Page 155 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Teacher Prompts
• How does the number of tiles added each time in a concrete pattern relate to the slope of the graph representing this relation?
• How can you determine the slope of a line from a graph? From a table of values?
• What information do you need to determine the equation of a line?
• Why can you use any two points on a line to determine the slope?
• What happens to this linear pattern if we move backwards from term 2 to term 1 to term 0?
What might term −1 look like? How would you represent it on a graph?
Sample Tasks
1. Have students use concrete materials to build several terms of a linear pattern and write the general rule for the pattern. Then have them plot the given terms of the pattern on a graph and use the graph to predict what happens before term 0. Have them make connections between the general rule for the pattern and the rule written in the form y = ax + b.
2. Have students determine an equation to represent the relationship between the number of sides of a polygon and the sum of the interior angles of the polygon, using the information in the table below.
3 180°
4 360°
5 540°
3. Have students plot this relation on a graph, determine the slope of the line, and discuss how the slope is related to the context.
4. Provide students with sets of cards, each showing an equation, a graph, a table of values, or a visual model. Have them match cards that represent the same relation and discuss how the equation connects to the other representations. Include representations where non-consecutive values are given, and some cards that are missing information so that students can complete them.
A completed set might look like the following:
154
Number of Sides
Sum of the Interior Angles