C2.2 Evaluate algebraic expressions that involve whole numbers and decimal tenths.
Activity 1: Lock
Boats navigating rivers occasionally encounter rapids. To get around these obstacles, locks are built to allow boats to move up and down the river. When all the boats have entered the lock, the lock operator activates the gates that are used to change the water level between the gates.
Michel is on his sailboat. He has just entered a lock to go down to another river. In this lock, the water level is 12 m and, every minute, it goes down of \(\frac{1}{2}\) metre.
The algebraic expression that represents the water level lowering over time is
12 - 0.5t
where t is the time elapsed since the valves were opened, in minutes.
- What is the water level 15 minutes after the lock operator opened the gates? 20 minutes after?
- What is the maximum time, in minutes, that the lock operator can have the gates opens?
Source: L'@telier - Online Educational Resources (atelier.on.ca).
Activity 2: Weekly Pocket Money
Two friends discuss the amount of spending money they each receive from their parents each week.
Martha receives $14 each week as compensation for doing various tasks around the house.
Sofia's parents give her an amount based on the number of tasks she does during the week. She receives a base amount of $5, plus $0.50 for each task she does during the week. The algebraic expression that represents this relationship is 5 + 0.5t, where t is the number of tasks completed.
- If Sofia completed 14 tasks last week, that is making her bed and picking up her clothes each day, how much spending money will she have at the end of the week?
- How many tasks does Sofia have to do to equal the amount of her allowance to Martha's?
Source: L'@telier - Online Educational Resources (atelier.on.ca).