- Level 8
- Number and Algebra
- Money and financial mathematics
- Profit and loss

###### Money and financial mathematics • Level 8

# Profit and loss

VCMNA278

## Teaching Context

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At this level, students express profit and loss as a percentage of the cost price and use this to compare the difference. They also investigate methods used in retail stores to express discounts.

$\text{PercentageProfit/loss=}\frac{\text{profit/loss}}{\text{originalcost}}\text{\xd7100\%}$

A common misconception when calculating the percentage profit or loss is understanding whether the profit or loss is divided by the original cost or the selling price. The formula above illustrates that the profit or loss is divided by the original cost. Support students to understand that all comparisons are made to the original cost by providing an example to highlight this (see example below). Students need to understand why the profit/loss is divided by the original cost and not the new selling price. It is divided by the original cost because it is necessary to see how much of a profit (or loss) the product made as compared to the original cost of the item.

For example, a car was originally purchased for $10 000 but sold for $8000. Find the percentage profit or loss.

Loss = $8000-$10 000 = - $2000

Percentage Loss = $-\frac{2000}{10000}\times 100\%=-20\%$

* Note: *If the original price minus the selling price is a negative value then a loss
has occurred.

When writing the answer ensure we say that the car sold for a 20% loss not a loss of -20%.

If the $2000 loss had been compared to the selling price of $8000 it would have given a 25% loss. Stating that the car sold for a 25% loss would indicate that the owner sold the car for $7500 which is incorrect.

Using examples that involve a power of ten (100, 1000 etc.) help to support student understanding of why the original cost is used when calculating percentage loss or profit as they can check if their answer seems reasonable without digital technology.

Following on from this, students then build
their knowledge of financial mathematics
to include simple interest calculations in
VCMNA304**.**

### Victorian Curriculum

Solve problems involving profit and loss, with and without digital technologies (VCMNA278)

VCAA Sample Program: A set of sample programs covering the Victorian Curriculum Mathematics.

VCAA Mathematics glossary: A glossary compiled from subject-specific terminology found within the content descriptions of the Victorian Curriculum Mathematics.

##### Achievement standards

Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context.

Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions.

Students solve linear equations and graph linear relationships on the Cartesian plane.

## Online Resources

## Teaching ideas

### Using percentages

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This activity is designed to get students thinking about the benefits of using percentages when comparing profit and loss in various scenarios.

Provide students with two different scenarios in which two ‘shop owners’ have both made a profit or both made a loss.

Example: Bike shop A purchased a mountain bike for $780 and plans to sell it for $1000. Bike shop B purchased a mountain bike for $1020 and plans to sell it for $1270. Which store made the greatest percentage profit?

Ask students to calculate the profit amount made by each store.

These questions may be used to support the discussion:

- Which store made the greatest profit?
- What amount did each store pay originally?
- What other information could we obtain that may make it easier to compare the two profit amounts?
- What benefit would it be to calculate the percentage profit for each store?

Now ask students to calculate the percentage profit for each store and determine which store made the greatest percentage profit.

For further investigation students can be provided with a scenario in which two stores have made the same amount of profit (or loss) but the original purchase prices are different, which will yield a different percentage profit.

For example: A furniture shop purchases an armchair for $750 (wholesale) and sells it for $1000 (retail). Another furniture shop buys the same armchair for $820 and sells it for $1070. Which store has made the greatest profit?

An additional activity could be used based on commissions. An artist supplies their artwork to a gallery for sale. The gallery takes 50% of the sale price as commission.

- An artist wishes to receive $100 from the sale of their artwork. What should the sale price be to enable this to happen?
- Repeat this question for other amounts that the artist wishes to receive. Use these to find a rule for calculating the ‘mark up’ to allow for a commission of 50%.
- Try other commission percentages, such as 25%. Explore this with different amounts for the artist after the commission is deducted. Adjust your rule to allow for different commission rates.

### Share market

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Introduce the share market to the class by spending 5 -10 minutes discussing the history of the share market. Advise students that they will be using information in the actual share market for this activity.

Divide students into pairs or small groups and provide each group with a set amount (eg, $5000) to ‘invest’.

Each group then uses the internet to research share prices online. Ask students to decide on a company to invest their money in and determine how many shares they can purchase given the current share purchase price. You may like to guide students towards certain companies or give them a list to select from, so they don’t take too much time researching. Alternatively, you may like to provide students with a list of factors to consider when investing (stability of the share price, longevity of the company etc) to help them make their decision.

Advise each group that they will need to track the value of their shares over the next fortnight and determine when they will sell their shares to try and make the largest profit. Each group will need to keep a record of the daily share price and decide on which day they think they would sell their shares and what their profit/loss would be. Even if a group decides to ‘sell’ their shares on Day 1 they should keep recording the daily share price for a fortnight to see if they made the ‘right decision’ for the best profit.

You may then ask each group to present their profit (or loss) to the class and see which group made the largest profit.

Alternatively, you may offer groups the option to sell part of their shares and reinvest their money in another company before the fortnight is finished. The aim is for students to reinvest their money to compete with other groups, for the highest profit.

### Cost and revenue

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Give students opportunities to apply their knowledge of profit and loss with a practical scenario such as organising a concert or planning a school fete. You may like to choose a scenario based on current events or interest amongst the class

Ask students to form small groups of 3 or 4 students. Provide students with an opportunity to brainstorm some of the ‘costs’ for their given scenario and guide them where necessary. Allow students time to research so they obtain realistic quotes for their costs.

For instance, students may investigate the costs associated with organising a concert. You might suggest that the students consider how many staff are required or the concert duration to assist their planning and cost estimate. They could then determine:

- Cost of the performer
- Staff wages (25 staff needed for 8 hours)
- Venue hire cost
- Inclusion of food trucks

Once students have calculated the cost of hosting their event they can then set a ticket price and determine what profit margin they can make for different amounts of tickets sold (eg 1000, 5000, 10 000 etc). Students should consider factors such as venue size and how many people need to buy tickets to break even. You may like to discuss with each group about setting a price that is reasonable but will also enable them to make a profit.

The final costs and selling prices can be presented as a project with each group justifying why they chose their selected selling price and how much profit they are expecting to make from their event.

Alternatively, students can also provide graphs showing their costs, revenue and break-even point.

### SA Conceptual Narratives

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This learning sequence, developed by the SA Education Department, outlines the conceptual development of the substrand 'Money and financial mathematics' of the 'Number and Algebra' Strand of the Australian Curriculum level 8.

This sequence covers the **Victorian Curriculum** content descriptors: VCMNA278.

The sequence connects the content descriptors with the proficiencies.

### Learning from home

Tab Content

This activity is designed to get your child thinking about the benefits of using percentages when comparing profit and loss in various scenarios.

Provide two different scenarios in which two ‘shop owners’ have both made a profit or both made a loss.

For example:

*Bike shop A purchased a mountain bike for $780 and plans to sell it for $1000. Bike shop B purchased a mountain bike for $1020 and plans to sell it for $1270. Which store made the greatest percentage profit?*

Ask your child to calculate the profit amount made by each store.

These questions may be used to support the discussion:

- Which store made a greater profit?
- What amount did each store pay originally?
- What other information could we obtain that may make it easier to compare the two profit amounts?
- What benefit would it be to calculate the percentage profit for each store?

Now ask them to calculate the percentage profit for each store and determine which store made the greatest percentage profit.

Another part of this task could be to provide a scenario in which two stores have made the same amount of profit (or loss) but the original purchase prices are different, as this will yield a different percentage profit.

For example:

*A furniture shop purchases an armchair for $750 (wholesale) and sells it for $1000 (retail). Another furniture shop buys the same armchair for $820 and sells it for $1070. Which store has made the greatest profit?*

An additional activity could be used based on commissions. An artist supplies their artwork to a gallery for sale. The gallery takes 50% of the sale price as commission.

- An artist wishes to receive $100 from the sale of their artwork. What should the sale price be to enable this to happen?'
- Repeat this question for other amounts that the artist wishes to receive. Use these to find a rule for calculating the ‘mark up’ to allow for a commission of 50%.
- Try other commission percentages, such as 25%. Explore this with different amounts for the artist after the commission is deducted. Adjust your rule to allow for different commission rates.