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Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: How would you describe the graph of the ordered pairs for
a relationship where the ratio of change is constant?
Ask students to sketch a prediction on the back of the Little Treasure Map for what the line would look like if change Y and the change in X were to be different from point to point. Then, have them start at the original point and use the slope 1/1 to plot another point, then 2/5 to plot a third point, then -3/2 to plot a fourth point.
Lesson Segment 2: How can a ratio be used to describe the “steepness” of a
line? Why does slope remain constant?
Slopes from graphs:
Discuss lines with a positive, negative, 0, or not slope at all. A mnemonic for this is the
Dance: “Slope Dance”- Students stand and face the front of the room. You stand behind them. Put on music and have them use their arms to show a positive, negative, 0, or no slope line as you call each of these out.
Journal: Fold and cut the Finding the three Ways To Find Slope foldable. Fill in the example for finding slope from a graph of a line.
Lesson Segment 3: How can ordered pairs for a linear relation show that slope of a line is constant?
Slope from a table
To find patterns leading to the concept of slope, type an equation in the Y=. In Table Set, set the Independent and Dependent to “ask”. Press the Table key and type values in the X list. Press the Enter key to put a few intermittent values in Y list. Leave some of the values out of the Y list. Have students determine what the missing values are. Ask, “How did you decide that?” Some students will remember this activity from the last lesson for writing an equation. Others will reply that they saw the pattern in the change in the Y values rather than in relating Y to X. Tell them for slope they will be using the change from Y2 to Y1 and from X2 to X1 Have them copy the tables on an assignment paper and write the change in Y to the change in X as a ratio. Do several equations in this manner. Some possible equations you may wish to try are: y = x, y = -x , y = 2x, y = -3x, y = ½ x, y = 1/3x, y = 5, y = x, y = -x
Connect the “change in Y over change in X” from the table to counting that change when they were looking at the graph. Discuss that just as the ratio of rise to run on the graph was always the same ratio, the ratios of change in Y to change in X in the table must be equivalent. On their assignment paper ask them to begin with X being 0 and y being any number they choose and construct tables of values that having the following slope:
Game: Truth or Dare Give each team one of the tables from the Tables and Slope Transparencies. The team works together to determine if the tables show a linear relationship by checking for a constant ratio for change in y to change in x. A team member is then selected to bring the transparency to the overhead and ask the class members to determine if the table shows a linear relation or not and how they determined their answer. Class members are given 30 seconds to check with their team to reduce risk. The student at the overhead then selects a person from the class to either tell the truth or take a dare. If the selected student can tell the truth and explain their reasoning, they needn’t take the dare. If not, the challenging team gives the dare such as, “Jump up and down while barking like a dog.” All dares must be respectful and the teacher can veto a dare if is inappropriate. Students should copy all tables on an assignment paper and write the slope of the line IF the table indicates a linear relation.
Journal: Fill in the example for finding slope from a table on the foldable.
Slope from ordered pairs.
Four-Corners practice: Use the ordered pairs on the 10 cards (attached). Ask person # 1 from a team to come draw out any two ordered pairs. Then, have person #2 from another team come do the same, and person # 3 from a team, and person # 4 from another team. Do Four Corners where all the #1’s go to a corner, the # 2’s to another corner, the # 3’s to a third corner and the # 4’s to the fourth corner of the room. In the corner they look at the 2 ordered pairs that were drawn. Together, they find the slope of the line that would contain those two points. Have the students return to their desks and teach their teams how to find the slopes. These four problems should also be recorded on the back of the Slopes from Graphs worksheet.
Journal: Fill in the example for finding slope using two ordered pairs.
Lesson Segment 4: How can right triangles be used to show that slope is constant?
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