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Focus Plan Texarkana Independent School District GRADING PERIOD: Teacher: 2nd 6 Weeks PLAN CODE: Winton Course/subject: Mathematics Grade(s): 8 Time allotted for instruction: 1 ½ - 2 hours Title: Working with Ratios, Rates, and Unit Rates Lesson TOPIC: Ratios, Rates, Unit Rates TAKS Objective: Objective 2: The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning FoCUS TEKS and Student Expectation: (3) Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations and solves problems. The student is expected to: (B) estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates (1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: (B) select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships Supporting TEKS and Student Expectations: Concepts Ratio Rate Unit Rate Enduring Understandings/Generalizations/Principles The student will understand that A ratio is the comparison of two numbers by division. The ratio of 2 to 3 can be stated as 2 out of 3, 2 to 3, 2 : 3, or 2/3. A rate is a ratio of two measurements having different units. In a percent proportion, the ratio of a number to 100. A unit rate is a rate with a denominator of 1. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District I. Sequence of Activities (Instructional Strategies) A. Focus/connections The beginning of class will be spent working on a survey. Divide the class in half as they enter the classroom. After class has been divided, ask for a volunteer to be the group recorder for each group. After the recorders have been determined, give the each a copy of the Class Survey Worksheet. The recorder will ask the questions on the worksheet and record the results for their half of the class. B. Instructional activities (demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.) After time has been given to complete the survey, ask the recorders to give you some of the numbers involved. Write the different ratios given on the board. Discuss the survey results. Tell your class that in this example, a comparison was made. A comparison of two numbers is called a ratio. There are several ways a ratio can be expressed: 4 to 5, 4: 5, 4 out of 5, or 4/5. Survey the class again with the following question: How many of you like to drink Pepsi? Count the number of hands raised and the number of hands not raised. Demonstrate the different formats the ratio from this survey could produce. Next discuss rates. A rate is a ratio which compares two measurements with different units. For example, miles to gallons, cents to pounds. Give the class the following scenario: The Candy Factory at the mall sells candy by the pound. Suppose you spend $10 on 2.5 pounds of candy. The rate $10 / 2.5 pounds compares the money spent to the number of pounds of candy. The unit rate for this problem could be set up as follows: $10 / 2.5 = x / 1. This would let us know the amount 1 pound of candy would cost. C. Guided activity or strategy Pair each student with a peer and let them work together to reinforce the lesson objectives by completing the Practicing with Rates, Ratios, and Unit Rates Worksheet. Circulate around the room and assist students as needed. After time has been given for pairs to complete the activity, go over answers with the class. Answer any questions that may arise. Teacher will then give each student the worksheet titled: Working with Ratios, Rates, and Unit Rates Worksheet. D. Accommodations/modifications Students requiring modifications may be paired with a peer to complete the guided activity. E. II. Enrichment STUDENT PERFORMANCE A. Description Students will complete the Working with Ratios, Rates, and Unit Rates Worksheet independently. iii. B. Accommodations/modifications C. Enrichment Assessment of Activities A. Description Individual grades may be taken on the Working with Ratios, Rates, and Unit Rates Worksheet. B. Rubrics/grading criteria Grades may be taken based on the Working with Ratios, Rates, and Unit Rates Answer Key/Grading Rubric. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District IV. C. Accommodations/modifications D. Enrichment E. Sample discussion questions In what real world setting do you see ratios? Why is it important to know how to calculate unit rates? TAKS Preparation A. Transition to TAKS context The teacher will lead the class in a discussion of how rate and ratio problems may look in test format. The teacher will place the TAKS questions below on the board/overhead. B. Sample TAKS questions 1. The results of a random survey showed that 42 out of 80 people plan to vote for Mr. Vu for city council. Which is the best prediction of the total number of votes he will receive if 2,000 people vote? A. 25 B. 50 C. 120 D. 1,000 2. Vanita can read an average of 18 pages during a 30-minute reading period at school. At this rate, approximately how long will it take her to read a 380-page book? F. 11 h G. 21 h H. 23 h J. 42 h V. Key Vocabulary Rate, ratio, unit rate VI. Resources A. Textbook Glencoe Mathematics ~ Applications and Connections Course 3 Chapter 3: Using Proportion and Percent Ratios and Rates, pp. 104 – 106 Ratios and Percents, pp. 107 - 110 B. Supplementary materials Class Survey Worksheet Practicing with Rates, Ratios, and Unit Rates Worksheet Practicing with Rates, Ratios, and Unit Rates Answers Working with Ratios, Rates, and Unit Rates Worksheet Working with Ratios, Rates, and Unit Rates Answer Key/Grading Rubric C. Technology Students may be taken to the computer lab to utilize the following web sites: http://www.algebralab.org/practice/practice.aspx?file=Algebra1_2-8.xml http://www.321know.com/rat62ax2.htm (activity at bottom of page) http://www.321know.com/rat62bx2.htm (activity at bottom of page) Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District VII. follow up activities (reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.) A good follow up lesson would be one pertaining to solving proportions. VIII. Teacher Notes Point out to students the many uses of ratios and rates in everyday life. Some examples include the prices in stores, the speed of cars and airplanes, and the records of sporting events. Encourage students to think, estimate, and predict rates based on a given rate, such as "how much will 10 pencils cost if 3 pencils cost $1.25"? Have them discuss different strategies for solving the problem. Using facts about money, time, and distances provides meaningful experiences about unit rates and ratios in general. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District