Description of Lesson:

• Launch [10 mins] -
  • Open with a discussion of the previous lesson's homework. What was the 'best' buy? Concluding with their reasoning, students will engage in an admit ticket that will briefly revise 'Percentages' [follow the link to examine the previous Unit of Work on Percentages]. On the Admit Ticket:
    • If each ticket was worth $0.23, how much did the Carnival gain if they sold 1 ticket for $0.50?
    • What was the Carnival's profit expressed as a percentage?

*Note: Use the Vocabulary tab to explicitly define new terms "profit", "gain", "loss" etc.

• Explore
  • Activity 1 [15 mins] - Teacher to preface the digital activity "Tree Tops" and explain the following terminology (LIT). (Rather than students copying terms and definitions in their workbooks, teacher may choose to make an activity our of matching definitions to key terms):
    • 100% of an item means the full number or price.
    • Selling Price means how much the item was sold for.
    • Cost Price (original price) means how much the item was originally bought for.
    • Percentage profit means that I sold the item for more than it was originally worth. (Selling Price > Cost Price)
    • Percentage loss means that I sold the item for less than it is worth. (Selling Price < Cost Price)
    • To find percentage profit:
      1. Selling Price – Cost Price (original price) = Profit
      2. Profit / Cost Price (original price) = Percent Profit

One common misconception when calculating the percentage profit or loss is understanding that profit or loss is divided by the original cost. This is because we need to see the profit or loss compared to the original cost of the item and not what the selling price of the item is.

**Some calculative examples should be completed on the board as practice before beginning the next activity. Some examples can be found in the Textbook.

• Activity 2 [15 mins] - Set the scene for the problem:

Imagine you have a large plot of land ideal for planting a forest. First you plant the trees. Then, after 10 years, the forest is thinned to give the remaining trees more room to grow. The forest needs to be thinned again after another 10 years. The wood from the thinning is sold. Finally, the time will come when you cut down all the trees in the forest and sell the timber. You might decide to do this 30 or 40 years or even longer after first planting your trees! Your job is to find the best strategy for maximising profits for your forestry company.

• Hand out the resource sheet [preparation before the lesson needs to be done to cut the three separate sections - Terry's Trees, Theo's Thinning Company, and Lou's Lumber]. In pairs, students are to brainstorm the following:"What things do you need to consider to help establish a good strategy? What mathematical processes might you need to use?" (LIT)

Give them some time to discuss with their partner, and then bring the class together and write up the proposed considerations on the board. Some example questions that might emerge:

1. Which tree should you choose to minimise the cost of planting the forest? (Which tree is the cheapest to plant?)
2. Which tree should you choose to minimise your loss after 20 years?
3. What would the profit be for each type of tree after 30, 40, and 50 years?
4. What happens to the prices paid for each type of wood over the 100 year period? Why might this be the case?
5. What's the maximum profit you could make after 100 years?
• Students engage with the digital activity as if they were foresters and determine profit/loss margin (specifically in the form) as a percentage of the cost price. [See Worksheet 6 for further explanation]

• Summarise [5 mins] - Exit Slip to recap calculating "percentage profit".