1. Week 18 Understand and use scale & general revision of task 2
Functional MATHS
Week 18
Understand and use scale & general revision of task 2

2. Starter Activity- A Mean Set
A set of five numbers has:
A mode of 12
A median of 11
A mean of 10
What could the numbers be?
7, 8, 11, 12, 12

3. Recap – what did we do last lesson?

4. What did we do last lesson?
Statistics: Understand and use graphs
and charts
Extract and interpret information from tables, diagrams, charts and graphs
Collect and represent data in different ways
Bar charts
Line graphs
Pie charts (L2)
Scattergraphs
Find mean and range (L1), median and mode (L2) of data

5. Re-cap Charts and Graphs
What charts and graphs can you remember from week 2 (and from our revision session last week)? 1. 2. 3. 4.

6. Bar Charts Bar charts are used to compare data
The bars are usually vertical but can be horizontal
What must bar charts contain?
Title
Horizontal and vertical axes
Correct scale – going up in equal amounts
Labels
Must start at zero

7. Draw a Bar Chart
Using the data below create a bar chart to show the amounts of different colour cars
Remember to include a title and labels and USE A RULER!
Car Colour
Frequency
Black 10
Blue 7
Red 16
Yellow 4
White 9

8. How did you do?
What is the modal colour car?

9. Scattergraphs
Scatter graphs are used to see if there is a connection (relationship) between 2 sets of data
Like the line graph the axes must be evenly spaced, but the scales don’t have to be the same on each axis
How do we plot a scattergraph?
Horizontal and vertical axis – data labels
You plot points on the grid, but you do not join the points
Use a ruler to draw a line of best fit
Describe the correlation (relationship) – positive, negative or no correlation

10. Example – is there a relationship?

11. Number of ice-creams sold
Scattergraph – your turn
The data below shows how many ice-creams a beach shop sells over a number of days in June.
Create a scattergraph to see whether there is a link between the temperature and the number of ice-creams sold.
Temperature (°C) 21 26 15 23 18 29 20 27 22 17 30 19
Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54
100 62

12. Hint – what scale should I use?
Temperature (°C) 21 26 15 23 18 29 20 27 22 17 30 19
Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54
100 62
First decide on the scale for your axes.
Highest x value = 30
Lowest x value = 15
Highest y value = 100
Lowest y value = 50

13. Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54 100 62
Temperature (°C) 21 26 15 23 18 29 20 27 22 17 30 19
Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54
100 62
Plot the values on your axes, x first, then y.
100
Number of ice-creams sold 90 80 70 60 50 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)

14. Make a comment about what the trend line shows
Temperature (°C) 21 26 15 23 18 29 20 27 22 17 30 19
Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54
100 62
Draw a line of best fit.
100
Number of ice-creams sold 90 80 70 60
Make a comment about what the trend line shows 50 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)

15. Number of ice-creams sold
100
Number of ice-creams sold 90 80 70 60 50 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)
Estimate how many ice creams will be sold when the temperature is forecast to be 25°C.
Identify 25°C.
Draw a line to meet the line of best fit…
Then to the other axis.
=83 ice creams.

16. Number of ice-creams sold
Averages re-cap
Now calculate the mean, mode, median and range for the temperature and the number of ice creams sold
Temperature (°C) 21 26 15 23 18 29 20 27 22 17 30 19
Number of ice-creams sold 70 86 50 80 58 96 66 92 74 54
100 62

17. Why are they misleading?
Misleading graphs
Why are they misleading?

18. True or False: Sales are rising rapidly!
4370
4360
4350
4340
Sales
4330
4320
The graph is misleading because it suggests that sales have increased significantly over a five year period. In reality they have only increased by 70 units, which is not much given that they are selling thousands.
4310
4300
2000
2001
2002
2003
2004
2005
Year

19. This may help to explain the previous slide

20. 1. Which is the better graph – and why. 2
1. Which is the better graph – and why? 2. Where is the spelling mistake – and why?

21. Scale made very small to make graph look very big

22. Scale made very small to make graph look very big

23. The scale is so compressed that it’s hard to see any difference among the brands.

24. Although the vertical scale starts at 0, it does not go up in even steps. This distorts the graph, and makes it look as though the biggest jump is between 1 and 2, rather than 3 and 4.
Also, there are no labels on the axes, so we have no idea what this graph represents!

25. The graph suggests that the stock will continue to increase through 2020, but there’s no way to foresee the future.

27. On this pictogram, there is no category for people who do not own a pet. The pictures are different sizes, and it appears that more people own a horse than any other animal.
An improvement would be to redraw the pictogram, with each of the animals the same size and aligned with one another.

28. True or False: There are more 15 year old boys than girls.
18 year olds
18 year olds
15 year olds
15 year olds
17 year olds
17 year olds
False. We cannot make this conclusion from these graphs because we don’t know the totals. There might be 10 boys in total, making roughly 5 aged 15, but 100 girls, 30 of which are 15. It only tells us the proportion of 15 year olds.
16 year olds
16 year olds

29. True or False: Twice as many people like Thrillers than Romance films.
150
120
100 60
Number of People 40 25
The scale on the vertical axis is not linear, so even though the green bar is twice as big as the purple bar, it does not represent twice as many people. 20 5
Horror
Comedy
Action
Romance
Thriller
Favourite Films

30. Summary of points Scale doesn’t start at zero
Scale made very small to make graph look very big
Scale values or labels missing from the graph
Information missing from a pie chart
Incorrect scale placed on the graph
Size of images used in pictograms are different for the different categories

31. Hand in for marking please!
Directed study
Hand in for marking please!

32. What are we going to do today?
Understand and use scale and general revision of task 2
Use metric units in everyday situations (and imperial at Level 2)
Understand, estimate, measure and compare length
Use and interpret maps or scale drawings / draw to scale
Practice task 2 question

33. Can I … create a bar chart?
Display the following information on a bar chart, remember labels and a title
Pets
Amount
Cat 7
Dog 9
Hamster 3
Snake 1
Fish

34. Can I … draw a trend line/line of best fit?
Draw a trend line on the scattergraph
What can you use a trend line/line of best for?

35. Can I … check my answer using a reverse calculation?
Example question: Show a check of one of your calculations.
Check it by a different method to the one you originally used – in this case use reverse calculation
Original Calculation
Reverse Calculation
= 175
686 – 321 = 365
284 ÷ 4 = 71
522 x 39 = 20358

36. Can I … create a probability scale?
What is the likelihood of the person being selected having more than 3 cups of tea per day?
Show your working.
Probability
Working

37. Can I … calculate a percentage of an amount?
Calculate 17% of £90

38. Can I … create a flow chart?
Create a flow chart to put the steps of how to calculate the cost of a £90 coat with a 17% discount
Start
Answer

39. Can I … create a time line?
Create a time line to show the following events:
Leave house at 8am, arrive at train station at 8:15am, train leaves at 8:25am and arrives in London at 11:55am

40. Can I … calculate a fraction of an amount?
Calculate of £90

41. Can I … use formula?
The cost of hiring a cement mixer is calculated using the following formula:
C = 50+15d
Where
C = cost in £
d = number of days the cement mixer is hired for
Calculate the cost of hiring the mixer for 7 days

42. Can I … round appropriate to the situation?
A company spends £ on lunch for it’s staff day. There are 179 members of staff. How much do they spend on lunch for each staff member?
A relay race is being organised. There are 163 people who want to take part. Each team needs 4 people in. How many teams will be able to take part?

43. Can I … use correct units of measure?
1 foot is equivalent to metres.
You want to install a desk that is 5 feet long along a wall that is 1.5m. Do you have enough room? Is there any room left over? Give your answer in mm and cm
You must show your working.

44. Can I … use correct money format?
Can you spot which line has the money written all in the same format?
£ £ p
£ £ £8.7
99p + £ £567.90
£ £ £23.60
£0.9 + £27 + £1.99
Line is correct
Circle all the other mistakes and write the
money in the correct format

45. Can I … work out mean, mode, median and range?
Calculate the mean, mode, median and range for the data below 5 9 3 1 7
Mean
Mode
Median
Range

46. Can I … create scale drawings?
Below is a sketch of a flower bed. Can you draw a scale drawing of the flower bed and label your diagram. 2m 3m

47. Can I … check lines are the correct scaled length?
Using the scale drawing you done in the previous question, explain how you know one of the lines on your diagram is the correct scaled length

48. Can I … provide written explanations for my answers?
After calculating the average and the range for 5 different people you have chosen the Bob and Sally to be on your darts team. Explain why.
Name
Average Score
Range
Bob
154 24
Tracey
109 22
Sally
132 20
Trish 45
Lucy
113 56

49. Can I … calculate time?
Fred is meeting Clive for dinner in town at 6:15pm. Before he meets him he needs to visit the Doctors and Argos. He thinks he will be at the doctors about 35 minutes and in Argos for about 20 minutes. It will take him 15 minutes to walk from the doctors to Argos. He is meeting Clive at a restaurant that is a 5 minute walk from Argos. It will take him 30 minutes to walk to the doctors.
What time does Fred need to leave his house?
Explain your reason

50. Can I … work out area, perimeter and volume?

51. Can I … display my results in a table?
You have been calculating the cost of a family holiday. You have worked out the following costs:
Flights are £450
Accommodation costs are £345
Airport taxes are £40
10% early booking discount is £83.50
Display your results in a table, showing the cost of the flights, accommodation, taxes, discount and total cost.

52. Name:
Can I …
Create a bar chart
Draw a trend line/line of best fit
Check my answer using a reverse calculation
Create a probability scale
Calculate a percentage of an amount
Create a flow chart
Create a time line
Calculate a fraction of an amount
Use formula
Round appropriate to the situation
Use correct units of measure
Use correct money format
Work out mean, mode, median and range

53. Name:
Can I …
Create scale drawings
Check lines are the correct scaled length
Provide written explanations for my answers
Calculate time
Work out area, perimeter and volume
Display my results in a table
Create a pie chart
Create a scattergraph
Create a line graph
Calculate ratio

54. Practice question: task 2 Building a Patio
You have half an hour to complete the questions
You may use a calculator
You may wear headphones
Do this on your own please

55. Practice question: task 2 Building a Patio

62. Directed study
World Maths
E3 to L1
L1 to L2