Page 139 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• continue to make connections between the rate of change and the initial value and what they represent in a given context;
• introduce the terms partial variation and direct variation as connected to initial values and proportionality;
• encourage students to identify relationships using functional thinking by making connections between the term value (dependent) and corresponding term number (independent) as well using recursive thinking by making connections from term value to term value.
Teacher Prompts
• How can you determine the rate of change from each representation? Do you find it easier to determine the rate of change with some types of representations than with others?
• How can you determine the initial value from each representation? Do you find it easier to determine the initial value with some types of representations than with others?
• Given one of the four types of representations (concrete materials, table of values, graph, and equation), how do you create the others for the same relation?
• Given four representations of different types, how do you know they all represent the same relation?
• What does the rate of change mean in this context? What does the initial value mean in this context?
Sample Tasks
1. Provide students with a set of 20 cards (concrete or digital). Each card should have one of five different linear relations, each represented in one of four ways: visual, table of values, graph, and equation. Have them match sets of cards that show different representations of the same linear relation. For an added challenge, replace some of the representations with blank cards for students to complete.
2. Provide students with one representation of a linear relation in context, and ask them to create a different representation of the relation. Some examples of contexts that might be relevant to students’ lives are:
• cost of participating in various classes (e.g., dance, yoga, martial arts, fitness, music)
• distance travelled over time
• number of hours worked and total pay
• mass of bulk goods purchased and cost
• area of land and crop yield
3. Have students create one representation of a linear relation that illustrates a scenario they have created. Then have them trade representations, describe the scenario, and create a different representation of it.
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