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This is a similar lesson with the emphasis on determining slope steepness and rates of change
9, 10, 11, 12
Title – Slopes and Rate-of-Change
By – Mikel Whiting
Primary Subject – Math
Grade Level – 9-12
Overview: This lesson is about determining the steepness of slopes and the rates of change.
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. investigate real-world situations that relate to slopes and rates of change, and 2. determine the steepness of slopes by viewing and recording data.
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: Tell the students that on each table are construction paper and markers. Assign students to teams of four and have them work as a team to make paper airplanes. Have half of the group members to fly the planes and the other members to time the flights in seconds. Have the students to graph their data in the form of sloping lines. Have students turn in their airplanes in fifteen minutes. Students are to find three sloping objects and determine the difference in their “rise” and “run”.
(15 min.) DISCUSSION: Ask the students: “Who can explain what they think “slope” means?” (list their ideas on the board) Give examples such as roads, walkways, ramps, stairs, or slides. Explain what the words “vertical” and “horizontal” mean. Ask the students: “Who can describe ways in which the steepness of a slope might be measured?” Ask students: “What terms have you used in the past to describe how quickly or how slowly something changes?” (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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