2. Functional Maths revision September 2012. Kindly contributed by Joaquin Llorente, Trafford College. Search for Joaquin on www.skillsworkshop.orgwww.skillsworkshop.org Visit the download page for this resource to find detailed teaching notes, curriculum links and related resources. September 2012. Kindly contributed by Joaquin Llorente, Trafford College. Search for Joaquin on www.skillsworkshop.orgwww.skillsworkshop.org Visit the download page for this resource to find detailed teaching notes, curriculum links and related resources. Curriculum links Covers many aspects of Level 1 and Level 2 Functional Mathematics and Adult Numeracy. References: Excellence Gateway (2009), Skills for Life, Core Curriculum http://www.excellencegateway.org.uk/sflcurriculum http://www.excellencegateway.org.uk/sflcurriculum Ofqual (2009), Functional Skills criteria for English, Mathematics and ICT http://www.ofqual.gov.uk/qualification-and-assessment-framework/89-articles/238-functional-skills-criteria

3. Choose an option AveragesRatioRounding Units of Measure Area & Perimeter Tables GraphsChartsFormula Averages & Range Ratio, Scale & Proportion Fractions & Percentages Units of Measure Perimeter, Area & Volume Coming soon: Tables Coming soon: Time & Money Charts and Graphs Coming soon: Formula

4. Return Averages & Range

5. Ratio, Scale & Proportion Return

6. Units of Measure

7. Return Charts

8. Median and mode Return MOde is the MOst common value - there may be more than one mode - or no mode at all MEDian is the MIDdle value, but remember to put them in order first

9. Mean The other averages are easy to work out; this one is a “mean” sum... Add them all together and divide by how many there are Return

10. Range Return Difference between the highest and the lowest values Range = highest - lowest 301020

11. Ratio in everyday life Mixing cordial and water Making cocktails Baking Mixing hair dyes and peroxide Mixing paint colours Continue

12. Ratio – Key Facts juice : water 1 : 4 Continue Written as a sequence of two or more whole numbers separated by a colon (Read as 1 to 4) To make a Victoria sponge you will need butter, sugar and flour in the ratio butter : sugar : flour 1 : 1 : 1

13. Ratio – Key Facts The order is important Continue juice : water 1 : 4 means 1 part of juice is mixed with 4 parts of water juice : water 4 : 1 means 4 parts of juice are mixed with 1 part of water

14. Ratio – Key Facts Mix juice and water in a 1:4 ratio to make a drink Continue juice : water 1 : 4 1 part of juice is mixed with 4 parts of water to make 5 parts of drink 1 litre of juice will make 5 litres of drink 1 cup of juice will make 5 cups of drink

15. Ratio – Key Facts Sometimes, ratios can be simplified 2 : 6 is the same as 1 : 3 6 : 3 : 9 is the same as 2 : 1 : 3 Continue ÷ 2 ÷ 3

16. Ratio – Key Facts Can be converted into fractions Return juice : water 1 : 4 1 part of juice is mixed with 4 parts of water to make 5 parts of drink 1 out of 5 parts of the drink is juice 1 5 4 out of 5 parts of the drink are water 4 5

17. Scales in everyday life Model toys Prototypes / simulations Maps / Sat-navs Floor plans Continue

18. Scale – Key Facts model size : real size 1 : 75 Continue Usually written as a ratio INTERPRETATION In real size, everything is 75 times bigger than in the model plan size : real size 1 : 200 INTERPRETATION In real size, everything is 200 times bigger than in the plan

19. Scale – Key Facts Scale 1 cm : 10 km Return Sometimes it includes units of measure to make it easier to read Scale 1 : 1,000,000 …is the same, but easier to use than

20. Proportion in everyday life 1 litre of paint covers 10 m 2 12 m of wall paper cost £8 the minimum pay rate for an apprentice is £2.60 per hour Continue

21. Proportion problems 1 litre of paint covers 10 m 2 Continue 10 m 2 1 l 0 0 4 l 40 m 2 How many m 2 can I cover with 4 litres? 20 m 2 2 l 30 m 2 3 l 1 l covers 10 m 2 4 l cover 4 x 10 = 40 m 2

22. Proportion problems 1 litre of paint covers 15 m 2 Return 15 m 2 1 l 0 0 How many litres of paint do I need to cover a surface of 75 m 2 75 m 2 ? To cover 15 m 2 I need 1 litre of paint To cover 75 m 2 I will need 75 ÷ 15 = 5 l

23. Return Tables

24. Fractions and percentages Most Level 1 and Level 2 tests include a question where you need to work out the value of a fraction or a percentage “Normal price £27 Special discount: 1/3 off ” “Manager’s Special: 30% off ” “Out of 250 people, 2/3 chose chocolate cake for their dessert” 90% of students lose marks in the exams because they don’t read the questions properly Continue

25. Fractions and percentages So, how do you work out the value of a fraction or a percentage with a calculator? FractionsPercentages

26. Fractions 3 7 3 7 271of 271 ÷x 22 55 of 75 x÷ Continue

27. Fractions – Checkpoint Use a calculator to work out the value of these fractions: 1 of260 4 2 of75 3 1 of140 7 5 of132 6 ReturnPercentages

28. 4198 ÷ 100x of% 41%98 27126 ÷ 100x of% 27%126 Continue

29. Percentages – Checkpoint 1575of% 32150of% 517of% 1.398of% 14456of% 755of% 12.590of% 3725of% Use a calculator to work out the value of these percentages: ReturnFractions

30. Charts Most charts and graphs are worth 3 marks These are awarded for: Linear scale Clear labelling Plot accuracy Return

31. Charts – Linear Scale 40 30 20 10 5 0   Return

32. Charts - Labelling Manchester Sales MonthFlats sold Jan25 Feb40 Mar30 Apr20 Continue

33. Charts - Labelling  Return

34. Chart – Plot accuracy The bars are the correct height All the bars are the same width Return

35. Bar Charts Show patterns in data Continue

36. Bar Charts Show patterns in data Return Sales in the West region were unusually high in Q3 Otherwise, sales were flat in each region throughout the year

37. Pie Charts Show proportions Return

38. Pie Charts Show proportions Return More than half of the sales were made in the 3 rd Quarter Sales in Q1, Q2 and Q4 were similar

39. Pie Charts Show proportions Return The North region made the most sales (almost 50%) The East region made the least number of sales (just under ¼)

40. Line Graphs Return

41. Line Graphs Return Can be used to show how something changes over time

42. Line Graphs Can be used to convert between currencies (£ and €) units ( o C and o F; km and miles…) Continue

43. Line Graphs Convert €8 into £ € 8 = £6.50 Return

44. Perimeter, Area & Volume P A V

45. Continue Perimeter Is the distance around the outside of a 2-D shape d1 d2 d3 d4 P =+++

46. Continue Perimeter It is measured in units of distance: m, cm, inches… For any 2-D shape, the perimeter can be calculated by adding up the length of all its sides 5cm 4cm 3cm P = 5cm 4cm 3cm ++ P = 12cm

47. Return Perimeter - Checkpoint Work out the perimeter of these shapes 5 cm 3 cm 4 cm P1 5 cm 2 cm P2 P3 8 cm 2.5 cm 3 cm 2.5 cm 4 cm 1 cm 2 cm

48. Area Is the amount of space inside a 2-D shape A square metre (m 2 ) is the area of a 1m by 1m square 1m A = 8 m 2 Continue

49. Area The area of a rectangle can be calculated as the length times the width The length of the rectangle is 6m; we can fit 6 tiles of 1m 2 in a row A = L x W 1m 2 1m 1m 2 L = 6m W = 3m The width of the rectangle is 3m; we can fit 3 rows of 6 tiles A = 18 m 2 A = 6m x 3m

50. Return Area of common shapes A = L x W L W b hA = b x h ÷ 2 r A =  x r 2 (  = 3.14)

51. Continue Volume Is the amount of space contained within a 3-D shape Is measured in cubic units

52. Continue Volume 1m 1m 3 One cubic metre (m 3 ) is the volume of a cube that has 1m edges

53. Continue Volume 1m 3 L=5m W=4m H=3m The length of the cuboid is 5m, so we can fit a row of 5 cubes (5 x 1m 3 = 5m 3 ) The width of the cuboid is 4m, so we can fit 4 rows of 5 cubes (4 x 5m 3 = 20m 3 ) The height of the cuboid is 3m, so we can fit 3 layers of 20 cubes (3 x 20m 3 = 60m 3 ) The volume of a cuboid can be calculated as length x width x height V = L x W x H

54. Return Volume of common shapes V =  r 2 x h r h V = b x h ÷ 2 x l l w h b h l V = l x w x h

55. Return Time

56. Return Tables

57. Return Formula

58. The Metric System The International Metric System was developed and introduced in Europe in the times of Napoleon It is based on the decimal numbering system Conversion factors are always powers of 10 (i.e. larger units are 10, 100, 1000 of the base unit and smaller units are 1/10, 1/100, 1/1000 of the base unit) Return

59. The seven column table This table and 3 simple rules will be the key to converting between units successfully The middle column, with red borders, will hold the basic unit, metre (m), litre (l) or gram (g) Larger units such as kilometre (km) or kilogram (kg) will go to the left and smaller subunits such as centimetre (cm), millimetre (mm), centilitre (cl), millilitre (ml) or milligram (mg) will go to the right

60. Metric Units - Distance m The base unit for measuring distance is the metre (m) We use metres to measure: The height of a door The length of a corridor The length and width of a room

61. Metric Units - Distance kmm We use kilometres (km) for longer distances, such as: The distance between cities (for example, between Madrid and Barcelona, or Manchester and Leeds) The distance to the next services on the motorway The distance from the Earth to the moon (400 000 km)

62. Metric Units - Distance kmmmm We use millimetres (mm) for very small things: The thickness of a coin The diameter of a screw

63. Metric Units - Distance kmmcmmm We use centimetres (cm) for things like: The width or depth of a washing machine The height of a table The width of a shelf

64. Metric Units - Distance kmmcmmm There are other units in the empty columns, but we rarely see or use their names.

65. Check point 1 How many columns do you need for the Metric Unit Conversion Table? In the Metric System … What is the basic unit for distance? What other metric units for distance do you remember? Can you place them in the table?

66. Using the 7 column table In the next few slides we are going to see how to use this table to convert between m, km, mm and cm. We will start by writing the original measurement on the table Then we will see how to convert into the desired unit

67. Convert 32 cm into mm STEP 1 - Write the original measurement into the table kmmcmmm cm23 23

68. Convert 32 cm into mm STEP 2 – Put the decimal point to the right of the target unit kmmcmmm cm23 23 mm=.

69. Convert 32 cm into mm STEP 3 – Fill in with 0s as required kmmcmmm cm23 23 mm= 0 320.

70. Check point 2 Draw the table and the column headings for distance Use the table to convert the following numbers into cm: 350 m 78 mm 5 km 3 mm Return

71. Metric Units - Weight g The base unit for measuring weight is the gram (g) A sugar cube weighs a few grams We use grams to weigh sliced ham (200 g)

72. Metric Units - Weight kgg A more familiar unit for weight is the kilogram (kg): A bag of sugar weighs 1 kg A normal wash-load is 1.5 kg My weight is about 81 kg

73. Metric Units - Weight kggmg We use milligrams (mg) for very small things: The amount of paracetamol in a tablet Return

74. Metric Units - Capacity l The base unit for measuring capacity is the litre (l) A large bottle of Coke contains 2 l The petrol tank of an average car holds 40 l

75. Metric Units - Capacity kll Kilolitres (kl) are rarely used in everyday life The capacity of a swimming pool could be measured in kl but is more commonly measured in thousands of litres instead

76. Metric Units - Capacity kllml A teaspoon is about 5 ml A can of coke is bout 330 ml

77. Metric Units - Capacity kllclml A bottle of wine is 75 cl A drinking cup (paper) is about 20 cl Return

78. Metric Units - Summary kmmcmmm kggmg lclml

79. Conversion of Metric Units Harder examples

80. Convert 3.2 kg into g STEP 1 - Write the original measurement into the table kggmg kg23 23..

81. Convert 3.2 kg into g STEP 2 – Put the decimal point to the right of the target unit kggmg kg23 23.. g=

82. Convert 3.2 kg into g STEP 3 – Fill any gaps with 0s kggmg kg23 23.. g= 00 3 200

83. Check point 3 In the Metric System… What is the base unit for weight? What other weight units can you remember? What is the base unit for capacity? What other units of capacity can you remember?

84. Harder examples - STEP 1 Write on the table: km kg mglmgl cm cl mm mg ml 0.5 m 3.5 kg 2.7 cl 51.2 m 5 3 72 521 0.. 5..

85. Harder examples - STEP 2 Move the decimal point: km kg mglmgl cm cl mm mg ml 0.5 m 3.5 kg 2.7 cl 51.2 m 5 3 72 521 0.. 5.. = = = = cm mg ml km

86. Harder examples - STEP 3 Fill any gaps with 0s: km kg mglmgl cm cl mm mg ml 0.5 m 3.5 kg 2.7 cl 51.2 m 5 3 72 521 0.. 5.. = = = = 0 50 3 500 000 00000 27 00 0.0512 cm mg ml km

87. Check point 4 Use the conversion table to answer these questions: How many cm in 1 m? How many cl in 2 l? How many g in 1kg? 1m is the same as _________ km 1mg is the same as __________ g