MS Algebra A-F-IF-6 – Ch. 5.5b Finding the Rate of Change ALGEBRA SUPPORT Finding the Rate of Change

SUPPORT Class Learning Target Title: 5.5b Find Rate of Change Date: SUPPORT Class Learning Target By the end of the period, I will find the rate of change of various intervals in given graphs. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.5 Pg. 288-289 3) Section ______ TxtBk. Prob.#31,32,33,35,38 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

HW # 31 Use the graph, which shows the distance traveled by a car during a 2 hour drive The slope of each line segment gives the car’s speed, which is the rate of change in distance traveled with respect to time. Find the car’s speed during the first hour. (2, 100) y 100 80 60 40 20 (1, 60) (0,0) 0.5 1 1.5 2 2.5 3 x Time(hr.) STEP 1) Choose 2 points ( , ) and ( , ) STEP 2) Make a table of points x y STEP 3) Find the difference Find the difference - - STEP 4) Make a fraction with the values from STEP 3. m= = = =  denominator  numerator 4

HW # 32 Use the graph, which shows the distance traveled by a car during a 2 hour drive Find the car’s speed during the second hour. (2, 100) y 100 80 60 40 20 (1, 60) (0,0) 0.5 1 1.5 2 2.5 3 x Time(hr.) STEP 1) Choose 2 points ( , ) and ( , ) STEP 2) Make a table of points x y STEP 3) Find the difference Find the difference - - STEP 4) Make a fraction with the values from STEP 3. m= = = =  denominator  numerator 5

The car travels faster in the _______ hour. HW # 33 Use the graph, which shows the distance traveled by a car during a 2 hour drive During which hour is the car traveling faster? How does the graph show this? (2, 100) y 100 80 60 40 20 The car travels faster in the _______ hour. (1, 60) (0,0) 0.5 1 1.5 2 2.5 3 x Time(hr.) The graph shows this because_______ _______________________________ ______________________________. 6

Storm Check (Think, Write, Discuss, Report) How do you find the slope for a given region of a graph? (3 or 4 sentences) To find the slope for a given region of a graph, I have to ________________________________ ___________________________________________ __________________________________________.

The kiln showed the greatest rate of change between________and_______ HW # 35 Determine the time interval when the temperature in the kiln showed the greatest rate of change. (8.95, 1920) Firing a piece of pottery in a kiln takes place at different temperatures for different amounts of time. The graph shows the temperatures in a kiln while firing a piece of pottery. (after the kiln is preheated to 250⁰F) (4.65, 1680) Temp(F) (2.5, 1300) 1500 1000 500 (1.5, 1000) (0,250) 1 2 3 4 5 6 7 8 9 Time(hr.) The kiln showed the greatest rate of change between________and_______ because________________________. 8

The kiln showed the least rate of change between________and_______ HW # 35 Determine the time interval when the temperature in the kiln showed the least rate of change. (8.95, 1920) Firing a piece of pottery in a kiln takes place at different temperatures for different amounts of time. The graph shows the temperatures in a kiln while firing a piece of pottery. (after the kiln is preheated to 250⁰F) (4.65, 1680) Temp(F) (2.5, 1300) 1500 1000 500 (1.5, 1000) (0,250) 1 2 3 4 5 6 7 8 9 Time(hr.) The kiln showed the least rate of change between________and_______ because________________________. 9

Which statement about the graph is true? HW # 38 Determine the time interval when the temperature in the kiln showed the least rate of change. The graph shows the number (in thousands) of undergraduate students who majored in biology, engineering, or liberal arts in the U.S. from 1990 to 2000. Which statement about the graph is true? ─- Engineering ─- Biology ─- Liberal Arts 90 80 70 60 50 40 30 Students (thousands) ‘90 ‘92 ‘94 ‘96 ‘98 2000 Year For the period 1990-1992, the major with the greatest rate of change in students was liberal arts. For the period 1998-2000, the major with the least rate of change in students was engineering. For the period 1994-1998, biology had a negative rate of change in students. For the period 1992-1996, liberal arts had a negative rate of change in students. 10

Vocabulary – Rate of Change Slope Rise Run Slope-Intercept Form Point-Slope Form

Vocabulary Acquisition Friendly Definition Sketch Wordwork Sentence DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch DAY 1 Use Visuals Introduce the word Friendly Definition Physical Representation Use Cognates Write friendly definition Word List Vocabulary Acquisition DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example DAY 5 1. Review the word Friendly definition Physical Representation 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

Rate of Change Notes: A Rate of Change compares a change in one quantity to a change in another quantity. SLOPE and RATE of CHANGE You can interpret the slope of a line as a rate of change. When given graphs of real-world data, you can compare rates of change by comparing slopes of lines.

Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: ___________________ 2) ________________ 3) _________________ 4) ________________

Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: Positive 2) Negative 3) Zero (horizontal) 4) Undefined (vertical)

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: How are the two images similar? How are they different? How can these two images be related to math? IMAGE 1 IMAGE 2

Title: 5.5b Find Rate of Change Date: Learning Target By the end of the period, I will find the rate of change of various intervals in given graphs. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

____________________________ CHALLENGE Interpret a graph COMMUTING TO SCHOOL A student commutes from home to school by walking and by riding a bus. Describe the student’s commute in words. (3-4 sentences) ____________________________