22.1: Revisiting Interest and Depreciation (5 minutes)
The warm-up reminds students of their understanding of percentage increase and decrease in preparation for the shares questions later in the lesson. Some students will use different strategies; identify those for the discussion after the activity.
Remind students that they can use any strategies from sixth grade for answering the percentages questions.
- Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 1 year? After 2 years?
- Diego wants to sell his bicycle. It cost $150 when he bought it but has depreciated by 15%. How much should he sell it for?
If students forget about using an equation to calculate percent increase or decrease, remind them that they can use the equation \(y=kx\) to figure out the answers to the questions.
The most important thing is to recall efficient methods of calculating percent increase and decrease, such as setting up an equation in the form A% of B is C. Select students to share their methods in preparation for the next activity.
22.2: Gains and Losses (10 minutes)
Students are introduced to the idea of the stock market and how the value changes. They apply their understanding of negative numbers to percentage change as well as money (MP4).
Introduce the concept of shares in a company. They have a specific value at a specific time that can change up or down. They represent a measure of the worth of the company. We sometimes express the change as a value in dollars, so investors can see how much money they will make or lose. We can also present these as a percentage to compare companies in terms of growth.
Before students begin working on the task consider asking how they would represent an increase or decrease in value so that it was easily apparent.
To familiarize students with the information in the table, consider asking which companies’ stocks increased in value and which companies’ stocks decreased in value from day 1 to day 2. Have students explain their reasoning and come to an agreement before anyone begins doing calculations.
Supports accessibility for: Memory; Conceptual processing
Design Principle(s): Cultivate conversation
- Here is some information from the stock market in September 2016. Complete the table.
company value on day 1 (dollars) value on day 2 (dollars) change in value (dollars) change in value as a percentage of day 1 value Mobile Tech Company 107.95 111.77 3.82 3.54% Electrical Appliance Company 114.03 2.43 2.18% Oil Corporation 26.14 25.14 -3.83% Department Store Company 7.38 7.17 Jewelry Company 70.30 2.27%
- Which company's change in dollars had the largest magnitude?
- Which company's change in percentage had the largest magnitude?
The important part of this activity is that students use a directed quantity for percentage change to model decrease in value as negative and increase as positive. Ask students how they would prefer the information to be presented, and ask them to support their conclusions.
22.3: What is a Stock Portfolio? (15 minutes)
This task introduces the concept of a stock portfolio being a selection of stocks an investor might own to try to make money—students examine the change in portfolio and evaluate the value. They must use both positive and negative change, and percentage change.
Introduce the concept of a portfolio of shares in a company.
Supports accessibility for: Language; Social-emotional skills
Design Principle(s): Support sense-making; Maximize meta-awareness
A person who wants to make money by investing in the stock market usually buys a portfolio, or a collection of different stocks. That way, if one of the stocks decreases in value, they won’t lose all of their money at once.
- Here is an example of someone’s stock portfolio. Complete the table to show the total value of each investment.
name price (dollars) number of shares total value (dollars) Technology Company 107.75 98 Airline Company 133.54 27 Film Company 95.95 135 Sports Clothing Company 58.96 100
- Here is the same portfolio the next year. Complete the table to show the new total value of each investment.
company old price (dollars) price change new price (dollars) number of shares total value (dollars) Technology Company 107.75 +2.43% 98 Airline Company 133.54 -7.67% 27 Film Company 95.95 87.58 135 Sports Clothing Company 58.96 -5.56% 100
- Did the entire portfolio increase or decrease in value over the year?
The important part of this activity is that it extends on the context previously examined, ahead of students building their own portfolio in a later activity.
22.4: Your Own Stock Portfolio (15 minutes)
Distribute copies of the "Stocks Prices"
Students calculate their own portfolio
Distribute copies of the "Changes in Stock Prices after 3 Months" so they can calculate the change.
Distribute copies of the Stock Prices Blackline Master. Have prepared the Changes in Stock Prices after 3 Months Blackline Master.
Supports accessibility for: Memory; Organization
Your teacher will give you a list of stocks.
- Select a combination of stocks with a total value close to, but no more than, $100.
- Using the new list, how did the total value of your selected stocks change?
Have students trade with a partner and check each other's work. (Answers vary because each student worked with a different selection of stocks.)
Have students examine the "Changes in Stock Prices after 3 Months" page and discuss:
- How can you tell if the price of a stock increased or decreased from looking at this list?
- Which company's stock price increased or decreased by the most?
- Without doing any calculations, predict which company's stock price had the largest increase as a percentage of its starting value.
- Without doing any calculations, predict which company's stock price had the largest decrease as a percentage of its starting value.
Design Principle(s): Optimize output (for description)
Key learning points:
- There are a number of contexts in which using negative numbers to represent directed change is important; the stock market is one of them.
- Percentage change down can be represented with a negative percentage
- Which way of showing the change do you prefer, percentage or monetary value?
- Can you think of other situations in life where using a negative to represent a change would be useful?