Measurement

1. Measurement Year 7 & 8

2. Length • A length is a distance. • In Australia we use the metric system for measurement and the base unit is the metre. • The length of an object is commonly measured in: • millimetres (mm) • centimetres (cm) • metres (m) • kilometres (km).

3. 1km = 1000m (km m = x1000) • 1m = 100cm (m cm = x100) • 1cm = 10mm (cm mm = x10) From this information you can create a Length conversion chart: km 1000 1000 m 100 100 cm 10 10 mm

4. Length Conversions • Write the question. • Use the conversion chart to identify conversion factor. • Multiply or divide original measurement. • Put correct units. Eg/ Complete the following metric conversions. • 756m=__________ km • 0.034km (m) • 374cm=_________m • 54cm (mm) • 380mm (cm) • 374cm (km)

5. Length Conversions

6. Length Conversions

7. Classwork Year 7 Text: Cambridge Essential Maths 7: Chapter 11 • Ex 11B Q4a-f, 5a-c, 6g-h, 7a-f, 10a, b, 12, 13, 17, 19

8. Length Conversion: Exit questions Complete the following metric conversions. • 38m=__________ km • 24cm=_________mm • 49cm (m) • 380m (mm)

9. Geometric symbols • Similarly marked segments are congruent (the same length) • A box in the corner of an angle denotes a right angle

10. Perimeter • Perimeter is the measurement of the distance (length) around the outside of a 2D shape. • To calculate the perimeter of an object we add the length of all of the sides together once they are in common units. 8cm 5cm

11. Calculating Perimeter • Convert all dimensions (measurements) to the same units (mm, cm, m, km). • Calculate and record any missing lengths. • Add all lengths together. • Put correct units. Examples: 5m 98cm 4cm 1. 3. 4m 8cm 4m 9cm 10m 5cm 2. 4. 9mm 8mm

12. Calculating Perimeter

13. Calculating Perimeter

14. Calculating Perimeter

15. Classwork Year 7 Text: Cambridge Essential Maths 7: Chapter 11 • Ex 11C Q1, 3, 4, 5, 6, 8, 11 Remember to show all working Year 8 Text: Cambridge Essential Maths 8: Chapter 4 Ex 4A Q3, 5a,b,e,f,I,j,m,n, 6, 7c-f, 8a-d, 10 Remember to show all working

16. Perimeter: Exit questions

17. Area is the amount of space inside a 2D shape. • The area is measured in squared units (mm2, cm2, m2 or km2). • Units are squared units as you are calculating how many 1x1 squares would fit inside the shape! Area • 1km2=1 000 000m2 (km2 m2= x10002) • 1m2=10 000cm2 (m2 cm2= x1002) • 1cm2=100mm2 (cm2 mm2= x102) if 1cm = 10mm then 1cm x 1cm = 10mmx10mm =102 mm2 =100mm2 10mm 1cm

18. Calculating Areas of 2D shapes • Convert all dimensions (measurements) to the same units (mm, cm, m, km). • Write formula and dimensions. • Substitute values into formula. • Solve. • Put correct units.

19. Area (Year 7&8)

20. Area (Year 7&8)

21. Area (Year 7&8)

22. Area (Year 7&8)

23. Area (Year 8)

24. Area (Year 8)

25. Area (Year 8)

26. Classwork Year 7 Text: Cambridge Essential Maths 7: Chapter 11 • Ex 11D 6a-f • Ex 11E 4a-e • Ex 11F 3a-d Remember to show all working Extension • Ex 11D 7, 10, 12 • Ex 11E 3, 6, 10, 11 • Ex 11F 6, 8 Year 8 Text: Cambridge Essential Maths 8: Chapter 4 • Ex 4C 5a-f • Ex 4D 3a,b,d,e,g,h,j,k Remember to show all working Extension • Ex 4C 1a,b, 2, 6 • Ex 4D 6, 7, 8

27. Area: Year 7 exit questions Write the formulae for the following shapes a) b) c) d) e) f)

28. Area Conversions • Remember: Area is the amount of space inside a 2D object. Units are squared units as you are calculating how many 1x1 squares would fit inside the shape! if 1cm = 10mm then 1cm x 1cm = 10mmx10mm =102 mm2 =100mm2 • 1km2=1 000 000m2 (km2 m2= x10002) • 1m2=10 000cm2 (m2 cm2= x1002) • 1cm2=100mm2 (cm2 mm2= x102) 10mm 1cm

29. Area continued • From this you can create an area conversion chart: km2 10002 10002 m2 1002 1002 cm2 102 102 mm2

30. Area conversion

31. Area conversion

32. Circles • Diameter (D): The distance across a circle from one side to the other, passing through the centre. • Radius (r): The distance from the side of a circle to the centre. r D • Calculations for measurements involving circles involve a special number called π (pi pronounced pie). • The value of πis close to 3.14159… However, you should always use the πbutton on your calculator when calculating with πunless told otherwise.

33. Circumference of a circle • The circumference of a circle is the distance around the outside (perimeter) of a circle. The formula for the circumference of a circle is: Circumference =πx Diameter =πD or Circumference = 2xπxradius =2πr C=2πr To remember: Twinkle, Twinkle little star Circumference of a circle is 2πr

34. Area of a circle • The formula for the area of a circle is: Area = πx radius x radius =πr2 Area =πx r x r =πr2

35. Circumference and Area of a circle: Examples Calculate the circumferences and areas of the following circles. a) b) c) d) 8cm 20mm 13m 52km

36. Area of a circle

37. Area of a circle

38. Classwork Year 8 Text: Cambridge Essential Maths 8: Chapter 4 • Ex 4B Q5a,b,d,e • Ex 4E Q3, Q5a,d,e, Q6a,d,f Remember to show all working Extension: • Ex 4B Q6 • Ex 4E Q

39. Circles: Exit questions Calculate the circumferences and areas of two circles below. a) b) 5km 25cm

40. Area of a circle

41. Areas of composite shapes

42. Areas of composite shapes

43. Areas of composite shapes

44. Areas of composite shapes

45. Areas of composite shapes

46. Areas of composite shapes

47. Areas of composite shapes

48. Areas and perimeters of sectors • A sector is a portion of a circle enclosed by two radii.