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

Recap – what did we do last lesson?

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

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.

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

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

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

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

Example – is there a relationship?

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

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

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)

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)

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.

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

Why are they misleading? Misleading graphs Why are they misleading?

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

This may help to explain the previous slide

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?

Scale made very small to make graph look very big

Scale made very small to make graph look very big

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

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!

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

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.

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

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

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

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

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

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

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?

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 123 + 52 = 175 686 – 321 = 365 284 ÷ 4 = 71 522 x 39 = 20358

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

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

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

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

Can I … calculate a fraction of an amount? Calculate 2 5 of £90

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

Can I … round appropriate to the situation? A company spends £142.20 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?

Can I … use correct units of measure? 1 foot is equivalent to 0.305 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.

Can I … use correct money format? Can you spot which line has the money written all in the same format? £5.27 + £4.90 + 97p £22.10 + £7.90 + £8.7 99p + £34.90 + £567.90 £1.99 + £0.89 + £23.60 £0.9 + £27 + £1.99 Line is correct Circle all the other mistakes and write the money in the correct format

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

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

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

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

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

Can I … work out area, perimeter and volume?

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.

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

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

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

Practice question: task 2 Building a Patio

Directed study World Maths E3 to L1 L1 to L2