given to you! 5m

38. Capacity 1 cm 3 = 1ml 1.How many ml in 10cm 3 ? 2.How many ml in 1000mm 3 ? 3.How many ml in 1m 3 ? 4.How many cm 3 in 23ml? 5.How many cm 3 in 2l? 6.How many mm 3 in 25ml? 7.How many mm 3 in 0.5ml? 1.10 ml 2.1000mm 3 = 1cm 3 so 1ml 3.1m 3 =100x100x100 cm 3 so 1000000ml 4.23cm 3 5.2l = 2000ml so 2000cm 3 6.25ml = 25cm 3 so 10x10x10x25 =25000mm 3 7.= 0.5cm 3 = 10x10x10x0.5 =500mm 3

39. Time 4:10 6:45 7:25 12:05 7:15 3:50 Time is measured in Seconds 60 seconds gives a minute 60 minutes gives an hour 24 hours give a day 7 days give a week 52 weeks give a year Time during the day is measured using 12 hour or 24 hour time With 12 hour time am = morning pm = afternoon 12:00 am = midnight 12:00 pm = midday With 24 hour clock, you add 12hours to the pm time. It is always written with 4 digits e.g. 1:30 pm = 12 + 1:30 = 13:00

40. 6:10 am 2:23 pm 11:45pm 6:13 am 0:27 am 5:37 pm 8:56 pm 6:28am 9:05pm 4:38am 02:05 17:30 21:15 01:55 12:35 05:23 21:45 14:07 11:07 18:57

41. 4hours 53 mins 6 hours 22mins 5km 10 mins 2 km 30 mins 4 km5.5 km/hour

42. Fearless Flyers Build a paper aeroplane (follow the provided instructions if you need them) Fly your plane 5 times – each time measuring and recording the distance it flew with a tape measure. Use a stopwatch to time the length each flight takes. Calculate the average of your top 3 values for both distance and duration. Using calculate the speed for your average flight s d t

43. Distance, speed (velocity) and time Units Distance km or m Speed km/h or m/s Time Hours or seconds s d t Distance = speed × time Speed = distance ÷ time Time = distance ÷ speed

44. Try these: 1.A car travels for 2 hours at a steady speed of 85 km/h. What distance has it covered? 2.A bus makes a journey of 180km. It takes 3 hours. Calculate the average speed of the bus. 3.A truck travels at an average speed of 75km/h for a distance of 300km. What time does the journey take? 4.How many minutes does it take to run 1500m at an average speed of 10km/h? 170km 60 km/h 4 hours 0.15 hours = 9 minutes

45. Rosie, Millie and Hayley are all members of a cycling club. The table shows their training schedule. Complete the missing entries. 1. Change 45km/h into m/s. 2. Change 74m/s into km/h. 3. Change 10.8m/s into km/h. DistanceSpeedTime Rosie12 km40 km/h Millie90 km2 hours Hayley60 km/h1½ hours 18 mins 45 km/h 90 km 12.5 m/s 266.4 km/h 38.88 km/h

46. $0.87 $46 $6.25 $0.15 12.5cper g if sold per kg 13.5c if sold per 100g

47. Rates A rate compares two quantities measured in different units. It describes how one quantity changes compared with another. Speed - compares distance travelled with time taken, often measured in m/s or km/hr. Growth – compares increase in numbers or size over time. Eg. A goat eats 110kg of grass in 50 days. Calculate the rate at which the goat is eating per day. 110kg = 2.2kg/day 50complete worksheet 15.01

49. Do Now: Find the perimeter of this shape: Find the volume of the golf ball: Find the surface area of the box: 8cm 5cm 3cm 5cm 15cm 61.46cm r = 1.8cm 24.4cm³ 158cm²

50. Try these: 170 m 120 m 240 m Find the area of this paddock in ha Work out the volume: a)in cm³ b)in litres (round to the nearest whole number) 88cm 52cm A = 34 800m² = 3.48 ha a) V = 186 887 cm³ b) 187 litres