1. Travelling to School

2. What is the main way you usually travel to school?
Objectives
Children should learn:
• the different ways to travel to school.
Activities
The class can discuss what other ways there are to travel to school.
Other?

3. Do you think a bar chart of your class’s results would look the same?
Objectives
Children should learn:
to interpret a bar chart
Activities
Do they think their class will have the same results as this group of children?
Is 404 a large sample?
Does this sample represent all children in the UK?
What extra information do you need?
Is a bar chart a good way to display this information?
Do you think a bar chart of your class’s results would look the same?

4. How far is it from your home to school as the crow flies?
to school by road?
How long does it take you to
travel from home to school?
Objectives
Children should learn:
the difference between crow flight distance and road distance.
Activities
The class can discuss:
how much further they have to walk, drive or cycle than if they could travel in a straight line;
the different ways they could express this.
Point to note
Children can find answers to the above questions by completing the CensusAtSchool 2012/13 online questionnaire.

5. Is there a relationship between the road and crow flight distances between home and school for children at your school?
Is the relationship between the road and crow flight distances between home and school the same for children in all UK schools?
Objectives
Children should learn:
the difference between crow flight distance and road distance.
Activities
The class can discuss:
if they think the two variables are related and if so in what way;
the different ways they could express this.
Point to note
Children can find answers to the above questions by completing the CensusAtSchool 2012/13 online questionnaire.

6. What is the average distance children at your school usually travel from their home to school?
Is the average distance children usually travel from home to school the same for all UK schools?
Objectives
Children should learn:
what we mean by average.
Activities
The class can discuss:
what average should they use, mean, mode or median;
whether they think the average would be different for their journeys to school;
the geography of the area in which they live.

7. What is the average time children at your school take to travel from home to school?
Is the average time children take to travel from home to school the same for children in all UK schools?
Objectives
Children should learn:
what we mean by average.
Activities
The class can discuss:
what average should they use, mean, mode or median;
whether they think the average would be different for their journeys to school;
the geography of the area in which they live.

8. Use the mapping tool in CensusAtSchool. org
Use the mapping tool in CensusAtSchool.org.uk to find the distances from your home to school.
Objectives
Children should learn:
to identify the crow flight distance and road distance on the map.
Activities
The class can discuss:
why the road distance is longer;
can any modes of travel follow the crow flight distance;
how Google calculated the time the journey takes;
express the two distances in a ratio.

9. The Statistical Problem Solving Approach
Plan
Collect
Process
Discuss
DHCycle
You can build on the first try by continuing here...
First you decide what problem to solve and what data you need
Plan
Discuss
Collect
Objectives
Children should learn:
the structure of the ‘Problem Solving Approach’;
where their current task fits within the whole ‘Problem Solving Approach’.
Points to note
This slide will be followed by a series of similar slides, which shows which stage in the ‘Problem Solving Approach’ we have reached.
Then you collect suitable data.
Process
Have you got all the evidence you want? 9

10. The Problem Solving Approach
Plan
Collect
Process
Discuss
DHCycle
The Problem Solving Approach
Plan
Discuss
Collect
Process
Objectives
Children should learn:
where their current task fits within the whole ‘Problem Solving Approach’.
Points to note
This is the first slide, from a series of similar slides, which shows which stage in the ‘Problem Solving Approach’ we have reached.
First the key questions need to be specified.

11. Plan
Collect
Process
Discuss
Plan
Is there a relationship between the road and crow flight distances between home and school for children at a school in Hertfordshire?
Objectives
Children should learn:
the difference between primary and secondary data;
to think about when it might be appropriate to use secondary, as opposed to primary data, sources.
Points to note
Plan is emphasised at the top of the slide – this part of the stage involves planning which data to collect.
The example presented on the following slides is based on a random sample of distances from home to school for a school in Hertfordshire.

12. Collect
Process
Discuss
Plan
In Hertfordshire
An example using a sample of distances from a school in Hertfordshire.
For this example the data is provided.
Objectives
Children should learn:
the difference between primary and secondary data;
to think about when it might be appropriate to use secondary, as opposed to primary, data sources.

13. An example in Hertfordshire
Collect
Process
Discuss
Plan
Collect
Collect
An example in Hertfordshire
Road distance
4.8 miles
Objectives
Children should learn:
the difference between a crow-flight distance and a road distance;
to think about how they could collect the data for their journey from home to school;
what data was collected;
what things need to be considered when planning to collect data.
Both Plan and Collect are emphasised at the top of the slide – this part of the stage involves planning which data to collect.
Activities
The class can discuss:
How could they collect the data?
What problems might they encounter?
How could they ensure the data is truthful?
Crow flight distance
3.1 miles

14. Collect Data for a school in Hertfordshire Plan Process Discuss
Age (years)
Method of travelling to school
Estimated time to travel to school (mins)
Crow flight distance from home to school (miles)
Road distance from home to school (miles)
Time from home to school (mins) 10
Walk
0.5
0.7 2 1
0.2
0.1
Cycle 15
0.3 4 11 5 .
Objectives
Children should learn:
how to investigate a question using collected data;
to think about the data collected and the best ways to process them.
Activities
Pupils could be asked what they would need to do with the data to answer the questions posed.
Points to note
Suggestions for processing these data are shown in the next few of slides.
These data are provided in the Excel spread sheet Travelling to school in Hertfordshire.xls

15. The Problem Solving Approach
Plan
Collect
Process
Discuss
DHCycle
The Problem Solving Approach
Plan
Discuss
Collect
Objectives
Children should learn:
where their current task fits within the whole ‘Problem Solving Approach’;
to review their prior work.
Points to note
Now we have collected our data, we need to process it. We need to get it into a form that is easier to manage by drawing some graphs and charts and doing some calculations.
You are
now here.
Process

16. Process Graph or statistic? Mean? Standard Deviation? Median?
Plan
Collect
Discuss
Process
Graph or statistic?
Mean?
Standard Deviation?
Median?
Interquartile Range?
Objectives
Children should learn:
to think about appropriate methods for presenting the data they have collected.
Activities
Learners to discuss:
which graph/chart they should use to display the data;
why they have chosen this graph/chart;
what the graph/chart they have chosen will display. For example, scatter graphs show correlation or relationship between two variables, boxplots are used to compare.

17. Process What are the distances like?
Plan
Collect
Discuss
Process
What are the distances like?
Statistic
Key
Crow flight distance from home to school (miles)
Road distance from home to school (miles)
Minimum Value
Min
0.1
0.2
Quartile 1 Q1
0.3
Median Value (Quartile 2)
Med
0.5
Quartile 3 Q3
0.4
1.6
Maximum Value
Max
14.9
21.9
Do you notice anything odd about these results?
22 miles is a long way to travel everyday to school.
Is this a real entry or an error?
Objectives
Children should learn:
about quartiles and median;
maximum and minimum values;
to investigate outliers;
when it is appropriate to plot a box plot.
Activities
Learners can work through the example led by the teacher or take part in this interactive presentation;
The point (14.9, 21.9) seems extreme so further investigation is needed.
Points to note
These data are provided in the Excel Spreadsheet Travelling to school in Hertfordshire.xls

18. Looking at the raw data On inspection this person is over 18 years old
Age (years)
How you travel to School
Time to travel to school (mins)
Direct distance from home to school (miles)
Road distance from home to school (miles)
Time from home to school (mins)
Over 18
Other 30
14.9
21.9 44
On inspection this person is over 18 years old
and travels by other means.
What do you conclude?
Objectives
Children should learn:
to investigate outliers;
when it is necessary to clean data;
to decide when data are errors or genuine values.
Activities
Learners can consider the age and mode of travel of this person to decide if the data should be included;
In this case this is a teacher so is removed from the data for this analysis as we are investigating children’s journeys;
Learners could discuss if they think this is the correct procedure.

19. Process Remove this point and recalculate statistics
Plan
Collect
Discuss
Process
Remove this point and recalculate statistics
Statistic
Key
Crow flight distance from home to school (miles)
Road distance from home to school (miles)
Minimum Value
Min
0.1
0.2
Quartile 1 Q1
0.3
Median Value (Quartile 2)
Med
0.5
Quartile 3 Q3
0.4
1.6
Maximum Value
Max
2.3
3.5
What difference has removing this
point made to the statistics.
Objectives
Children should learn:
to think about extreme values and outliers;
to understand the difference removing an outlier will have on the quartiles, maximum and minimum values.
Activities
Learners can discuss why removing the outlier only affects the maximum value.

20. Comment on the box plots below
Plan
Collect
Discuss
Process
Comment on the box plots below
Objectives
Children should learn:
about quartiles and median;
how a box plot is drawn;
when it is appropriate to plot a box plot;
to think about extreme values and outliers.
Activities
This box plot is plotted using Minitab and shows the extreme points as crosses outside the main box plot. Learner need to note these values;
Both distributions are positively skewed with one or some extremely large values. The spread for road distance is much larger than that for crow flight distance. Discuss why this is the case.

21. How much further by road?
Plan
Collect
Discuss
Process
How much further by road?
Crow flight distance
1.1miles
Road distance
1.8 miles
Objectives
Children should learn:
to make figures more easy to use and understand;
to calculate percentages.

22. How much further by road?
Plan
Collect
Discuss
Process
How much further by road?
Road distance – Crow flight distance = 1.8 – 1.1 = 0.7 miles
Or as a percentage
Road distance as a percentage or crow flight distance =
= 63 % extra by road
Objectives
Children should learn:
to make figures more easy to use and understand;
to calculate percentages.
Activities
Ask learners to calculate the percentage difference between crow flight and road distance for the above journey.

23. How much further by road?
Plan
Collect
Discuss
Process
How much further by road?
Work out the percentage difference for road distance 0.2 to crow flight distance 0.1
= 50 % extra by road
Objectives
Children should learn:
to make figures more easy to use and understand;
to calculate percentages.
Activities
Ask learners to calculate the percentage difference between crow flight and road distance for the above journey;
Ask learners what this means to them;
Why are the percentages in the last two slides different;
Ask learners what they understand by variation.

24. How much further by road?
Plan
Collect
Discuss
Process
How much further by road?
What graph should be plotted to look at the relationship between the crow flight and road distances for this school?
Objectives
Children should learn:
when displaying data using a scatter graph is appropriate;
what a scatter graph is used for;
the idea of correlation.
Activities
Discuss which graph you should use.
Discuss the possible relationship between crow flight and road distances;
Would you expect there to be a correlation between the two variables?

25. Is there a relationship between crow flight and road distance?
Plan
Collect
Discuss
Process
Is there a relationship between crow flight and road distance?
Objectives
Children should learn:
to look at graphical information and interpret it.
Activities
Discussion of the questions posed.
Do the children think there is a pattern in the graph?
Is there a relationship between the two variables?
Learners to estimate where the line of best fit would be drawn on the graph;
What would happen if the points in the red circle were removed?
Should these points be removed?
Points to note
There is a group of journeys under a mile long by crow flight that seem to take further by road than another group. Discuss why this might be the case. (All live in a particular area where there is some barrier they have to cross that makes their journey a lot longer.)
The first school has crow distance = 0.1
and road distance = 0.2 miles.
All the schools can be plotted on this graph.
Comment on the graph.

26. Process Line of best fit Plan Collect Discuss Objectives
Children should learn:
to look at graphical information and interpret it.
Activities
Discussion of the questions posed.
Do the children think there is a pattern in the graph?
Is there a relationship between the two variables?
Learners to estimate where the line of best fit would be drawn on the graph.

27. Use the graph to predict road distance using crow flight distance
Plan
Collect
Discuss
Process
Use the graph to predict road distance using crow flight distance
Crow flight
distance
2 miles
Road distance
about 3 miles
Objectives
Children should learn:
to estimate using the line of best fit.
Activities
Learners to estimate where the line of best fit would be drawn on the graph.

28. Process Equation of the line of best fit
Plan
Collect
Discuss
Process
Equation of the line of best fit
Objectives
Children should learn:
the definition of the line of best fit;
to question presented information;
to recognise extreme values or outliers.
Activities
Discuss questions such as:
are there any extreme values?
is there a large amount of variability (scatter) about the line of best fit?
is it a good model to use to predict road distances from crow flight distances that are less than 3 miles?
is it a good model to use to predict road distances from crow flight distances that are greater than 3 miles?
Road distance = 1.4 x Crow flight distance + 0.3
For a crow flight distance of 2 miles
Road distance = 1.4 x = 3.1 miles
Does this agree with your prediction?

29. Equation of the line of best fit from the scatter graph
Plan
Collect
Discuss
Process
Equation of the line of best fit from the scatter graph
2.47 miles
1.80 miles
Objectives
Children should learn:
to read information from a graph;
how to find the gradient and intercept of the line of best fit.
Activities
Use this slide to explain how to find the intercept and gradient of the line of best fit.
Gradient = = 1.37 = 1.4 (1 dp)
Intercept = 0.3 (1 dp)

30. Plan
Collect
Discuss
Process
We can predict road distance from crow flight distance using the equation of the line of best fit.
Road distance = × Crow flight distance
(Y variable = gradient × X variable intercept)
Using the equation above find the road distance for a crow flight distance of 2.5 miles.
Road distance = x Crow flight distance + 0.3
= x (2.5) + 0.3 =
= miles
Objectives
Children should learn:
to make figures more easy to use and understand;
to make predictions using the equation of the line of best fit.
Activities
Learners should calculate predictions of the road distance from crow flight distances using the equation of the line of best fit;
They should be aware not to use the line to predict values outside the range of the data.
Why would it not be a good idea to use this equation predict a road distance for a crow flight distance of 25 miles?

31. Process Interpreting the line of best fit.
Plan
Collect
Discuss
Process
Interpreting the line of best fit.
Road distance =1.4 × Crow flight distance + 0.3
Gradient ~ for every mile travelled by crow flight we would expect to travel 1.4 miles by road.
Intercept ~ if we travel zero miles by crow flight we would expect to travel 0.3 miles by road.
Objectives
Children should learn:
how to interpret the intercept and gradient for a line of best fit.
Activities
To interpret gradient and intercept.
Points to note
Again it is worth mentioning these are not exact values as there is variation about the line of best fit.
Does the last statement make sense in real life?

32. Plan
Collect
Discuss
Process
Based on the analysis in this lesson which one of the following statements is correct?
It is 40 % longer to travel from home to school by road rather than by crow flight.
In Hertfordshire it is 40 % longer to travel from home to school by road rather than by crow flight.
On average in Hertfordshire for every mile travelled by crow flight we would expect to travel 1.4 miles by road.
On average for a particular school in Hertfordshire for every mile travelled by crow flight we would expect to travel 1.4 miles by road from home to school for distances less than 3 miles.
Objectives
Children should learn:
how to state findings accurately.
Activities
Learners to discuss the above statements. D is the correct statement;
Learners could be asked to make the statement using the 40 % value.
Points to note
Again it is worth mentioning this is not an exact value as there is variation about the line of best fit.

33. The Problem Solving Approach
Plan
Collect
Process
Discuss
DHCycle
The Problem Solving Approach
Plan
Discuss
Collect
Objectives
Children should learn:
where the current task fits within the whole ‘Problem Solving Approach’;
to review prior work.
Points to note
Now we have processed the information by drawing charts and doing calculations, we need to discuss what our results show us and how they help us consider the problem.
Process
You are
now here.

34. Discuss Are there any issues with the graphs created from
Plan
Collect
Process
Discuss
Discussion
Are there any issues with the graphs created from
the distances?
Were there any patterns linking crow flight distance and road distance in Hertfordshire?
How do your class results relate to the Hertfordshire data?
Would you expect a graph of road distance against crow flight distance to look the same wherever pupils live?
Would you expect a graph of road distance against crow flight distance to look the same for a school in Scotland?
Objectives
Children should learn:
to discuss their findings and relate them to the original problem and the data;
to come up with new questions or hypotheses about the information.
Activities
Discussion around the questions on the slide.
Further investigations
Would you expect a graph of road distance against crow flight distance to look the same for Scotland?
How do your class results relate to the Hertfordshire data?

35. The Problem Solving Approach
Plan
Collect
Process
Discuss
DHCycle
The Problem Solving Approach
You can develop another solution by continuing here...
Plan
You are
now
here.
Discuss
Collect
Objectives
Children should learn:
where their current task fits within the whole ‘Problem Solving Approach’;
to review their prior work.
Points to note
At the end of the work, having discussed our findings we could now start the whole cycle again.
Process

36. Plan
Collect
Process
Discuss
End of
slideshow