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THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS
Linear Relations
Overall Expectations
By the end of this course, students will:
• apply data-management techniques to investigate relationships between two variables; • demonstrate an understanding of the characteristics of a linear relation;
• connect various representations of a linear relation.
Specific Expectations
Using Data Management to Investigate Relationships
By the end of this course, students will:
– interpret the meanings of points on scatter plots or graphs that represent linear rela- tions, including scatter plots or graphs in more than one quadrant [e.g., on a scatter plot of height versus age, interpret the point (13, 150) as representing a student who is 13 years old and 150 cm tall; iden- tify points on the graph that represent stu- dents who are taller and younger than this student] (Sample problem: Given a graph that represents the relationship of the Celsius scale and the Fahrenheit scale, determine the Celsius equivalent of –5°F.);
– pose problems, identify variables, and formulate hypotheses associated with rela- tionships between two variables (Sample problem: Does the rebound height of a ball depend on the height from which it was dropped?);
– design and carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology (e.g., surveying; using measur- ing tools, scientific probes, the Internet) and techniques (e.g., making tables, draw- ing graphs) (Sample problem: Design and perform an experiment to measure and record the temperature of ice water in a plastic cup and ice water in a thermal mug over a 30 min period, for the purpose of
comparison. What factors might affect the outcome of this experiment? How could you design the experiment to account for them?);
– describe trends and relationships observed in data, make inferences from data, com- pare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses (e.g., describe the trend observed in the data. Does a relationship seem to exist? Of what sort? Is the outcome consistent with your hypothesis? Identify and explain any outlying pieces of data. Suggest a formula that relates the variables. How might you vary this experiment to examine other relationships?) (Sample problem: Hypo- thesize the effect of the length of a pendulum on the time required for the pendulum to make five full swings. Use data to make an inference. Compare the inference with the hypothesis. Are there other relationships you might investigate involving pendulums?).
Understanding Characteristics of Linear Relations
By the end of this course, students will:
– construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations (Sample problem: Construct a table of values, a graph, and