B2.7 Multiply and divide integers, using appropriate strategies, in various contexts.
Activity 1: Finances (Operations on Integers)
Divide the class into teams of four students.
Each team will receive situations related to finances.
They have to find the mathematical expressions and the solution to each problem.
The solution must include a detailed explanation (may be in the form of an expression or equation). Take pictures of two or three approaches.
Ask team members to explain them to the class.
Examples of situations
- After completing an activity, five friends realized that they had run up a $40 deficit. They decided to divide the debt so that they would each put in the same amount, bringing the account to zero. Illustrate each person's debt with a mathematical expression.
- A business loses $150 each month. Calculate the deficit after 11 months.
- A house has an initial value of $280 000. Six months later, its value increases by $32 000. However, for the next two years, its value decreases by $14 000 every six months. What expression represents the new value of the house? Find this new value.
- A new scooter sells for $7550 with taxes. Its value decreases by $875 per year for the first six years. What mathematical expression represents the new value of the scooter? What is this value?
- Olivia has $750 in her savings account. During the holidays, she makes three withdrawals of $75 and two deposits of $25. At the end of the holidays, she decides to make a donation to charity. The amount of the donation is one fourth of her balance. What mathematical expression represents Olivia's banking transactions? What is the new account balance?
- Three friends share a debt of $900. What mathematical expression represents one person's debt? Identify this debt.
Activity 2: The Table (Multiplication and Division of Integers)
Materials
- whiteboard (one per student)
- erasable marker (one per student)
Prepare a PowerPoint with a series of small mathematical expressions containing negative integers. Project one expression at a time. The student solves the problem and writes the answer on the whiteboard. After a few seconds, ask the student to erase the board. Check the answers.
Examples of expressions
- \(-4\; \times \;-6\)
- \(\frac{{ - 24}}{{ - 8}}\)
- \( - 9\; \times \;3\)
- \(\frac{{ - 36}}{9}\)
- \( - 4\; \times \; - 6\; \times \; - 3\)
Problem
The temperature dropped by two degrees Celsius each day last week. Calculate this temperature drop.