2. Key ideas Data can be collected from a relatively small sample size, that can be used to make predictions Calculators have statistical functions that calculate the line-of-best-fit The formula for a line-of-best-fit can be used to make predictions

3. Setting the scene… Sending a hand squeeze around a group of people. Ask 3 people to stand in a circle and hold hands.

4. Nominate one person as leader. The leader sends a hand squeeze to the person on their left. They pass on the hand squeeze to the next person. And onto the next.

5. Use a stopwatch (hand-held or computer-based) to record the times. Stopwatch available from http://www.online-stopwatch.com

6. Record the data in a table. No. PeopleTime (s) 3 5 9 11 16 22 25

7. Repeat this process, adding more people into the circle. How many you add each time is not important (adjust the numbers in the left hand column as needed). Finish recording your data. The next step is to graph the data. No. PeopleTime (s) 3 5 9 11 16 22 25

8. Example data: sending a hand squeeze around a group Time (s) No. People Time (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03

9. Example data: sending a hand squeeze around a group Time (s) No. People Time (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03 Choose an appropriate scale for your graph axes

10. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03

11. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03 Plot the data collected from the class

12. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03

13. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03 Is there an obvious trend line that we can draw in (line-of-good-fit)?

14. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03

15. Example data: sending a hand squeeze around a group Time (s) No. People 10 8 6 4 2 0 02468101214161820222426 No. PeopleTime (s) 30.87 51.62 94.51 114.79 165.89 226.81 259.03 We can use a TI-30XB calculator or a spreadsheet to find the equation of the line-of-best-fit

16. Using a spreadsheet, the graphed data with tend line (same as line-of-best-fit) will look like:

17. Using a TI-30XB calculator, we can enter the data to find the coefficients for the equation of the line-of-best- fit, in the form of: y = mx + b

18. Entering the data… To enter data, use the data key and key to enter the data from the above table for the number of people in List L 1. Use the key to move across to List L 2, and then use the key to move down the list. Enter the corresponding data for the time taken for the hand squeeze to be transferred around the group at each time.

19. Analysing the data… Use the statistical functions on the TI-30XB calculator to make sense of the data. Press and choose 2: 2-Var Stats (refers to statistics with two variables). The calculator will default to choosing L 1 for x-data (independent variable – Number of People) and L 2 for y-data (dependent variable – Time in seconds).

20. Use the key twice to scroll down to CALC and press. This will display a range of statistical results. Use the key 14 times to scroll down until you see the values displayed for this data set: D: a=0.3302392344 E: b=0.4954613807 F: r=0.9668908586

21. D: a=0.3302392344 E: b=0.4954613807 F: r=0.9668908586 Round these numbers to two decimal places: D: a = _______________ E: b = _______________ F: r = _______________

22. D: a=0.3302392344 E: b=0.4954613807 F: r=0.9668908586 Round these numbers to two decimal places: D: a = 0.33 E: b = 0.50 F: r = 0.97

23. Time Taken = a x No. People + b Using the example data, our rule (from our ‘line-of-best-fit’) is: Time Taken = ____ x No. People + ____ We can shorten this up to: T = ____ x P + ____

24. Time Taken = a x No. People + b Using the example data, our rule (from our ‘line-of-best-fit’) is: Time Taken = 0.33 x No. People + 0.5 We can shorten this up to: T = ____ x P + ____

25. Time Taken = a x No. People + b Using the example data, our rule (from our ‘line-of-best-fit’) is: Time Taken = 0.33 x No. People + 0.5 We can shorten this up to: T = 0.33 x P + 0.5

26. Time Taken = 0.33 x No. People + 0.5 T = 0.33 x P + 0.5 For the given data, a ‘rule of thumb,’ we can quickly estimate the time (in seconds) taken for a handsqueeze to be transferred by dividing the number of people by 3.

27. We can use the rule for the line-of-best-fit to calculate the time taken for a hand squeeze to be passed around a circle for larger groups of people. No. PeopleTime (s) 50 200 1,200 5,000 25,000 1,200,000 20,000,000

28. Discussion points: Where does the extra half a second come from? Can we ignore the extra half a second when making predictions for large numbers of people?

29. Use the class data to complete this table:

30. Repeat the steps used in the hand squeeze activity to a different context… Investigation: How strong is spaghetti? Can we predict how many weighted Objects (eg. nails) it will take to break 5, 6 & 7 strands of spaghetti?

31. 1.Poke a single strand of spaghetti through a foam cup, or devise a hanger as in the picture on previous slide, to suspend the cup below the spaghetti and then hang both across a 15 cm gap between two desks. 2.Add the weighted items (nails, nuts, or bolts) one by one to the foam cup. Record how many weighted items are needed for the spaghetti to break. 3.Record this data in your table. 4.Poke two strands of spaghetti through the foam cup, and repeat the process. 5.Repeat the process for three and four strands of spaghetti.

32. No. Pieces of Spaghetti No. Weighted Items 1 2 3 4

33. No. Pieces of Spaghetti No. Weighted Items 1 2 3 4 The graphing of the class data can be modelled on a large grid or a tea-towel