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This slope lesson explores real world situations
9, 12, 11, 10
Title – Slopes
By – Mikel Whiting
Primary Subject – Math
Grade Level – 9-12
Overview: This lesson explores real world situations as it relates to slopes, such as stairways and inclines.
Lesson Plan Objectives:
MA.C.3.4.2: Using a rectangular coordinate system (graph), applies and algebraically verifies properties of two- and three-dimensional figures, including distance, midpoint, slope, parallelism, and perpendicularity.
In this lesson students will learn to:
1. determine value of a slopes’ incline by using the slope-intercept formula, and
2. investigate real-world situations such as escalators, airplanes, and calorie burning.
Teaching and Instructional Strategy
(15 min.) MODELING
(10 min.) DISCUSSION
(20 min.) SEE-SAY-DO
(10 min.) LECTURE/BRAINSTORM
(20 min.) QUESTIONING
(15 min.) TEXTBOOK EXERCISE
(15 min.) MODELING: Read the example: “When you jog, you burn 7.3 calories/min. When you run, you burn 11.3 calories/min. Write an equation to find the times you would need to run and jog in order to burn 500 calories.” Explain to the students that “x” represents minutes spend jogging and “y” represents minutes spent running. Explain that relating this information to an equation would be: 7.3x + 11.3y = 500. (Answer: x-intercept = 13.5, y-intercept = -4.5) Remind students of the slope formula, slope-intercept formula, and point-slope formula.
(15 min.) DISCUSSION: Ask the students: “How is the slope-intercept form (y = mx + b) of an equation like or unlike a recipe”
(20 min.) SEE-SAY-DO: Read the sentence: “Slope equals vertical change (rise) divided by horizontal change (run).” Have students read the sentence aloud. Read the “slope equation” in sentence form: “Slope equals vertical change “y2 minus y1 divided by x2 minus x1 (where x2 and x1 is not equal to 0).” Have the students read the sentence aloud. Read the sentence: “Rate of change equals change in dependent variable (vertical change) divided by the change in independent variable (horizontal change). Have the students read the sentence aloud. Therefore, “Rate of change equals Slope.” Ask the students: “Find the slope of the line passing through each pair of points (-3,-1)(-1,5).” Ask the students: “How would they place these coordinates in the “slope equation. Model the equation on the board: “Slope equals vertical change “y2 minus y1 divided by x2 minus x1 (where x2 minus x1 is not equal to 0).” Have the class to repeat the equation sentence: (5)-(-1)/(-1)-(-3). Ask if there are any questions. Remind the students that a number cannot be divided by zero. Explain to the students that if y2-y1 = 0, then the slope is a “horizontal line”, and if x2-x1 = 0, then the slope is a vertical line and is considered “undefined”.
(10 min.) LECTURE/BRAINSTORM: Tell the students that today’s lesson is to review “Slopes” and “Rates of Change”. Have students brainstorm other situations, such as airplane flight landings or takeoffs, which it is more practical to explain slopes and rates of change and to determine the steepness of slopes and rates of change by viewing and recording this data. Remind students that the dependant variable goes in the numerator and the independent variable goes in the denominator. Point out that by convention we read slopes from left to right. (When lines rise from left to right, its slope is “positive”, and when lines fall from left to right, its slope is “negative”)
LEP, IEP, ESE, ESOL students will be allowed more time to answer questions during discussion and will be given extra time to complete the five individual seatwork problems. These students will also be allowed to complete seatwork with peer tutor.
(15 min) TEXTBOOK EXERCISE: Students will correctly solve five slope and rate of change problems provided by teacher.
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