# Graphing and analysing superannuation data

SubjectMathematics YearYear 7 CurriculumAC v8.4 Time150

## Introduction

This set of resources provides opportunities for students to use and extend their data display and analysis skills. They will use technology (spreadsheets) to assist in their calculations and graphing of data and investigate the relationship between data and the mean and median in the context of superannuation in Australia.

Australian Curriculum or Syllabus

## Achievement standard

By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes.They calculate mean, mode, median and range for data sets They construct stem-and-leaf plots and dot-plots.

## Content descriptions

Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157).

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158).

Describe and interpret data displays using median, mean and range (ACMSP172).

## Student learning resources

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Explainer

Investigation

Data sheet

## Suggested activity sequence

This sequence is intended as a framework to be modified and adapted by teachers to suit the needs of a class group. If you assign this activity to a class, your students will be assigned all student resources on their 'My learning' page. You can also hand-pick the resources students are assigned by selecting individual resources when you add a work item to a class in 'My classes'.

Part A: Exploring superannuation

• Use a grouping strategy to organise students in groups of 3 or 4.
• Students read the explainer and groups decide on a definition of superannuation and write their definition on the board.
• When all definitions are displayed, discuss the concept of superannuation and develop a simple class definition.

Part B: Calculating super

1. Explicitly teach students how to calculate the superannuation guarantee using a gradual release of responsibility model.

To calculate the money your employer puts into your super account for you:

$Super=9.5\%\times salary$

For example: You’re a third year apprentice plumber and your weekly wage is \$669.53 per week. How much super should your employer pay into your super account?$Super=9.5\%\times salary=0.95\times\$669.53$

$=\$63.61$2. Ask students to do 5 simple calculations and a sixth one which is a bit more challenging – perhaps a 'working backwards' question, e, if your employer pays \$72.30 into your super account, what’s your salary?

$Super=Percentage \times salary$

Dividing both sides of the equation by the percentage:

$\require{cancel}\frac{Super}{Percentage} = \frac{\cancel{Percentage} \times{Salary}}{\cancel{Percentage}}$ $\frac{Super}{Percentage} = {Salary}$

Substitute in known values:

$Salary=\frac{Super}{Percentage}$

$=\ \frac{72.30}{0.095}$

$Salary=\$761.05$Part C: Exploring super data 1. Discuss with students some of the key concepts around super such as: 1. Why do we need super – what about the age pension? 2. How much might you need to retire comfortably? 3. How long does retirement last? 4. Why do we need to start so young? 5. How else can you increase your super? 6. What happens if you’re out of the workforce for a while? 7. Do they think women and men are likely to have the same amount of super? Why, why not? 2. Model the task students will do by doing a simple example as a whole class. If you’re all working together on this, everyone will need access to a computer with spreadsheet software. This is the weekly wage of 5 people in a netball team. Two people in the team didn’t want to share their information. \$1,845  \$1,529 \$2,135  \$1,150 \$986

1. Set up a spreadsheet and put the weekly pay data in excel (Include weekly pay, employer superannuation contributions and total cost to employer).
2. Sort from lowest to highest.
3. Put in a formula to calculate super (=0.095*B2).
4. Put in formulas to calculate average and median and total cost to employer (for example: =AVERAGE(C2:C6) and =MEDIAN(C2:C6) and =B2+C2)
5. Discuss with students about the average and the median being the same.
3. The rest of the team have decided they will share what they get paid too. One gets \$950 and the other gets \$3,428. Add rows, sort, check the formulas then examine the mean and median. Again, discuss what’s happened to these 2 measures of central tendency.

Model how to find the mode by setting up a table in your spreadsheet so that the salaries can be recorded into the following categories: 0-99, 1000-1999, 2000+ (see table 1 below as an example).

• Sort from lowest to highest.
• Add the formula to calculate total people – discuss with students what they expect the figure to be and what should they do if it’s not.
• Add a chart. Try both a line graph and a column graph, change the colours and add titles.
4. Students complete the investigation. To do so, they will need copies of the data sheet.
5. Walk students through the instructions, reminding them of the similarities to the problem you modelled.
6. Students may benefit from working individually and/or in small discussion groups.

Table 1

Category Number of people in this category

0-999

1000-1999

2000 +

Total

Put in a sum formula here