Objective reference		AAcross the full range:	BAcross a range:	CIn routine situations:	DIn rehearsed simple situations:	EEvidence of some:
Knowledge and Procedures	rules and formulas	Perfect Response	accurate use of rules and formulas ·         to find statistical features	accurate use of rules and formulas ·         to find statistical features	use of rules and formulas ·         to find statistical features	use of rules and formulas	attempted use of given rules and formulas	No Meaningful response
	mathematical procedures		accurate application of sequences of mathematical procedures ·         to investigate data sets	accurate application of mathematical procedures ·         to investigate data sets	application of mathematical procedures ·         to investigate data sets	application of simple mathematical procedures	attempted use of simple mathematical procedures
	mathematical technology and instruments		appropriate selection and accurate use of technology ·         to present findings from given data sets ·         to manipulate self-generated data sets	selection and accurate use of technology ·         to present findings from given data sets ·         to manipulate self-generated data sets	selection and use of technology ·         to present findings from given data sets	use of technology	attempted use of technology
Modelling and Problem Solving	strategies	Perfect Response	accurate use of appropriate strategies to model and solve problems ·         to compare and contrast data sets in a range of formats	accurate use of appropriate strategies to model and solve problems ·         to compare and contrast data sets	use of familiar strategies for problem solving ·         to compare data sets	use of strategies for problem solving	attempted use of given strategies for problem solving	No Meaningful response
	procedures and decisions		informed decisions based on mathematical reasoning ·         with written evidence of reasoning	informed decisions based on mathematical reasoning ·         with written evidence of reasoning	informed decisions based on mathematical reasoning ·         with written evidence of reasoning	decisions based on mathematical reasoning	decisions based on mathematical reasoning
	reflecting, including strengths and limitations		comprehensive reflection on the effectiveness of mathematical models including recognition of the strengths and limitations of the model ·          to compare datasets to reach meaningful conclusions ·          to accurately predict run times 40 years from now	thoughtful recognition of the strengths and limitations of the model ·         to compare datasets to reach conclusions ·         to predict run times 40 years from now	recognition of a strength or a limitation of the model ·         to compare datasets to reach conclusions	cursory recognition of a strength or a limitation of the model	attempt at recognition of a strength or a limitation of a model
Communication and Justification	terminology, symbols and conventions	Perfect Response	accurate and appropriate use of mathematical terminology and conventions	accurate and appropriate use of mathematical terminology and conventions	appropriate use of mathematical terminology and conventions	use of mathematical terminology and conventions	use of mathematical terminology or conventions	No Meaningful response
	representations		coherent and logical organisation and presentation of information in a variety of representations accurate analysis and translation of information displayed from one representation to another	logical organisation and presentation of information in a variety of representations analysis and translation of information displayed from one representation to another	logical organisation and presentation of information in a variety of representations translation of information displayed from one representation to another	presentation of information	presentation of information
	sequences		use of mathematical reasoning to develop logical sequences in using every day and/or mathematical language	use of mathematical reasoning to develop logical sequences using every day and/or mathematical language	development of logical sequences	development of simple logical sequences	development of sequences
	justification		coherent and logical justification of procedures used, including of the reasonableness of results	logical justification of procedures used, including of the reasonableness of results	justification of procedures used	simple justification of procedures used	rudimentary justification of procedures used

Setting the scene

In this assignment, you will access, interpret and use real-world data to make predictions based on that data using a variety of models. You will also analyseyour processes to identify strengths and limitations of the strategies you used in responding to the tasks.
 
Item 1. How fast can they run?
The following raw data was collected at a recent athletics meet in Brisbane (all times in format mm:ss.00):

100 M Event
Men	Women
00:10.22     00:10.58     00:11.04     00:12:33 00:15.32     00:10.99     00:11.55     00:11.01 00:10.55     00:10.67     00:11.37     00:12.55	00:10.98     00:11.04     00:11.33     DQ 00:11.57     00:13.13     00:12.02     00:12.44 00:11.87     00:12.02     00:11.88     00:12.59
200m Event
Men	Women
00:20.98     00:20.97     00:22.95     DQ 00:20.95     00:22.17     00:21.56     00:22.02 00:21.37     00:21.67     00:22.11     00:25.79	00:22.34     00:23.03     00:23.07     00:24.65 00:24.01     00:23.98     00:24.65     00:25.18 00:22.69     00:24.14     00:24.76     00:24.98
400m Event
Men	Women
00:44.12     00:43.98     00:45.67     00:46.87 00:45.56     00:48.88     01:01.33     DQ 00:44.77     00:44.22     00:47.54     00:46.06	00:49.56     00:50.13     00:47.90     00:48.98 00:49.67     00:51.33     00:49.99     00:50.25 00:50.33     01:00.32     00:51.86     00.49.86

DQ = Disqualified
 
Using any means that you see fit, describe the relationship between time and distance, and the differences in terms of gender.
In your response, you will need to use mathematical arguments to support your decisions. These arguments will be show clearly how they support your decisions and conclusions.

Item 2. How fast will they run forty years from now?
World record times for the men’s 1500 metres run have been continually dropping over the past 100 years, as shown in the table below.
In this section, you need to comprehensively analyse data in the table to write a mathematical report as outlined over the page.
 

World record times: men’s 1500 metres run
Date	Athlete	Time (mm:ss.0)	Date	Athlete	Time (mm:ss.0)	Source: International Association of Athletics Federations  (IAAF) 2009, 12th IAAF World Championships in Athletics: IAAF Statistics  Handbook, p. 549, www.iaaf.org/mm/document/competitions/competition/05/15/63/20090706014834_httppostedfile_p345-688_11303.pdf, Berlin.
8/06/1912	Abel Kiviat	03:55.8	6/09/1955	Gunnar Nielsen	03:40.8
5/08/1917	John Zander	03:54.7	3/08/1956	István Rózsavölgyi	03:40.6
19/06/1924	Paavo Nurmi	03:52.6	11/07/1957	Olavi Salsola	03:40.2
11/09/1926	Otto Peltzer	03:51.0	11/07/1957	Olavi Salonen	03:40.2
5/10/1930	Jules Ladoumegue	03:49.2	12/07/1957	Stanislav Jungwirth	03:38.1
9/09/1933	Luigi Beccali	03:49.2	28/08/1958	Herb Elliott	03:36.0
17/10/1933	Luigi Beccali	03:49.0	6/09/1960	Herb Elliott	03:35.6
30/06/1934	Bill Bonthron	03:48.8	8/07/1967	Jim Ryun	03:33.1
6/08/1936	Jack Lovelock	03:47.8	2/02/1974	Filbert Bayi	03:32.2
10/08/1941	Gunder Hägg	03:47.6	15/08/1979	Sebastian Coe	03:32.1
17/07/1942	Gunder Hägg	03:45.8	15/07/1980	Steve Ovett	03:32.1
17/08/1943	Arne Andersson	03:45.0	27/08/1980	Steve Ovett	03:31.4
7/07/1944	Gunder Hägg	03:43.0	28/08/1983	Sydney Maree	03:31.2
15/07/1947	Lennart Strand	03:43.0	4/09/1983	Steve Ovett	03:30.8
29/06/1952	Werner Lueg	03:43.0	16/07/1985	Steve Cram	03:29.7
4/06/1954	Wes Santee	03:42.8	23/08/1985	Saïd Aouita	03:29.5
21/06/1954	John Landy	03:41.8	6/09/1992	Noureddine Morceli	03:28.9
28/07/1955	Sándor Iharos	03:40.8	12/07/1995	Noureddine Morceli	03:27.4
6/09/1955	László Tábori	03:40.8	14/07/1998*	Hicham El Guerrouj	03:26.0
			*Current record as of December 2015

 
Use the data in the table on the previous page to write a mathematical reportthat investigates the world record times of the 1500m race in the past, present and future. This report should include:
·          A brief introduction that describes the goals of the report and outlines what will be presented.
·          A description of the mathematical methods used, including any models developed and assumptions made.
·          A justified prediction on what you predict the world record time will be forty years from now?
·          Analysis of the data that investigates and makes informed decision regarding
i.      the year that the 4 minute mile was finally cracked?
ii.     Whether there will there be a time in the future when the record could never be broken?
iii.    How can different models be used to assist in solving this problem?
·          A discussion on the strengths and limitations identified within the devised models
·          A conclusion that comments on the plausibility, expectedness and significance of the findings.
 
Item 3  Bringing it all together…
In this third and final item on this assignment, you need to identify and accurately use appropriate data sampling methods to collect data about two related variables with which you can make your own comparisons, analyses and predictions, and to produce a mathematical report of your findings.
The data you collect must allow a valid investigation of the relationship between the two variables you have identified in your sampling processes. Your report must contain in-depth mathematical justification to support your processes and your analyses and predictions. This report format can be in any format that you see fit.
You will be given Lesson 2 on Tuesday, 24 February to collect data from your Year 12 Mathematics A peers that you can use (if you wish). If you intend to complete a survey or experiment for data, it would be expected that you have approved this with your teacher prior to this lesson (i.e. in the less on Monday, Feb 23).
 
 
A comprehensive data set is one that:
·          Shows consideration to the removal of outliers and anomalous data
·          Informs the reader on a topic using mathematical and everyday language
·          Details how errors have been minimised and eliminatedthrough the collection of data
·          Displays the information in an easy to interpret way such as a box and whisker plot, scatter plot with line of best fit or two way table.
·          Generates informed decisions and conclusions based on mathematical reasoning