Domain, Range, Independent and Dependent Variables

Transcription

1 Domain, Range, Independent and Dependent Variables Context: This lesson is designed for a pre-algebra class at Berkeley Middle School made up of about th graders. In previous lessons have included students learning about linear equations including, finding solutions, solving for y given x, determining if an ordered pair is a solution and writing linear equations. Objectives: Student will be able to define domain, range, independent and dependent variables. Students will be able to determine the domain, range, independent and dependent variables of real-life scenarios. SOL: Resources/ Materials: 8.17 The student will identify the domain, range, independent variable, or dependent variable in a given situation. While You Wait Note Worksheet Practice Worksheet Homework Approximate Time Required: 60 minutes Content and Instructional Strategies: 1. (Before the class) The teacher should cut out the real-life scenarios and tape them up around the room to have students complete during the second half of the lesson. 2. (5 minutes) Once the class period begins, the teacher will hand out the While You Wait to the students. The students will paste their While You Waits onto their weekly While You Wait sheet. While students are completing the While You Wait, the teacher will walk around the room, monitoring students' progress. 3. (5 minutes) The teacher will go over the While You Wait with the students, soliciting answers from the students. 4. (15 minutes) The teacher will complete the notes worksheet. The teacher will relate the vocabulary to science class, where the students have seen independent and dependent variable before. The teacher will solicit responses from students for filling in the second half of the notes sheet. 5. (20 minutes) The teacher will then hand out the practice problem worksheet and have students go around the room, filling in as many as they can solve. The students will be required to fill out at least two of the domain and range and of the independent and dependent variables questions. The teacher will walk around the room monitoring students and checking for understanding. 6. (10 minutes) The teacher will have student return to their desk and s/he will then review the

2 worksheet, soliciting answers from the students. The teacher will ask how many students completed each problem, to check the difficulty level and student's understanding. 7. (5 minutes) The teacher will hand out the homework worksheet and have students begin working on it, allowing time for questions to be asked in class. Evaluation: Homework worksheet Continuous monitoring students by walking around and calling on students to answer questions. Differentiation and Adaptations: The students will be allows to work in pairs while completing the practice activity, so students who might be struggling can receive help from their peers. For students who require a copy of the teacher's notes, I will make a copy of the notes that I filled out in class.

3 While You Wait Suppose you buy DVDs for $15 each. Find the cost of buying 3, 4 and 5 DVDs. DVDs Cost ($) If 6 DVDs are purchased, what is the total cost? 2. Explain how to find the total cost of 9 DVDs. While You Wait Suppose you buy DVDs for $15 each. DVDs Cost ($) If 6 DVDs are purchased, what is the total cost? 2. Explain how to find the total cost of 9 DVDs.

4 Functions A is a relation in which each member of the (input value) is paired with exactly one member of the (output value). The variable for the domain is called the because it can by any number. The variable for the range is called the because it depends on the domain. Suppose you are buying hotdogs for $2 each. Find how much it would cost to buy the following number of hotdogs. Hotdogs Cost ($) Equation: The independent variable is: The dependent variable is: Yesterday, Mike decided to go to the store to buy hotdogs for tonight's dinner. He only brought $12 to the store with him. How many hotdogs can he buy? How much money can he spend?

5 1.) Independent Variable: 6.) Dependent Variable: 2.) Independent Variable: 7.) Dependent Variable: 3.) Independent Variable: 8.) Dependent Variable: 4.) Independent Variable: 9.) Dependent Variable: 5.) Independent Variable: 10.) Dependent Variable:

6 1.) A veterinarian needs to give medication to a dog. The dosage is 5 milligrams for every 1 pound of weight. The total amount of dosage d needed for a dog weighing p pounds can be represented by the function d = 5p. 2.) An air conditioner repair service charges $60 for a service call plus $30 per hour for labor. The total amount charge to the customer m, for any number of service hours, h can be represented by the function m = 30h ) A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. The total amount charge to the customer c, for any number of miles, m can be represented by the function c = 2m + 3.

7 4.) A phone company charges a base rate of $40 a month for service. The user is charged $.20 a minute for every minute used. The total amount charge to the customer p, for any number of minutes, m can be represented by the function p =.2m Identify the independent and dependent variables for one month use. 5.) Santa can deliver presents to 100 children per hour. The total amount of people p, for any number of hours h, can be represented by the function p = 100h. 6.) There are approximately 770 peanuts in a ounce jar of peanut better. The total number of peanuts p in any number of jars of peanut butter j can be represented by the function p = 770 j.

8 7.) A scrapbooking store is selling rubber stamps for $4.95 each. The total sales s for any number of stamps n can be represented by the function s = 4.95n. 8.) A online shoe store is have a sale on flip-flops for $8 each. When you order online, you have to order at least 3 flip-flops and no more than 20 flip-flops. The total price p for a number of flip-flops, between 3 and 20, s can be represented by the function p = 8s. 9.) Over the summer, you decide to open a lawn care business. You offer to cut your neighbor's grass for $10 an hour. However, you explain that in for a day's job, you will only work a minimum of 1 hour and a maximum of 4 hours. For one day's job, the total amount a, for the number of hours h can be represented by the function a = 10h.

9 10.) Peter needs to fill up his truck with gasoline to drive to and from school next week. If gas costs $2.79 per gallon, and his truck holds a maximum of 28 gallons. The the total amount of money m, for every gallon g of gas, between 0 and 28, can be represented by the function m = 2.78g.

10 Name: Date: Homework: 1.) Paul opens a savings account with $350. He saves $150 per month. Assume that he does not withdraw money or make any additional deposits. The total amount of money saved s, for every month m can be represented by the function s = 150m ) Conner has $25,000 in his bank account. Every month he spends $1,500. He does not add money to the account. The total amount of money a, in Conner's bank account, for every month m can be represented by the function a = m.