Ratios And Proportional Relationships: Lessons 1-6

2y ago
24 Views
3 Downloads
228.54 KB
17 Pages
Last View : 1d ago
Last Download : 2m ago
Upload by : Oscar Steel
Transcription

Unit 7-1Lesson 1-6CWRatios and ProportionalRelationships: Lessons 1-6NameDateClasswork BookMath 7: Mr. SanfordLessons 1-6:Proportional Relationship

Lesson 1-1Mathematics 7: Mr. SanfordCWLesson 1: An Experience in Relationships as Measuring RateExample 1: How fast is our class?Record the results from the paper passing exercise in the table below.Number of PapersTimeRatio of Number of PapersTrialPassed(in seconds)Passed to TimeRateUnit Rate1234Key Terms from Grade 6 Ratios and Unit RatesA ratio is an ordered pair of non-negative numbers, which are not both zero. The ratio is denoted 𝐴: 𝐵 to indicate theorder of the numbers: the number 𝐴 is first and the number 𝐵 is second.Two ratios 𝐴: 𝐵 and 𝐶: 𝐷 are equivalent ratios if there is a positive number, 𝑐, such that 𝐶 𝑐𝐴 and 𝐷 𝑐𝐵.A ratio of two quantities, such as 5 miles per 2 hours, can be written as another quantity called a rate.The numerical part of the rate is called the unit rate and is simply the value of the ratio, in this case 2.5. This meansthat in 1 hour the car travels 2.5 miles. The unit for the rate is miles/hour, read miles per hour.Example 2: Our Class by GenderNumber of boysNumber of girlsRatio of boys to girlsClass 1Class 2thWhole 7 gradeCreate a pair of equivalent ratios by making a comparison of quantities discussed in this Example.Grade 7 Lesson 1-1:An Experience in Relations as Measuring Rate3

Mathematics 7: Mr. SanfordLesson 1-1CWExercise 1: Which is the better buy?Value-Mart is advertising a Back-to-School sale on pencils. A pack of 30 sells for 7.97 whereas a 12-pack of the samebrand cost for 4.77. Which is the better buy? How do you know?Exercise 2: Problem SolvingEach year Lizzie’s school purchases student agenda books, which are sold in the school store. This year, the schoolpurchased 350 books at a cost of 1,137.50. If the school would like to make a profit of 1,500 to help pay for field tripsand school activities, what is the least amount they can charge for each agenda book? Explain how you found youranswer.Grade 7 Lesson 1-1:An Experience in Relations as Measuring Rate4

Lesson 1-1Mathematics 7: Mr. SanfordCWLesson 2: Proportional RelationshipsExample 1: Pay by the Ounce Frozen Yogurt!A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based upon the total weight of the yogurtand its toppings in a dish. Each member of Isabelle’s family weighed their dish and this is what they found.Weight (ounces)12.51058Cost ( )5423.20Cost WeightExample 2: A Cooking Cheat Sheet!In the back of a recipe book, a diagram provides easy conversions to use while cooking.0½11½20481216CupsOuncesOunces CupsExercise 1During Jose’s physical education class today, students visited activity stations. Next to each station was a chart depicting how manyCalories (on average) would be burned by completing the activity.Calories burned while Jumping Rope01234011223344Time (minutes)Calories Burneda.Is the number of calories burned proportional to time? How do you know?Grade 7 Lesson 1-2:Proportional RelationshipsNOTE:Proportional means therelationship is made up ofequivalent ratios5

Lesson 1-1Mathematics 7: Mr. Sanfordb.CWIf Jose jumped rope for 6.5 minutes, how many calories would he expect to burn?Example 3: Summer JobAlex spent the summer helping out at his family’s business. He was hoping to earn enough money to buy a new 220 gaming systemby the end of the summer. Halfway through the summer, after working for 4 weeks, he had earned 112. Alex made the sameamount of money each week that he worked. Alex wonders, “If I continue to work and earn money at this rate, will I have enoughmoney to buy the gaming system by the end of the summer?”To check his assumption, he decided to make a table. He entered his total money earned at the end of week 4.WeekTotalEarnings012345678 112a.Work with a partner to complete the table and answer Alex’s question.b.Are Alex’s total earnings proportional to the number of weeks he worked? How do you know?c.Try to write a multiplication problem using a number of weeks and the total earnings.Lesson Summary:Measures in one quantity are proportional to measures of a second quantity if the relationship is made up ofequivalent ratios.We can tell if a relationship is proportional by comparing the unit rates to see if they are the same. If each set ofvalues can be divided to get the same unit rate we can say that each measure multiplied by the unit rate gives youthe other measure.In the example given below, the distance is proportional to time since each measure of distance, 𝑦, can becalculated by multiplying each corresponding time, 𝑡, by the same value, 10. This table illustrates a proportionalrelationship between time, 𝑡, and distance, 𝑦.Time (hrs), tDistance (km), yGrade 7 Lesson 1-2:Proportional Relationships001102203306

Lesson 1-3Mathematics 7: Mr. SanfordCWLesson 3: Identifying Proportional Relationships in TablesOpening ExerciseYou have been hired by your neighbors to babysit their children on Friday night. You are paid 8 per hour. Complete the tablerelating your pay to the number of hours you worked.Hours WorkedPay1Based on the table above, is pay proportional to hoursworked? How do you know?2344½566.5Examples 1–4For Examples 1–3, determine if 𝑦 is proportional to 𝑥. Justify your answer.1. The table below represents the amount of snow fall in 5 counties (in inches) to hours of a recent winter storm.𝑥Time (hrs)𝑦Snowfall(In)2106128162.55714Grade 7 Lesson 1-3:Unit Rate(in/hr)Identifying Proportional Relationships in Tables7

Lesson 1-3Mathematics 7: Mr. Sanford2.3.4.CWThe table below shows the relationship between cost of renting a movie to the number of days on rent.𝑥Number ofDays𝑦Cost629324831Unit Rate( /day)The table below shows the relationship between the amount of candy (pounds) bought and the total cost.𝑥Pounds𝑦Cost510486128161020Unit Rate( /lb)Randy is planning to drive from New Jersey to Florida. Randy recorded the distance traveled and the total number of gallonsused every time he stopped for gas.Complete the table assuming miles driven is proportional to gallons consumed.GallonsConsumed2Miles Driven54481891012216In real life are miles driven proportional to gallons consumed?Grade 7 Lesson 1-3:Identifying Proportional Relationships in Tables8

Lesson 1-4Mathematics 7: Mr. SanfordCWLesson 4: Identifying Proportional Relationships in TablesExample: Which Team Will Win the Race?You have decided to run in a long distance race. There are two teams that you can join. Team A runs at a constant rate of 2.5 milesper hour. Team B runs 4 miles the first hour and then 2 miles per hour after that.Task: Create a table for each team showing the distances that would be run for times of 1, 2, 3, 4, ,5 and 6 hours.Time (hrs)Team ADistance(miles)Unit Rate(m/hr)Time (hrs)Team BDistance(miles)Unit Rate(m/hr)123456a.For which team is distance proportional to time? Explain your reasoning.b.Explain how you know distance for the other team is not proportional to time.c.If the race were 2.5 miles long, which team would win? Explain.If the race were 3.5 miles long, which team would win? Explain.Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs9

Mathematics 7: Mr. SanfordLesson 1-4CWIf the race were 4.5 miles long, which team would win? Explain.d.For what length race would it be better to be on Team B than Team A? Explain.e.Using this relationship, if the members on the team ran for 10 hours, how far would each member run on each team?f.Will there always be a winning team, no matter what the length of the course? Why or why not?g.If the race is 12 miles long, which team should you choose to be on if you wish to win? Why would you choose this team?Challenge: How much sooner would you finish on that team compared to the other team?Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs10

Lesson 1-5Mathematics 7: Mr. SanfordCWLesson 5: Identifying Proportional Relationships in GraphsOpening ExerciseIsaiah sold candy bars to help raise money for his scouting troop. The table compares the amount of candy he sold to the money hereceived.Is the amount of candy bars sold proportional to the money Isaiah received? How do you know?𝑥Candy BarsSold𝑦MoneyReceived ( )2345891212Example 1: From a Table to GraphComplete the table below if Isaiah earned 3.00 for every 2 candy bars.𝑥Candy BarsSold𝑦MoneyReceived ( )23Important Note:Characteristics of graphs of proportional relationships:Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs11

Mathematics 7: Mr. SanfordLesson 1-5CWExample 2𝑥2𝑦4681012143Similarities with Example 1:Differences from Example 1:Example 3𝑥0𝑦3861091212146Similarities with Example 1:Differences from Example 1:Lesson Summary:When two proportional quantities are graphed on a coordinate plane, the points lie on a straight line that passesthrough the origin.Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs12

Lesson 1-6Mathematics 7: Mr. SanfordCWLesson 6: Identifying Proportional Relationships in Graphs and TablesToday’s activity is an extension of Lesson 5. You will be working in groups to table, graph and identify whether or not the twoquantities are proportional to each other.ClassworkPoster LayoutUse for notesProblemTableGraphProportional or not? Explain.Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs13

Mathematics 7: Mr. SanfordLesson 1-6CWGallery Walk: Take notes and answer the following questions: Were there any differences found in groups that had the same problem.Did you notice any common mistakes? How could they be fixed?Was there any group that stood out by representing their problems and findings exceptionally clearly?Problem 1:Problem 2:Problem 3:Problem 4:Grade 7 Lesson 1-5:Identifying Proportional Relationships in Graphs14

Extra Notes Page

Grade 7 Lesson 1 -5: Identifying Proportional Relationships in Graphs 13 Lesson 6: Identifying Proportional Relationships in Graphs and Tables . Today’s activity is an extension of Lesson 5. You will be working in groups to table, graph and identify whether or not the two

Related Documents:

Proportional Relationship. Common Core Math 7 Unit Plan: Proportional Reasoning 2 Rates and Rationale: In grade seven students extend their reasoning about ratios and proportional relationships in several ways. They identify unit rates in representations of proportional relationships. They

Lesson 8: Identifying Proportional and Non-Proportional Relationships in Graphs (Tables to Graphs) Exit Ticket (2 points) For each of the graphs below state whether they represent a proportional relationship and how you know. If the graph does represent a proportional relationship find the unit rate.

Financial ratios can be classified into ratios that measure: (1) profitability, (2) liquidity, (3) management efficiency, (4) leverage, and (5) valuation and growth (Syamsuddin, 2009). In this study, for the purpose of financial ratio analysis, we use four ratios, namely liquidity ratios, activity ratios, leverage ratios, profitability ratios.

6. A summary of the five main categories of selected financial ratios over the period being analyzed are: a. Internal liquidity ratios b. Operating efficiency ratios c. Operating profitability ratios d. Business risk (operating) analysis ratios e. Financial risk (leverage) analysis ratios 7.

COMMON CORE STATE STANDARDS GRADE 7 CMP2 UNITS CONTENT Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

SCUSD Curriculum Map Grade 7 Mathematics 4 Unit #1: Proportional Reasoning and Relationships (Approx. # Days) Content Standards: 7.RP.1,2 and 7.G.1 Math Common Core Content Standards: Domain: Ratios and Proportional Relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 1.

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs Student Outcomes Students decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Animal nutrition is gained from grasses, grain crops, and pro-cessed products. Objectives: 1. Explain the functions of feed. 2. Describe the various types of feed. Key Terms: Functions of Feed Feed is any product consumed by an animal to meet nutritional needs. Feed provides the animal with energy to be mobile, protein to grow new or repair damaged cells, and vitamins and minerals to support .