Page 141 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• facilitate a discussion about the strengths and limitations of comparing relations graphically versus comparing them algebraically;
• support students in interpreting the point of intersection in the context of the problem by highlighting that this is the point that satisfies both equations and the point where, for a specific independent value, both relations have the same dependent value;
• provide students with opportunities to use digital tools or coding to compare linear relations;
• support students in making connections between the algebraic method of comparison that they
are learning now and the strategies they learned for solving equations with variables on both sides of the equal sign in Grade 8.
Note
The use of the algebraic method is intended to involve only the method of comparison, not to be extended to elimination, substitution, or other approaches to solving linear systems.
Teacher Prompts
• What is similar and what is different about these two linear relations?
• What does the point of intersection (if any) mean in this situation?
• Compare the rates at which these relations are growing.
• Thinking about the context of a situation shown graphically, describe what is happening on the
left and right sides of the point of intersection (if any) on the graph.
• List the strengths and weaknesses of both the graphical method and the algebraic method of
comparing relations.
• Will two linear relations always have a point of intersection? In what cases will they not intersect?
Sample Tasks
1. Have students compare two different linear relations and identify when they are equal (the point of intersection, if they have one) and when one is greater than the other. Some possible contexts are: pages read in a book, earnings from a job, cell phone plans, distance travelled, gym memberships.
For example: A salesperson has two different options for getting paid. The options are shown on the graph below. What should they consider when choosing the best option for them? What are the differences between the two options? Under what conditions would each option be better?
• Option A: A monthly salary of $400 plus a 5% commission on total monthly sales
• Option B: No set monthly salary, but with 10% commission on total monthly sales
140