1 Teaching Objective(s) *Lesson Plan designed for 3-5 days The student will: II (c): complete a function based on a given rule.

Transcription

1 ! "# Teaching Objective(s) *Lesson Plan designed for 3-5 das The student will: II (c): complete a function based on a given rule. II (e): appl the principles of graphing in the coordinate sstem. II (f): eplore slope as a rate of change. Instructional Activities Begin the class b having students engage in the activit, Life with the Wright Famil. ( Have students stand net to one another, forming a circle. Allow students to choose a piece of cand from a bag/basket and have them put it in their right hand. Then sa, You are about to hear me read the stor, Life with the Wright Famil. Ever time ou hear the word right, ou are to pass the piece of cand to the person on our right. Ever time ou hear the word left, ou are to pass the cand to the person on our left. Are there an questions? Begin the activit! Before introducing graphing linear functions, review students on identifing and eplaining the following: coordinate plane, -ais, -ais, point of origin, ordered pair (-coordinate, -coordinate). Recall the Wright Famil activit. Have students imagine that the are on a coordinate plane. Ask, if ou are on our coordinate plane, and ou passed the cand to the right; would ou be on the -ais or the -ais? Have them eplain their response. Ask students if the movement along the -ais will be positive or negative. Make sure the give eplanations for their answers. Now have students review graphing linear equations. Place the following on the overhead: (Transparenc & A) + = - Ask, How do we solve this equation and graph it? Have a student volunteer working this problem on the board. Once s/he is finished, discuss her/his answer with the class. Do the agree with the steps/procedures used? Then place transparenc back on the overhead. Walk through the steps with the class.

2 Step : Create a T table and have students give values for -coordinates X Y X Y - 0 Step : Solve for the value of the -coordinate. X + = - Y - (-) + = = 0 0 (0) + = = - = - () + = = - = -4 () + = = - = -6 Step 3: Graph the ordered pair on the coordinate plane. (Note: A graph paper transparenc should be used. The teacher will have to initiate drawing the graph.)

3 To introduce slope to our students, ask for two volunteers to come to the front of the class. Have one student (Student A) sit in a chair (located to the right of ou). Have the other student (Student B) stand to the left of ou. Ask Student A to stand up and sit down in the chair. Sa, See Student A. Can we sa that s/he is rising from the chair? Have student A to sit. Ask, Is student A declining when s/he sits down? Then have Student B to run in place. Instruct Student B to run forward and backward. Ask, Can Student B run an other wa besides running forward or backward? (Note: some ma sa run in a diagonal, but ask isn t that still running forward?) At this point define a slope. Relate what the have just witnessed to what a slope is/does. Introduce notes on the tpes of slopes. (Transparenc & A) Demonstrate how to calculate the slope. Place the following on the overhead. (Transparenc 3) To calculate the slope of a linear function, show the equation used: Slope (m) = difference in -coordinate difference in -coordinate m = If the coordinate A (4,) and B (3,) are given, can ou find the slope? m = = = 3 4 m =

4 Show students what the graph looks like. Draw attention to the positive direction of the slope. (Transparenc 4) 4 (4,) (3, ) Once students are comfortable with solving for the slope, ask if the slope is positive or negative? How do ou know? What does it mean? Now have students take out their graphing calculators to find/determine slopes of linear functions. Using the overhead graphing calculator, demonstrate creating a graph for = +, + = 3, =. Bring attention to the similarities in each line. Ask is the slope positive or negative? Tr = -3 +, = , = -3. Is the slope positive or negative? How do ou know?

5 Introduce the -intercept b placing Transparenc A back on the overhead projector. Ask: At what point did the line intersect the -ais? Draw attention to (0, -). Identif that point as the -intercept. Make sure to stress the -intercept as the point where the line crosses the -ais. Understanding how to calculate the slope and how to identif the -intercept is necessar to write rules for linear function. Inform students that a rule is an equation that describes the function. The rule/equations is f() = m + b, but it is generall seen as = m + b. = m + b slope -intercept In order to write the equation, look for a specific pattern in the -coordinates and the - coordinates (of ordered pairs as the relate to the slope. Place the following on the overhead projector. (Transparenc 5) Hallelujah Value X Bring attention to the pattern of the -coordinate. Notice how the value of increases b. Bring attention to the pattern of the -coordinate. Notice how the value of increases b 6. This pattern can be represented in the slope equation: Y m = 6 = 3

6 Eplain that the hallelujah value is given to zero in the -coordinate because it will alwas represent the point where the line crosses the -ais or the -intercept. With all information computed and provided, write the rule for this linear function. = m + b slope = m + b = 3 + -intercept A good activit that reinforces the concept of identifing slope and writing linear functions is Height vs. Shoe Size ( Discuss the findings as a group. A great activit for finding slopes using the graphic calculator is Spaghetti Bridges activit ( 3 Materials and Resources o Overhead projector/ markers o Student portfolio o Graphing calculator (Overhead/Teacher) o Student graphing calculator o Paper cups o Pennies (00 coins per group) o Large packages of uncooked spaghetti o Small pieces of cand 4 Assessment Observation/Student Participation Student Portfolio Spaghetti Bridges Activit Height vs. Shoe Size Activit

7 + = - Transparenc Step : Create a T table and have students give values for -coordinates X Y X Y - Step : Solve for the value of the -coordinate. X + = - Y 0 - (-) + = = 0 0 (0) + = = - = - () + = = - = -4 () + = = - = -6

8 Transparenc A Step 3: Graph the ordered pair on the coordinate plane. (Note: A graph paper transparenc should be used. The teacher will have to initiate drawing the graph.) 4 (,0) -5 5 (0, -) - (, -) (, -3) -4

9 Transparenc Positive Slope

10 Transparenc A Negative Slope

11 Transparenc 3 To calculate the slope of a linear function, show the equation used: Slope (m) = difference in -coordinate difference in -coordinate m = If the coordinate A (4,) and B (3,) are given, can ou find the slope? m = = = 3 4 m =

12 Transparenc 4 4 (4,) (3, )

13 Transparenc 5 = m + b slope -intercept X Y - -5 Hallelujah Value