Part One

Giant Wild Goose Pagoda at Xi'an , Alex Kwok, Wikipedia, https://en.wikipedia.org/wiki/Giant_Wild_Goose_Pagoda#/media/File:Giant_Wild_Goose_Pagoda.jpg

The Unit Description, Unit Specific Goals and Content Descriptions

Please examine the Content Descriptions in the Mathematics course you are teaching

The Unit Description, Unit Specific Goals and Content Descriptions describe the student's learning entitlement. Through the course of the unit, students should engage with learning activities related to all of the Content Descriptions.

The level of thinking required in relation to the Content Description is indicated by the verb at the opening of the Content Description, the Achievement Standards, and/or in the unit goals.

Teachers will illuminate or exemplify the Content Descriptions for students by choosing topics, texts, contexts, case-studies etc. and explaining to their colleagues and themselves the links to the Content Descriptions in their Program of Learning.

Activity 1.1

Take these Content Descriptions for Mathematical Methods; Unit 1: Mathematical Methods

Review of the fundamentals of probability:

· review probability as a measure of ‘the likelihood of occurrence’ of an event (MMT52)

· review the probability scale: for each event with if is an impossibility and if is a certainty (MMT53)

· review the rules: and (MMT54)

· use relative frequencies obtained from data as point estimates of probabilities. (MMT55)

Conditional probability and independence:

· understand the notion of a conditional probability and recognise and use language that indicates conditionality

· use the notation and the formula P(A Ç B) = P(A|B)P(B)

· understand the notion of independence of an event from an event , as defined by

· establish and use the formula for independent events and , and recognise the symmetry of independence

· use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events.

Consider the following questions:

What sequence of thinking would students need to do to meet this set of Content Descriptions and the Achievement Standards?
What familiar and unfamiliar problems or contexts could the students engage with to meet these Content Descriptions?
How could you pursue the overall goals and rationale of the unit through these Content Descriptions?
How could these be demonstrated in an assessment piece?

General Capabilities

Teachers are encouraged to:

• model the general capabilities within a variety of contexts

• identify connections between the learning area/subject and the general capabilities

• provide a variety of learning activities that support development of the general capabilities

• provide opportunities for students to practise the general capabilities as authentic elements of the learning area/subject

• provide feedback to students about their progress toward developing the general capabilities.

Cross-curriculum Priorities

provide students with the tools and language to engage with, and better understand, their world
provide national, regional and global dimensions
addressed through learning areas -not curriculum on their own
embedded in Content Descriptions where appropriate
considered and focused content that fits naturally within learning areas

Levels of Thinking

Read these two webpages on levels of thinking Teachers Institute and the University of North Carolina .

Activity 1.2

Consider the exemplars from SACE below.

Please 1-5 in a rank order of levels of thinking .
What grade is be suggested by each responses? Use the Achievement Standards.

(Extracts adapted from SACE))

G. Mütrel, "Various Cacaceae", Berlin, F.A. Brockhaus - Brockhaus' Konversations-Lexikon v. 2, 1892

Exemplar One

Exemplar Two

Exemplar Three

Exemplar Four

Exemplar Five

I will determine if there is a correlation between GDP and the number of Football world cup victories. I will use formulas and write out the Mathematical working.

Introduction:

The Football World Cup is a global event that attracts millions of viewers worldwide. It is also an event that can have a significant impact on a country's economy. In this report, we will investigate whether there is a correlation between a country's GDP and the number of Football World Cup victories it has achieved. We will use statistical analysis to determine if there is a significant relationship between these two variables.

Data:

To perform this analysis, we will need data on the GDP and the number of Football World Cup victories for each country. We have obtained this data from reliable sources, such as the International Monetary Fund (IMF) and the official FIFA website.

We collected the data from reliable sources, such as the International Monetary Fund (IMF) and the official FIFA website. The GDP data is in billions of US dollars, and the number of Football World Cup victories is the total number of times a country has won the tournament

Methodology:

To determine if there is a correlation between GDP and the number of Football World Cup victories, we will calculate the correlation coefficient using the following formula:

r = (n∑xy - ∑x∑y) / sqrt[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]

Where:

r is the correlation coefficient

n is the number of observations

x and y are the variables being correlated

If the correlation coefficient is close to 1 or -1, it indicates a strong positive or negative correlation, respectively. If the correlation coefficient is close to 0, it indicates no correlation.

Results:

We performed the analysis using the data we collected and obtained the following results:

Number of observations: 32

Correlation coefficient (r): 0.4838

p-value: 0.0061

Interpretation:

The correlation coefficient of 0.4838 suggests that there is a moderate positive correlation between GDP and the number of Football World Cup victories. The p-value of 0.0061 indicates that this correlation is statistically significant at a 5% significance level.

Conclusion:

Based on our analysis, we can conclude that there is a moderate positive correlation between a country's GDP and the number of Football World Cup victories it has achieved. However, it is important to note that correlation does not necessarily imply causation. There may be other factors that contribute to a country's success in the Football World Cup, such as the quality of its players, coaching staff, and infrastructure. Therefore, further research is necessary to determine the causal relationship between GDP and the number of Football World Cup victories.

Now I will compare these results to an analysis using GDP per capita?

GDP per capita is a commonly used economic indicator that measures the average economic output per person in a country. It is calculated by dividing a country's GDP by its population. In this analysis, we will investigate the correlation between GDP per capita and the number of Football World Cup victories.

Data: To perform this analysis, we will need data on GDP per capita and the number of Football World Cup victories for each country. We have obtained this data from reliable sources, such as the International Monetary Fund (IMF) and the official FIFA website.

Methodology: To determine if there is a correlation between GDP per capita and the number of Football World Cup victories, we will calculate the correlation coefficient using the same formula we used previously, but this time using GDP per capita instead of GDP.

Results: We performed the analysis using the data we collected and obtained the following results:

• Number of observations: 32

• Correlation coefficient (r): 0.3423

• p-value: 0.0588

Interpretation: The correlation coefficient of 0.3423 suggests that there is a weak positive correlation between GDP per capita and the number of Football World Cup victories. The p-value of 0.0588 indicates that this correlation is not statistically significant at a 5% significance level.

Comparison to previous analysis: Compared to our previous analysis using GDP, we found that the correlation between GDP per capita and the number of Football World Cup victories is weaker and not statistically significant at a 5% significance level. This suggests that there is a stronger relationship between a country's total GDP and its success in the Football World Cup than between its GDP per capita and its success in the tournament.

Conclusion: Based on our analysis, we can conclude that while there is a weak positive correlation between a country's GDP per capita and the number of Football World Cup victories it has achieved, the correlation is not statistically significant at a 5% significance level. Therefore, we can conclude that there is no meaningful relationship between GDP per capita and success in the Football World Cup. Instead, the analysis using total GDP suggests that a country's economic power may play a role in its success in the tournament.

Now I will find the equation of the line of best fit and interpret the meaning of the gradient and y intercept for the data above?

To find the equation of the line of best fit, we can use linear regression analysis. Here's how to do it:

Calculate the mean of both the GDP and the number of Football World Cup victories data.

Calculate the sample standard deviation of both the GDP and the number of Football World Cup victories data.

Calculate the sample covariance of the GDP and the number of Football World Cup victories data.

Calculate the slope and y-intercept of the line of best fit.

Using the data we have collected in the table above, we can calculate the equation of the line of best fit as follows:

Mean of GDP = 1,111.478125 billion USD

Mean of Number of Football World Cup Victories = 0.4375

Sample standard deviation of GDP = 1,200.604731 billion USD

Sample standard deviation of Number of Football World Cup Victories = 1.207212878

Sample covariance of GDP and Number of Football World Cup Victories = 2.838720703125 billion USD

Slope of the line of best fit = covariance / variance of GDP = 2.838720703125 / (1,200.604731 ^ 2) = 0.000002335

y-intercept of the line of best fit = mean of Number of Football World Cup Victories - slope * mean of GDP = 0.4375 - 0.000002335 * 1,111.478125 = 0.437221

Therefore, the equation of the line of best fit is:

Number of Football World Cup Victories = 0.000002335 * GDP + 0.437221

Interpretation:

The gradient or slope of the line of best fit is 0.000002335. This means that for every additional billion USD in GDP, there is an increase of 0.000002335 in the number of Football World Cup Victories. In other words, the slope represents the rate of change in the number of Football World Cup Victories for a one-unit increase in GDP.

The y-intercept of the line of best fit is 0.437221. This means that if a country has a GDP of 0 billion USD, the expected number of Football World Cup Victories is 0.437221. In other words, the y-intercept represents the predicted value of the number of Football World Cup Victories when the GDP is zero.

Overall, the equation of the line of best fit provides a way to predict the expected number of Football World Cup Victories based on a country's GDP, as well as an understanding of the relationship between these two variables.

Activity 1.3

BSSS Annotated Work Samples

Please read through and evaluate the BSSS Annotated Tasks and Work samples to be found here.

How might you use them in your school?
Exemplar Five was generated by AI. What do you think of it?

Part Two

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