In this unit students investigate the times taken and the distance travelled in coming to school, using a spreadsheet to produce data displays and investigate distributions. This unit follows on from Travel to School I.
Specific Learning Outcomes
- plan an investigation;
- use spreadsheets to display and analyse data
- discuss features of data display
- compare features of data distributions
Description of Mathematics
In this unit students use spreadsheets to produce data displays and investigate distributions
Required Resource Materials
Copymaster of Tallysheet (distance)
Copymaster of Sample Table
Copymaster of Tallysheet (time)
Computer with Excel spreadsheet (or equivalent) and Internet Access
Prior to this unit.
The students will need to collect data on how long it takes them to get to school and the distance travelled.
Session 1: Looking at our travel data
- Discuss the kind of data that the class has collected about their daily travel to school. They have the time taken – some will be measured in seconds, minutes and even hours. They have the distance traveled – this will be in meters and kilometers and we can reinforce the use of decimal notation e.g. 3.4 km.
- Identify ways of organising and presenting this data in an easy to read form. A discussion of the difference between this kind of data which measures a continuously varying quantity and the category data in Travel to School Unit I is important.
- Students spend the rest of the session in groups organising the data in ways they decide on. They present and discuss the results of their work to the class.
Session 2: A standard way of organising our travel data
- In this session we introduce the idea of a frequency table.
- Discuss the idea of grouping the times and distances in order to represent this data. Introduce the idea and value of a frequency table and after allowing students the opportunity to make their own frequency tables you can use the tally sheets provided as copymasters.
Note: these sheets have been laid out in a form that will enable easier comparison with New Zealand and USA (time taken) data in the next sessions. There should be some discussion about the unequal classes in the distance frequency table, and whether this is, in general, a good idea. You might want to produce two tables, one with equal classes.
- We are going to use the computer to help us display the results again. Students enter the data into Excel and then spend time deciding which graph(s) best display the data. They will no doubt try pie, line and bar graphs.
- A discussion of the graph results and why some ways of representing the data are more appropriate than others.
Session 3: How do we compare to the rest of New Zealand?
- Students from around New Zealand have also been asked how long it takes to travel to school. This data has been collected and is available on the CensusAtSchool site.
- Once the data has been collected from the site get the students to discuss how they might make a comparison with their own data. Consider questions such as:
Which of the columns of data should we take?
What should we do with the ‘not stated’ class?
- Once the students have decided on their approach they can be encouraged to enter the data into Excel and use Excel to draw the graph(s) they need (save the tables for a later session). They will need to consider the format they will enter the data in, whether they will need headings, etc. While the pie graph is again the easiest to make the comparison with they may come up with other methods. One way is to convert the class numbers into percentages using Excel and then to draw bar graphs.
- Conclude with a reporting time where the students are given the chance to show their graphs and to discuss what they have found out. Can they provide possible explanations for differences?
Session 3: How do we compare to the USA?
- We will again make a comparison with the data from other students from around the world who have also been asked how long it takes them to travel to school. This data has been collected and is available on the CensusAtSchool USA site.
- Once again they use Excel to produce the graphs they need to make the comparisons they want (save the tables for a later session).
- Again conclude with a reporting time where the students are given the chance to show their graphs and to discuss what they have found out. Stress the importance of trying to give reasons for any differences they have found.
Session 5: Comparisons using ‘averages’.
Note that measures of centre are not introduced in The New Zealand Curriculum until level 5. This material may not be suitable for all of your students.
- Discuss the value of having a single figure to compare two sets of data and get ideas on what might be a good one to use.
- Introduce the idea of the mode (with the greatest frequency), and the median (the middle value). Discuss how we find the middle value for a distribution. Compare the time taken (class, NZ and USA) using these two statistics.
- The idea of the mean is more difficult. Introduce it as the sum of the values divided by the total number of values. Get them to calculate the mean time and distance for their data, using the original raw data. This could be done by hand or by entering the raw data into Excel and using the average formula (for example entering in A36 the formula = average(A1:A35)).
- However to make the comparison we have to have a way of estimating this exact average called the mean from a frequency table. Introduce the idea of representing the class by its middle value. We find the middle value by adding up the end points and dividing by 2 (Note - this is easier for the distance than the timetable. For distance we get 0. 5, 1. 5, 2. 5 etc, but for time it is necessary to talk about what goes into the 10-19 class etc. Does 19 minutes 22 secs? Does 19 minutes 48 secs? This leads to 14.5 minutes as the mid point. The first class is also a problem since there is no –0.5 minutes. 4.75 minutes is the mid point here. )
- Students go to their tables in Excel (previously saved). First they use there data to check the mean as an estimate of the actual mean they have calculated. They can either insert a column of mid-points between the two columns (better) or put it on the end as a third column. Get Excel to calculate the mid-point multiplied by the frequency and put it in a fourth column. Total this column and the frequency column and divide to find the mean. This might look like the Sample Table (see copymaster). Compare the answer with the actual mean and discuss estimates and how good they are.
- Students compare the USA and NZ means with their class means for distance and time respectively and try to come to conclusions. Does it confirm or alter their previous ideas?