B2.1 Use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations.
Activity 1: Take a Position (Priority of Operations)
Project a mathematical expression on the board that includes some or all of the following: addition/subtraction, multiplication/division, brackets, and exponents.
Recommendation: start with whole numbers and then increase the level of complexity. Ask the students to solve it. Circulate and point out the approach of two or three students who do not have the same answer. Take a picture of all the steps of each targeted student's work. For each station, project the approaches to solving. Give the students time to reflect individually. They must analyze the various solutions/comparison with their own and then take a position. Feedback and questioning are necessary in order to establish relationships with the many concepts required to master this content. Also, value different approaches to arrive at the correct answer.
Examples of mathematical expression
- \(3\; + \;4\; \times \;2\; - \;2\; \times \;1\; + \;4\)
- \(5\; \times \;7\; - \;2\; \times \;4\)
To more complex examples
- \(5\; \times \;{}^ - \frac{1}{4}\; + \;{\left( {2\; - \;\frac{1}{2}} \right)^ 2}\;-\;5\;\times\;0.5\)
- \({\left( {{}^ - \frac{1}{5}\; \times \;\sqrt {25} } \right)^2}\; - \;6\; \times \;50 \;\% \)
Activity 2: The Carousel (Priority of Operations)
On a daily basis, the student must use the priorities of operations.
Write problems (depending on the number of stations). Photocopy and laminate.
Arrange the desks in work islands. Each island corresponds to a station.
Group students together (3 or 4 per team). Manage the working time for each station.
Begin the Carousel. Throughout the activity, record comments, discussions and especially computational strategies.
Students can consult the Internet as needed and use the calculator. Take pictures of different student approaches (2 per station) and use these pictures to provide feedback to the students.
Examples of problems at stations
Station 1:
Josianne's cell phone plan includes an initial cost of $150.00 and a monthly cost of $32.50 thereafter. Alberto's plan includes a monthly fee of $55.00 and no initial cost. Josianne and Alberto have signed a two-year agreement with their respective companies. At the end of their agreement, what is the monetary difference between the plans?
Station 2:
The municipal pool is 20 metres long and 15 metres wide. The manager has just ordered a solar cover at a cost of $32 plus tax per square metre. How much will the bill be?
Station 3:
During a trip to France, the Poiriers purchased a beanie for 22.99 euros. At the time of the transaction, 1 euro = $1.33 CDN. When they arrived at Canadian customs, they had to pay an 18% customs fee and then the harmonized sales tax (HST). What is the price, in Canadian dollars, paid for the hat?