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Tasks | Early Adolescence | Predicting Gold for Australia

Tasks - Years 10, 11 & 12

Predicting Gold for Australia   by Stephen Spice, Shenton College

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s: Mathematics
Strand/s Substrand/s
Chance & DataCollect & Organise Data
Summarise & Represent Data
Interpret Data
Brief Description: Students research the number of gold medals won by Australia in the Commonwealth games since 1932 (using Internet or other means), then plot a scatter graph of year versus number of gold medals won. From this they apply a linear model and an exponential model to predict the number of gold medals that they think Australia will win in 1998, 2002 and beyond. They are then required to interpret their results.
Expected Outcomes:
  • Students will use the Internet or library to find the information.
  • Students will use their graphics calculators and pen and paper to record data and display data.
  • Students will use a linear an exponential model to predict the number of gold medals that will be won in future games.
  • Students will interpret and analyse their data.
Context:
  • Year 10, Foundations of Mathematics, Applicable Mathematics.
  • Used with pathway one Year 10 students and Foundation and Applicable students as an assessment item.
Learning Activities/
Experience:		 This activity could be used as a series of lessons, a small project where students have to research the topic, or as an assessment item.

Following is a series of questions which could be used as a basis for the desired activity.

Resources:
  • Graphics Calculators

Assessment

PREDICTING GOLD
[19 marks]

The year is 1998. Australia is competing in its 16th Commonwealth Games. The quest for Gold has never been greater and the results of the past 15 Commonwealth Games are recorded below:

Year (y)
No of Gold (g)
1930
1934
1938
1950
1954
1958
1962
1966
1970
1974
1978
1982
1986
1990
1994		 3
8
24
34
20
27
38
23
36
29
24
39
40
52
87

As a statistician it is your job to give the best possible prediction for this year's Games (1998)

  1. Enter the above data into your calculator and draw a sketch of the resulting scatter graph in the space provided on the next page.

    Scatter Graph of Number of Gold versus Year. [2 marks]

  2. Find the line of best fit and draw it on your graph above. [3 marks]

  3. Write the correlation coefficient between y and g and comment. [3 marks]

  4. Predict the number of gold medals won in 1998 and comment. [3 marks]

  5. Apply an exponential regression to your data and give the exponential equation that best fits the data. Draw this curve on your scattergram in part (1). [3 marks]

  6. Using your exponential regression curve obtained in (5) predict the number of gold medals that will be won in 1998. Compare your prediction with the one you made in part (4) and decide which is the most appropriate giving reasons to support your answer. [3 marks]

  7. If you were asked to predict the number of gold medals that would be won in the 2002 Commonwealth Games, which model would you use and why? [2 marks]

     

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