![]() ![]() ![]() If seventh grade students are given a real-world situation to analyze, they must be able to determine if the situation is proportional or not. This constant rate of change can also be thought of as, 'when x increases by some value, then y also increases by some constant rate.' Likewise, students can 'undo' the process to find the 'k' or constant rate of change, by division (y/x = k). Students will be able to determine the relationship by looking at the pattern in the table, in the written description, or in the graph. Also, from the written description (in words or equation form), there is a constant rate of change (miles per hour, people per class, etc.). The slope of proportional relationships is always the constant factor relating the two quantities. They will find that all proportional relationships that are represented in a table will have the same quotient (slope) for y/x. This constant rate of change can be found by dividing the y value by the x value, and comparing them. ![]() In a tabular representation, the relationship will be shown as a constant rate of change, increasing by the same value all the time. Seventh grade students will understand that if a relationship is proportional its graph will be a straight line climbing from left to right (has positive slope) and passes through the origin (0, 0). Seventh grade students are developing understanding that a function is a relationship between an independent and a dependent variable in which the change in value of the independent variable determines a direct corresponding change in value of the dependent variable. ![]()
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