PowerTeaching Math ® 3rd Edition Level 6 | Unit 5 Introduction to Ratios and Rates unit guide With Student and Assessment Pages PowerTeaching Math 3rd Edition Unit Guide: Level 6 © 2015 Success for All Foundation. All rights reserved Produced by the PowerTeaching Math 3rd Edition Team Angela Watson Kate Conway Nancy Madden Angie Hale Kathleen Collins Nick Leonhardt Cathy Pascone Kathy Brune Patricia Johnson Debra Branner Kenly Novotny Paul Miller Devon Bouldin Kimberly Sargeant Peg Weigel Erin Toomey Kris Misage Rebecca Prell Irene Baranyk Laura Alexander Russell Jozwiak Irina Mukhutdinova Laurie Warner Sarah Eitel James Bravo Luke Wiedeman Sharon Clark Jane Strausbaugh Mark Kamberger Susan Perkins Janet Wisner Marti Gastineau Terri Morrison Jeffrey Goddard Meghan Fay Tina Widzbor Jennifer Austin Michael Hummel Tonia Hawkins Joseph Wilson Michelle Hartz Wanda Jackson Karen Poe Michelle Zahler Wendy Fitchett We wish to acknowledge the coaches, teachers, and students who piloted the program and provided valuable feedback. The Success for All Foundation grants permission to reproduce the blackline masters of the PowerTeaching Math unit guides on an as-needed basis for classroom use. A Nonprofit Education Reform Organization 300 E. Joppa Road, Suite 500, Baltimore, MD 21286 PHONE: (800) 548-4998; FAX: (410) 324-4444 E-MAIL: [email protected] WEBSITE: www.successforall.org table of contents Unit Overview.. .................................................................. 1 Cycle 1 Introduction to Ratios and Rates........................................... 3 Student Pages Teamwork, Quick Check, Homework, and Assessments. . ...... 35 Cycle 1..................................................................... 37 This project was developed at the Success for All Foundation under the direction of Robert E. Slavin and Nancy A. Madden to utilize the power of cooperative learning, frequent assessment and feedback, and schoolwide collaboration proven in decades of research to increase student learning. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide iii Level 6 | Unit 5: Introduction to Ratios and Rates Level 6 | Unit 5: Introduction to Ratios and Rates Unit Overview Vocabulary introduced in this unit: ratio equivalent ratios rate per unit rate unit price pattern Think Like a Mathematician practice(s) used in this unit: Make sense of it. Translate into math. Defend and review. Build a math model. Be precise. Find the patterns and structure. Unit 5 consists of a single cycle. Students will learn the concept of a ratio first. Then, they will build on that basic understanding by using tables to create equivalent ratios, finding unit rates, and comparing rates. Throughout unit 5, students will use real‑world scenarios to make sense of ratios. Your students will draw on their knowledge of multiplying and dividing whole numbers, decimals, and fractions as they work through unit 5. As a result, they will continually review and reinforce these computation concepts. This will also provide you, the teacher, with additional opportunities to assess your students’ strengths and weaknesses in their computation skills, which are the foundation for most math skills. Cycle 1—Introduction to Ratios and Rates Lesson 1: What are ratios? Write ratios in three ways, and use ratio language. (CC 6.RP.A.1; TEKS 6.b.4.E; VA SOL 6.1CF, 6.2a) Lesson 2: Ratios and Tables Use tables to find equivalent ratios. (CC 6.RP.A.3a; TEKS 6.b.4.G; VA SOL 6.1CF, 7.4, and 7.12) Lesson 3: Rate and Unit Rate Identify and write rates, and find unit rates. (CC 6.RP.A.2; TEKS 6.b.5.B; VA SOL 6.1CF, 6.1, and 7.4) Lesson 4: Comparing Rates Compare rates in the context of real‑world problems. (CC 6.RP.A.3b; TEKS 6.b.5.B; VA SOL 6.1CF, and 7.4) Lesson 5: Think Like a Mathematician: Find the Patterns and Structure 1 Find a pattern to solve problems. (CC MP.7; TEKS 6.b.1.F) © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 1 Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 Lesson 1: What are ratios? Vocabulary: ratio Materials: none Lesson Objective: Write ratios in three ways, and use ratio language. By the end of this lesson, students will: • write ratios to compare data; • write ratios in three ways; • represent the ratios in simplest form; and • when given a ratio, explain what the ratio means in words. opening (3 minutes) get the goof • Ask teams to begin Get the Goof. Sam simplified _ 3 . He got _ 1 . What is wrong with his work? 12 3 Random Reporter Rubric | Possible Answer Answer: The correct answer is _ 1 . 4 Explanation: Sam needed to simplify by dividing by 3. Math Practice: I saw that because this is a case of simplifying fractions (TLM #3), Sam should have divided the numerator and denominator by the same number. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. active instruction (10–15 minutes) set the stage • Distribute team score sheets. Have students review their scores and set new team goals in lesson 1. • Post and present the lesson objective: Today you will learn to write ratios in three different ways. • Ask students to write this cycle’s vocabulary words in their notebooks: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern. • Remind students how to earn team celebration points. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 3 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 Access Code: fkwppf interactive instruction and guided practice • Show the “What is a ratio? or Who’s got moves?” video. • Use Think‑Pair‑Share to have students answer the following question: Explain what a ratio is in your own words. • Randomly select a few students to share. Possible answers: A ratio compares two quantities. For example, the ratio of boys to girls compares the number of boys with the number of girls in your class. • Use a Think Aloud to model writing ratios three different ways to show part‑to‑part, part‑to‑whole, and whole‑to‑whole comparisons. Write ratios three ways to show part‑to‑part, part‑to‑whole, and whole‑to‑whole comparisons. 3 layers Write a ratio three ways to compare: 1) the number of burger orders in Ms. Jay’s class with her class’s total orders. 2) the number of burger orders in Ms. Jay’s class with her class’s taco orders. 3) all the orders in Ms. Jay’s class with all the orders in Mr. Johnson’s class. Let me think about what this problem asks me to do. I have to compare different things using a ratio. A ratio is just a mathematical way to compare two related quantities. So in writing the ratios, I’ll be translating this information about lunch orders into math. That’s TLM practice #2. Show layer 1. The first comparison I have to make is about Ms. Jay’s class. I have to compare the number of burger orders with the total number of lunch orders in her class. So I have to find these numbers. There are 1, 2, 3, 4 burger orders and 8 tacos orders, so 8 1 4, or 12, orders in all in Ms. Jay’s class. What is the ratio of burger orders to total orders? That’s 4 to 12. I can write that ratio three different ways. In words, as a fraction, or with a colon. All three ways compare the number of burger orders with the total number of lunch orders in Ms. Jay’s class. 4:12, _ 4 , 4 to 12 12 Here I compared part of Ms. Jay’s class’s order with that class’s whole order, so 4 to 12 is a part‑to‑whole comparison. Show layer 2. The second comparison I have to make is also about Ms. Jay’s class. What ratio compares the number of burger orders with the number of taco orders? That’s 4 burgers to 8 tacos. Again, I can write that three ways. 4:8, _ 4 , 4 to 8 8 This ratio compares part of one class’s order with another part of the same class. So this is a part‑to‑part ratio. 4 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 Show layer 3. The last comparison I have to make is about Ms. Jay’s class and Mr. Johnson’s class. First, I’ll count the different orders in Mr. Johnson’s class. That’s 10 burger orders and 8 taco orders, or 18 orders in all. Now I have to write ratios to compare the total number of orders in Ms. Jay’s class with the total number of orders in Mr. Johnson’s class. That’s 12 to 18. 12:18, _ 12 , 12 to 18 18 This ratio compares all of one class’s order with all of another class’s order. So this is a whole‑to‑whole ratio. • Use Think‑Pair‑Share to have students answer the following question: Would the ratio 18 to 12 be a correct answer for question #3? Why or why not? • Randomly select a few students to share. Possible answer: No, 18 to 12 is not a correct answer. That ratio isn’t in the right order. You have to compare Ms. Jay’s total orders (12) with Mr. Johnson’s total orders (18), so the ratio has to be written as 12 to 18. • Use a Think Aloud to model writing ratios in simplest form. Write ratios in simplest form. 4 layers A fraction is actually a type of ratio. Think of _ 25 of a dollar. That’s a quarter, 100 right? That fraction is a ratio. It tells me the part of a whole dollar that I have. All fractions are part‑to‑whole ratios, and just like fractions, I can simplify ratios sometimes. Show layer 1. There are 4 burger lunch orders out of 12 total lunch orders. Because this problem is a case of comparing two quantities, I know that I can show this part‑to‑whole comparison as the ratio _ 4 . I also know that I can 12 simplify this ratio. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 5 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 Access Code: fkwppf Show layer 2. I can represent this ratio like this. I know that if there are this many burger orders, then there are this many orders in all. _ 4 . There are 12 4 cheeseburgers out of 12 orders. Show layer 3. I can reduce this ratio by looking at a portion of the orders. I know that if I look at half of the orders, there would be 2 cheeseburgers for every 6 orders. Show layer 4. What if there was just one burger order? I can reduce this even further by breaking it down to 1 burger order for every 3 lunch orders. That means 1 out of every 3 orders is a cheeseburger. 1 out of 3 is an equivalent ratio for 4 out of 12. Hey, I also just noticed that if I divide both the numerator and denominator by 4, which is the GCF of 4 and 12, then I also get _ 1 ! Neat! So the 3 simplest way to write this ratio is 1 cheeseburger for every 3 lunch orders. 6 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 • Use Think‑Pair‑Share to have students answer the following question: How could you simplify the ratio _ 8 ? 24 • Randomly select a few students to share. Possible answer: You could divide the numerator and denominator by 8 to simplify it to _ 1 . 3 • Use Team Huddle to have teams practice writing ratios. Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 1) Jason wrote the ratio 9:28 to compare the number of trout he caught with the number of fish he caught in all. Random Reporter Rubric | Possible Answer Answer: This ratio is a part‑to‑whole comparison. It means Jason caught 28 fish, and 9 of them were trout. Explanation: This ratio compares the number of trout with the number of fish that Jason caught in all. So the first number is trout, and the second number is the total number of fish caught. Math Practice: I translated the ratio into words (TLM #2). I had to pay attention to what each number represents and think about the relationship between the numbers. Here the number of trout is part of the whole number of fish that Jason caught. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. team mastery (10–15 minutes) • Ask students to follow the Team Mastery student routine. • Circulate and use the following questions to prompt discussions. –– How do you read this ratio? –– What does this ratio mean? © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 7 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 Access Code: fkwppf –– Does this number represent a part or the whole? How do you know? –– This is a part‑to‑part ratio. What part‑to‑whole ratio could you write to represent the same information? • When there are 5 minutes left in Team Mastery, prompt teams to prepare for the Lightning Round. Have teams discuss one Team Mastery problem that the whole team has completed. • Award team celebration points for good team discussions that demonstrate 100‑point responses. lightning round (10 minutes) • Tell students the Team Mastery problem that you will use for the Lightning Round. Write a ratio in simplest form in three different ways. 6) Libby’s produce stand sells mangoes and bananas. She has 36 mangoes and 62 bananas. Compare the number of bananas with the total amount of fruit. Random Reporter Rubric | Possible Answer Answer: 31:49, _ 31 , 31 to 49 49 Explanation: I added the number of mangoes and the number of bananas to get the total number of fruit and then simplified by dividing them both by 2, which is the GCF. Math Practice: I translated the situation into a mathematical ratio (TLM #2). I knew this ratio would be a part‑to‑whole comparison because I had to compare bananas with the total number of pieces of fruit. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. celebration (2 minutes) • Record team celebration points on the poster. • Have the top team choose a cheer. • Assign homework, and remind students about the Vocabulary Vault. • Ask students to follow the Quick Check student routine. (optional) Explain in words what the ratio means. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. Jenna wrote the ratio _ 9 to compare the number of questions she got correct on 1 her test with the number of questions she got wrong. Possible answer: It means that for every 9 questions Jenna got correct, she got 1 question wrong. This is a part‑to‑part comparison. 8 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 Lesson 2: Ratios and Tables Vocabulary: equivalent ratios Materials: none Lesson Objective: Use tables to find equivalent ratios. By the end of this lesson, students will: • find equivalent ratios; and • use ratio tables to find equivalent ratios and to compare two different ratios. opening (3 minutes) get the goof • Ask teams to begin Get the Goof. The ratio 2:3 compares the number of boys with girls in Rose’s homeroom. Rose said that means there has to be one more girl than boys in the homeroom. What is wrong with her thinking? Random Reporter Rubric | Possible Answer Answer: Rose is only correct if there are 5 students in the homeroom. If there are any more than 5, she is wrong. Explanation: Since this ratio could be in simplest form , a ratio of 2:3 does not necessarily mean that there are just 2 boys and 3 girls. Math Practice: This is a case of a part‑to‑part comparison (TLM #3). The ratio means there are 2 boys to every 3 girls. That same ratio represents 4 boys and 6 girls, 6 boys and 9 girls, or even 10 boys and 15 girls. So Rose can’t say for sure that there is only 1 more girl than boys. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. homework check • Ask teams to do a homework check. • Confirm the number of students who completed the homework on each team. • Poll students on their team’s understanding of the homework. • Award team celebration points. • Collect and grade homework once per cycle. Record individual scores on the teacher cycle record form. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 9 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 active instruction Access Code: fkwppf (10–15 minutes) set the stage • Post and present the lesson objective: Today you will find equivalent ratios. • Remind students how to earn team celebration points. interactive instruction and guided practice • Use a Think Aloud to model using a multiplication table to find equivalent ratios. Use a multiplication table to find equivalent ratios. 3 layers I know that good mathematicians use tools and math models to help them. A multiplication table is a very helpful math tool when you are making equivalent ratios. I can use a multiplication table here to help me find equivalent ratios for 2 to 4, 1 to 5, and 3 to 7. Show layer 1. First, let me find equivalent ratios for 2:4. I can start by highlighting these rows on the multiplication table. Circling the ratios will help me to identify the equivalent ratios more easily. 2:4, 4:8, and 16:32 are all equivalent ratios. What other ratios are equivalent to 2:4? All the ratios in these rows are equivalent ratios to 2:4! 10 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 Show layer 2. Now let me look at the equivalent ratios for 1:5. If I highlight the rows, it makes it much easier to identify the equivalent ratios. 1:5, 3:15, and 9:45 are all equivalent ratios. What other ratios are equivalent to 1:5? All the ratios in these rows are equivalent to 1:5! Show layer 3. I can repeat this same procedure to find ratios that are equivalent to 3:7. Using the multiplication table as a math tool is very helpful in identifying equivalent ratios! That’s TLM practice #5, using your math toolkit! One thing I should remember about this tool is that it only shows whole‑number products up to 100. There are plenty more ratios equivalent to 3:7 that aren’t shown in the table. For example, 300 to 700 is also equivalent to the ratio 3 to 7. This tool is very helpful, but I need to remember that it doesn’t show everything. • Use a Think Aloud to model using a table to find equivalent ratios. Use a table to find equivalent ratios. 5 layers Ashley is using red and white paint to make pink paint. She uses 2 cups of white paint and 3 cups of red. If she mixes more paint, how can she make sure it will be the exact same shade of pink? © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 11 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 Access Code: fkwppf What’s going on in this problem? Ashley is mixing paint to make pink paint. I have to figure out how she can mix more paint and have it look exactly the same. I know that good mathematicians use math models to help them. A table is a very helpful math model when making equivalent ratios. That’s TLM #4, building a math model! I can use a table here to help me show equivalent ratios for Ashley’s paint mixture. Show layer 1. Ashley uses 2 cups of white paint for every 3 cups of red paint. That’s a ratio of 2:3. Whenever Ashley mixes more paint, she will also have to mix it in the same ratio, 2:3. Show layer 2. So what would happen if Ashley doubles her paint mixture? If she doubles 2 cups of white paint to get 4 cups, then she has to double 3 cups of red paint to get 6 cups. Show layer 3. I can further extend the table to show more equivalent ratios for Ashley’s paint mixture. I can multiply 3 cups of red paint by 4 to get 12 cups. Show layer 4. Then I would have to do the same and multiply the 2 cups of white paint by 4 to find the equivalent ratio. 12 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 Show layer 5. If Ashley wants to make 6 times the amount of her original paint mixture, she must create an equivalent ratio. That means she needs to use 12 cups of white paint and 18 cups of red paint. The work on my table checks out because _ 12 simplifies to _ 2 . Using TLM #4, 18 3 building a math model, helped me find equivalent ratios to solve this problem. • Use Think‑Pair‑Share to have students answer the following question: Tell what an equivalent ratio is in your own words. • Randomly select a few students to share. Possible answer: An equivalent ratio is like an equivalent fraction; both numbers have to be multiplied by the same number. • Use Team Huddle to have teams practice using a table to make equivalent ratios. 1) Fill in the information missing from the table for Patty’s fruit dip. Patty’s Fruit Dip cream cheese (ounces) marshmallow crème (ounces) 8 16 30 60 75 Random Reporter Rubric | Possible Answer Answer: The missing numbers are 15, 32, and 40. Explanation: I used the ratio 16:30 to find equivalent ratios by seeing that half of 16 is 8, so half of 30 would be 15. Math Practice: I used the table as a math model (TLM #4) to find equivalent ratios. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 13 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 Access Code: fkwppf team mastery (10–15 minutes) • Ask students to follow the Team Mastery student routine. • Circulate and use the following questions to prompt discussions. –– How do you know the ratios are equivalent? –– How did you find the number(s) missing from the table? –– If the whole/part of this ratio is x, what do you estimate the whole/part of this equivalent ratio to be? –– What do you notice when you compare these two ratios? • When there are 5 minutes left in Team Mastery, prompt teams to prepare for the Lightning Round. Have teams discuss one Team Mastery problem that the whole team has completed. • Award team celebration points for good team discussions that demonstrate 100‑point responses. lightning round (10 minutes) • Tell students the Team Mastery problem that you will use for the Lightning Round. 4) If both Patty and Tina use 30 ounces of marshmallow crème, who will make less fruit dip in all? Explain your thinking. Patty’s Fruit Dip cream cheese (ounces) marshmallow crème (ounces) Tina’s Fruit Dip cream cheese (ounces) marshmallow crème (ounces) 8 15 2 5 16 30 4 10 32 60 12 30 40 75 16 40 Random Reporter Rubric | Possible Answer Answer: Tina will make less fruit dip. Explanation: I used the ratio information in the table and added the cream cheese and marshmallow crème to find the total ounces of fruit dip. Math Practice: I made sense of the ratio information in the table before I solved the problem (TLM #1). I saw that Tina and Patty use different ratios for their dips because 8:15 doesn’t simplify to 2:5. So I had to look at where both Tina and Patty used 30 ounces of marshmallow crème to find how many ounces of dip they each made in all. 14 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Tell students that it’s time to power up Random Reporter. Use the layers on the page to guide discussion. • Award team celebration points. celebration (2 minutes) • Record team celebration points on the poster. • Have the top team choose a cheer. • Assign homework, and remind students about the Vocabulary Vault. • Ask students to follow the Quick Check student routine. (optional) If both Ms. Anderson and Ms. Kraft have 20 students in their classes, which teacher will need fewer folders? Ms. Anderson’s School Supplies Ms. Kraft’s School Supplies number of students number of folders number of students number of folders 4 3 5 4 8 6 10 8 Possible answer: Ms. Anderson © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 15 Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 Lesson 3: Rate and Unit Rate Vocabulary: rate per unit rate unit price Lesson Objective: Identify and write rates, and find unit rates. By the end of this lesson, students will: • identify rates; • write rates in words and as ratios; and Materials: none • find unit rates. opening (3 minutes) get the goof • Ask teams to begin Get the Goof. Terry completed the ratio table. What’s wrong with her work? Geoboards for Ms. Lin’s Class Number of students Number of geoboards 4 3 8 6 16 9 Random Reporter Rubric | Possible Answer Answer: Terry counted by 3s to get to 9 instead of looking at the ratio of students to geoboards. Explanation: The ratio of students to geoboards is 4:3, so if there are 4 times as many students, there have to be 4 times as many geoboards, or 12. Math Practice: I used the table as a model (TLM #4), which helped me to see the relationship between the numbers in each column. I knew that to find equivalent ratios , I had to multiply each part of the original ratio by the same number. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. homework check • Ask teams to do a homework check. • Confirm the number of students who completed the homework on each team. • Poll students on their team’s understanding of the homework. • Award team celebration points. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 17 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 Access Code: fkwppf • Collect and grade homework once per cycle. Record individual scores on the teacher cycle record form. active instruction (10–15 minutes) set the stage • Post and present the lesson objective: Today you will learn about rates and unit rates. • Remind students how to earn team celebration points. interactive instruction and guided practice • Use a Think Aloud to model finding rates. Find rates. 4 layers It took Leo 6 hours to drive 330 miles to visit his friend. What was his driving rate? I see that this problem is about determining Leo’s rate, or speed, of travel. Good mathematicians think about strategies to help them solve problems more efficiently. Since we will determine Leo’s speed, I think I can model this problem with a visual representation of the situation, so I will use TLM #4 here. Show layer 1. For this problem, I will compare miles and hours. That means I will write this answer as a rate. A rate is a type of ratio that compares two different units of measure. For example, here I will compare Leo’s miles traveled with the time it took him to travel those miles. Show layer 2. Leo’s rate is 330 miles per 6 hours. Per means for each or for every. I need to include both units, miles and hours; that’s what makes this a rate! Show layer 3. I can show this rate as 330 miles over 6 hours. Show layer 4. I can also use a model to show this rate. • Use a Think Aloud to model finding unit rates. Find unit rates. 3 layers Leo’s driving rate is 330 miles per 6 hours. __ 330 miles 6 hours How far did Leo drive in 1 hour? 18 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 Now I can find out how far Leo drove in just 1 hour. Show layer 1. I can find the unit rate to see how far he drives for every 1 hour. A unit rate is a rate that compares a quantity with 1 unit of another measure. Show layer 2. To find the unit rate, I can divide the total miles by the total hours to get miles per hour. Basically, I’m finding an equivalent ratio with 1 in the denominator. A unit price, like a cost per ounce of juice, is also a unit rate. To find the unit price for juice, you divide the total cost by the number of ounces that you’ve bought. Show layer 3. I see that Leo drove 55 miles per hour. By using TLM #4, I was able to model this problem and figure out the unit rate at which Leo traveled. • Use Think‑Pair‑Share to have students answer the following question: What is a unit rate, and how do you find it? • Randomly select a few students to share. Possible answer: A unit rate is a rate that compares a quantity with 1 unit of another measure. You determine a unit rate by dividing. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 19 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 Access Code: fkwppf • Use Team Huddle to have teams practice finding unit rates. TEACHER’S NOTE: Although this Team Huddle problem has two parts, only the possible answer for part b is included here. 1) It cost Rosemary $6.68 for 4 pounds of apples. a.What is the rate that Rosemary paid for the apples? Write the rate in words and as a ratio. b.Write a unit price to describe the price Rosemary paid for 1 pound of apples. Explain your thinking. Random Reporter Rubric | Possible Answer for part b Answer: Rosemary paid $1.67 per pound of apples. Explanation: To find the unit price for 1 pound, I divided $6.68 by 4 pounds. Math Practice: I modeled this problem (TLM #4) with a sketch to show the situation and to help me solve it. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. team mastery (10–15 minutes) • Ask students to follow the Team Mastery student routine. • Circulate and use the following questions to prompt discussions. –– What does this rate/unit rate mean? –– How can you tell that this is a rate/unit rate? –– How do you write the rate/unit rate? Why? –– How did you find this rate/unit rate? • When there are 5 minutes left in Team Mastery, prompt teams to prepare for the Lightning Round. Have teams discuss one Team Mastery problem that the whole team has completed. • Award team celebration points for good team discussions that demonstrate 100‑point responses. 20 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 lightning round (10 minutes) • Tell students the Team Mastery problem that you will use for the Lightning Round. 15 sit-ups minute 7) Michaela does sit‑ups at a rate of __ . Explain how many sit‑ups Michaela will do in 2 minutes and 3 minutes and what the rate means in words. Random Reporter Rubric | Possible Answer Answer: This is a unit rate , so for every 1 minute, Michaela does 15 sit‑ups. In 2 minutes, she will do 30 sit‑ups. In 3 minutes, she will do 45 sit‑ups. Explanation: _ 15 3 _ 2 5 30 sit‑ups in 2 minutes 1 2 1 3 15 _ 3 _ 3 5 45 sit‑ups in 3 minutes Math Practice: I modeled this problem (TLM #4) with number sentences to show Michaela’s rate of sit‑ups and two equivalent rates. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. celebration (2 minutes) • Record team celebration points on the poster. • Have the top team choose a cheer. • Assign homework, and remind students about the Vocabulary Vault. • Ask students to follow the Quick Check student routine. (optional) JD was paid $45 for babysitting for 5 hours. What was JD’s rate of pay? Write a unit rate to describe how much JD made in 1 hour. Possible answer: JD was paid at a rate of $45 for 5 hours. His unit rate of pay was $9 per hour. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 21 Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 Lesson 4: Comparing Rates Vocabulary: none Materials: none Lesson Objective: Compare rates in the context of real‑world problems. By the end of this lesson, students will: • compare two rates by finding equivalent rates; • find equivalent rates using unit rates, common multiples, and common factors; and • use tables and double number lines as helpful tools. opening (3 minutes) get the goof • Ask teams to begin Get the Goof. Every 4 minutes, Regina completes 2 homework problems. She said that she does homework at a unit rate of 0.5 minutes per problem. What’s wrong with her work? Random Reporter Rubric | Possible Answer Answer: Regina did not divide correctly to find the unit rate . , so if Explanation: Regina is completing her homework problems at a rate of __ 4 minutes 2 problems Regina divided by 2, she would find that she actually takes 2 minutes to complete 1 problem. Math Practice: Because this is a case of finding a unit rate (TLM #3), Regina should have divided 4 minutes by 2 homework problems. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. homework check • Ask teams to do a homework check. • Confirm the number of students who completed the homework on each team. • Poll students on their team’s understanding of the homework. • Award team celebration points. • Collect and grade homework once per cycle. Record individual scores on the teacher cycle record form. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 23 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 active instruction Access Code: fkwppf (10–15 minutes) set the stage • Post and present the lesson objective: Today we will learn to compare rates. • Remind students how to earn team celebration points. interactive instruction and guided practice • Play the “Unit Pricing or Whose bargain is better?” video. • Use Think‑Pair‑Share to have students answer the following question: How can finding the unit price help you to know whether you are getting a good deal? • Randomly select a few students to share. Possible answer: Knowing the unit price can help me because I can determine the actual cost for each item that I am buying, and I can see what kind of deal I am getting. • Use a Think Aloud to model comparing rates to find the better deal. Compare rates. 6 layers Cooper is buying potting soil. He is choosing between Grow Great and So Green. Which is the better deal? Let me think about what this problem is asking me to do. I see that Cooper is trying to decide which deal is better. It’s hard to compare prices when you have different amounts, so to help me determine which deal is better, I will need to compare either like amounts or like prices. To do that, I can set up a table with equivalent ratios to model this problem. Using a model is TLM #4, so I’m thinking like a mathematician! Show layer 1. To compare these different brands, I have to find equivalent rates. Let’s see, I have to compare 16 quarts and 24 quarts. Hmm, I know the greatest common factor of 16 and 24 is 8, so I can find the cost of 8 quarts for both brands. Which brand costs less when buying the same amount? 24 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 Show layer 2. If 16 quarts cost $7, then 8 quarts cost half of that. If 24 quarts cost $9, then 8 quarts cost one‑third of that. Now I can compare the two brands much more effectively. Using this table and dividing really helped me to see which brand is the better deal. Show layer 3. Another way Cooper could compare these brands is by finding a common price. To do that, I have to find the amount of each brand of potting soil that he would get if he spent the same amount of money on both. To calculate that amount, I can use a common multiple to compare the amounts accurately. The LCM of 7 and 9 is 63. I know that 7 times 9 is 63, and therefore, 9 times 7 is 63. So which brand could Cooper get more of for the same price? Show layer 4. If $7 buys 16 quarts, then $63 buys 9 times that amount. If $9 buys 24 quarts, then $63 buys 7 times that amount. Now I can compare the brands. This method also shows that So Green is the better deal. Building a math model and using TLM #4 really helped me with representing the information in this problem. Show layer 5. Another way I could compare these prices is to find the unit price. To do that, I divide the cost by the number of quarts. That means I divide $7.00 by 16 to find the cost per quart for Grow Great and divide $9.00 by 24 to find the cost per quart of So Green. Show layer 6. Now I can compare these two brands effectively because I know the cost per quart of each. Grow Great costs $0.44 per quart, and So Green costs $0.38 per quart. Using TLM #2 and representing the problem in another way helped me to compare the two brands and determine that So Green is the better deal. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 25 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 Access Code: fkwppf • Use Think‑Pair‑Share to have students answer the following question: Which way would you use to compare rates? Do you think you might use different ways for different comparisons? • Randomly select a few students to share. Possible answer: I would find the unit rate to compare rates. I might use a different way if I could easily find a GCF or LCM to use. • Use Team Huddle to have teams practice comparing rates. 1) Mason rode his bike 13 miles in 80 minutes. Olivia rode her bike 15 miles in 120 minutes. Who travels at a slower rate? Explain your thinking. Random Reporter Rubric | Possible Answer Answer: Olivia travels at a slower rate. 3 3 _ 5 __ 39 mi Explanation: Mason: __ 13 mi 80 min 3 240 min 3_ 2 5 __ 30 mi Olivia: __ 15 mi 2 120 min 240 min Math Practice: I knew that I couldn’t compare the rates as written because the miles and minutes were all different. So I multiplied to find equivalent rates that I could compare (TLM #2). I chose to find how far they each travel in 240 minutes, which made it clear that Olivia goes slower. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. team mastery (10–15 minutes) • Ask students to follow the Team Mastery student routine. • Circulate and use the following questions to prompt discussions. –– How did you compare these rates? –– How do you know these rates are equivalent? –– Is there another way you could have compared these rates? • When there are 5 minutes left in Team Mastery, prompt teams to prepare for the Lightning Round. Have teams discuss one Team Mastery problem that the whole team has completed. • Award team celebration points for good team discussions that demonstrate 100‑point responses. 26 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 lightning round (10 minutes) • Tell students the Team Mastery problem that you will use for the Lightning Round. 4) A 4‑ounce strawberry yogurt contains 80 calories, and a 6‑ounce peach yogurt contains 130 calories. Which flavor has fewer calories per ounce? Explain your thinking. Random Reporter Rubric | Possible Answer Answer: The strawberry yogurt has fewer calories per ounce. Explanation: strawberry: __ 80 calories 4_ 2 5 __ 40 calories 4 oz 2 2 oz 130 calories 4_ 3 5 __ 43.3 calories peach: __ 6 oz 3 2 oz I found how many calories are in 2 ounces of each yogurt because 2 is the GCF of 4 and 6. Math Practice: I knew that I couldn’t compare the rates as written because the ounces and calories were all different. So I divided to get the GCF to find equivalent rates that I could compare (TLM #2). I chose to find the number of calories in 2 ounces of each kind of yogurt. That made it clear that strawberry has fewer calories per ounce. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. celebration (2 minutes) • Record team celebration points on the poster. • Have the top team choose a cheer. • Assign homework, and remind students about the Vocabulary Vault. • Ask students to follow the Quick Check student routine. (optional) Ethan and Emma check their heartbeats. Ethan’s heart beats at a rate of 26 beats per 20 seconds, and Emma’s beats at a rate of 42 beats per 30 seconds. Whose heart beats faster? Possible answer: Emma’s heart beats faster. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 27 Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 Lesson 5: Think Like a Mathematician: Find the Patterns and Structure 1 Vocabulary: pattern Materials: none Lesson Objective: Find a pattern to solve problems. By the end of this lesson, students will: • solve problems by finding patterns; • organize data to find patterns; and • use the pattern to determine the answer to the questions and predict additional data. opening (3 minutes) get the goof • Ask teams to begin Get the Goof. Zoe says the first spinner is faster because it makes 8 more revolutions than the second spinner. What’s wrong with her thinking? 32 revolutions 24 revolutions 19 seconds 13 seconds Random Reporter Rubric | Possible Answer Answer: Zoe did not compare the rates correctly because she only looked at the number of revolutions. She needed to look at the number of seconds also. Explanation: The second spinner is faster because it makes about 1.85 revolutions in 1 second. The first spinner only makes about 1.68 revolutions in 1 second. Math Practice: Because this problem is a case of comparing rates (TLM #3), I knew that Zoe couldn’t compare the given rates because the number of revolutions and seconds were all different. If she had divided both rates to find the unit rate (number of revolutions per second), she’d see that the second spinner goes faster. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 29 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 Access Code: fkwppf homework check • Ask teams to do a homework check. • Confirm the number of students who completed the homework on each team. • Poll students on their team’s understanding of the homework. • Award team celebration points. • Collect and grade homework once per cycle. Record individual scores on the teacher cycle record form. active instruction (10–15 minutes) set the stage • Post and present the lesson objective: Today we will find patterns to solve problems. • Remind students how to earn team celebration points. interactive instruction and guided practice • Use a Think Aloud to model finding and using patterns to solve problems. Find and use patterns to solve problems. 3 layers Lee’s Bakery has an order to make a gigantic cupcake display with 6 shelves for a movie premiere. 9 cupcakes on top shelf 18 on 2nd shelf 36 on 3rd shelf If the display continues this way, how many cupcakes in all does Lee need to bake to fill all 6 layers? Let me think about how I can solve this problem. I know that good mathematicians try to find patterns to help them solve problems. I wonder if there is a pattern here. I can make a table with this information and see if there are any patterns I can use. Using a pattern to help you solve problems is TLM #7! Show layer 1. There is a pattern here! This table shows the data from the problem. The first row includes each shelf, and the second row shows the number of cupcakes on each row. Show layer 2. I can see from the table that each shelf has twice as many cupcakes as the shelf before it. Knowing that there is a pattern in this problem and using TLM practice #7 will certainly help me to solve this! Show layer 3. Now all I need to do is use this pattern to figure out how many cupcakes Lee needs to fill all 6 shelves. I can find that by doubling the number of cupcakes for each shelf and then adding the total number of cupcakes together. That gives Lee a total of 567 cupcakes. Using a pattern to solve a problem is really helpful! 30 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: fkwppf Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 • Use Think‑Pair‑Share to have students answer the following question: How do you know when you have a pattern? • Randomly select a few students to share. Possible answer: You know you have a pattern when you find data that repeats. • Use Team Huddle to have teams practice finding and using patterns to solve problems. 1) Evan is building a tower with plastic cups. The first layer has 36 cups, the second layer has 32 cups, and the third layer has 28 cups. If his tower continues like this, how many layers of cups will Evan have? Random Reporter Rubric | Possible Answer Answer: Evan will have 9 layers of cups. Explanation: I found the pattern by subtracting the amount of cups in each layer from the number of cups on the layer before it, which gave me 4 fewer cups on each subsequent layer. Math Practice: I found a pattern (TLM #7) in the relationship between the number of cups in each layer and the number of layers. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. team mastery (10–15 minutes) • Ask students to follow the Team Mastery student routine. • Circulate and use the following questions to prompt discussions. –– What is the question asking? –– What pattern did you find? How did you find the pattern? –– How did you use your table to find the answer? –– Does this pattern continue forever? Why do you think that? –– Where do we find patterns in our schools, homes, or town? • When there are 5 minutes left in Team Mastery, prompt teams to prepare for the Lightning Round. Have teams discuss one Team Mastery problem that the whole team has completed. • Award team celebration points for good team discussions that demonstrate 100‑point responses. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 31 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 Access Code: fkwppf lightning round (10 minutes) • Tell students the Team Mastery problem that you will use for the Lightning Round. 4) A fisherman goes crabbing at the end of the crab season. The first morning he catches 128 crabs, the second morning he catches 64 crabs, and the third morning he catches 32 crabs. If the crabbing continues this way, how many crabs will he catch on the sixth morning? Random Reporter Rubric | Possible Answer Answer: On the sixth morning, he will catch only 4 crabs. Explanation: I subtracted the amount of crabs he caught each day and determined that the fisherman catches half the amount of crabs each day as he caught on the previous day. Math Practice: I found a pattern in the problem (TLM #7), which helped me to determine the number of crabs he would catch on the sixth morning. • Use Random Reporter to have teams share. Use the Random Reporter rubric to evaluate responses and give feedback. • Record individual scores on the teacher cycle record form. • Award team celebration points. celebration (2 minutes) • Record team celebration points on the poster. • Have the top team choose a cheer. • Assign homework, and remind students about the Vocabulary Vault. • Ask students to follow the Quick Check student routine. (optional) Zahra’s website had 14 visitors on day 1, 26 visitors on day 2, and 38 visitors on day 3. If she keeps getting visitors this way, how many more visitors will she have on day 8 than on day 1? Possible answer: 84 more visitors 32 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation Access Code: pqkwgz Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Assessment Day Assessment Day: Unit Check on Introduction to Ratios and Rates Materials: extra blank copies of the assessment Lesson Objective: Demonstrate mastery of unit content. assessment (20–30 minutes) • Confirm the number of students who completed the homework on each team. Award team celebration points. • Remind students that the test is independent work. • Distribute the tests so students can preview the questions. • Tell students the number of minutes they have for the test and that they may begin. Give students a 5‑minute warning before the end of the test. • Collect the tests. team reflection (5 minutes) • Display or hand out blank copies of the test. • Explain or review, if necessary, the student routine for team discussions after the test. • Award team celebration points. prep points (5–10 minutes) • Assign prep points for each team for the five questions indicated (#s 3, 7, 9, 11, 13). • Score individual tests when convenient. vocabulary vault (2 minutes) • Randomly select vocabulary vouchers, and award team celebration points. • Ask students to record the words that they explain on their team score sheets. team scoring (5 minutes) • Guide the class to complete the team scoring on their team score sheets. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition | Unit Guide 33 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Assessment Day celebration Access Code: pqkwgz (2 minutes) • Announce team statuses, and celebrate. • Poll teams about how many times they have been super teams. Celebrate those teams, and encourage all teams to work toward super team status during the next cycle. • Show the “Explain Your Ideas/Tell Why, Part Two” video. • Use Think‑Pair‑Share to have students discuss how this goal can help them reach super team status. Randomly select students to share. 34 PowerTeaching Math 3rd Edition | Unit Guide © 2015 Success for All Foundation student pages Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 1 1 teamwork Directions for questions 1–5: Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 1) Jason wrote the ratio 9:28 to compare the number of trout he caught with the number of fish he caught in all. 6 2) Mr. Bell wrote the ratio _ to compare the number of pepperoni pizzas with the number of pizzas in all. 30 3) Alisha wrote the ratio 5 to 10 to compare the number of pennies in her pocket with the number of pennies in her piggy bank. 4) The school cafeteria worker wrote the ratio 11:20 to compare the number of students drinking chocolate milk with the number of students drinking regular milk. 4 5) The tour guide wrote the ratio _ to compare the number of visitors from California with the number of 10 visitors in all. Directions for questions 6–10: Write a ratio in simplest form in three different ways. 6) Libby’s produce stand sells mangoes and bananas. She has 36 mangoes and 62 bananas. Compare the number of bananas with the total amount of fruit. 7) Christopher baked 14 white chocolate chip cookies and 10 milk chocolate chip cookies. Compare the number of white chocolate chip cookies with the number of milk chocolate chip cookies. 8) There are 15 cars in a parking lot. Some are red, and 10 are black. Compare the number of red cars with the number of black cars in the parking lot. 9) Jessica washed 5 loads of laundry this week. She washed 9 loads last week. Compare the number of loads that Jessica washed this week with the number of loads that she washed last week. 10) Carlton bought 9 concert tickets. 4 of the tickets were in row A, and the rest were in row B. Compare the number of tickets Carlton bought in row B with the total number of tickets he bought. Challenge 11) Marilee is selling 32 squash, 12 cucumbers, 38 peaches, and 54 watermelons at the farmer’s market. Write at least 5 ratios in simplest form to represent the produce she is selling. © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 37 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 1 1 teamwork answers 1) Possible answer: This ratio is a part‑to‑whole comparison. It means Jason caught 28 fish, and 9 of them were trout. This ratio compares the number of trout with the number of fish that Jason caught in all. So the first number is trout, and the second number is the total number of fish caught. I translated the ratio into words (TLM #2). I had to pay attention to what each number represents and think about the relationship between the numbers. Here the number of trout is part of the whole number of fish that Jason caught. 2) Possible answer: This ratio means that 6 pizzas out of all 30 pizzas are pepperoni. This is a part‑to‑whole comparison. It compares the number of pepperoni pizzas with the total number of pizzas. The number 6 describes the number of pepperoni pizzas because it is the first number in the ratio. 3) Possible answer: This ratio means that for every 5 pennies Alisha has in her pocket, there are 10 pennies in her piggy bank. This is a whole‑to‑whole comparison. It compares the number of pennies in her pocket with the number of pennies in her piggy bank. The number 5 describes the number of pennies in her pocket because it is the first number in the ratio. 4) Possible answer: This ratio means that for every 11 students who drink chocolate milk, there are 20 students who drink regular milk. This is a part‑to‑part comparison. It compares the number of students who drink chocolate milk to the number of students who drink regular milk. The number 11 describes the number of students who drink chocolate milk because it is the first number in the ratio. 5) Possible answer: This ratio means that 4 visitors out of every 10 visitors came from California. This is a part‑to‑whole comparison. It compares the number of visitors from California with the total number of visitors. The number 4 describes the number of visitors from California because it is the first number in the ratio. 31 6) 31:49, _ , 31 to 49 49 7 7) 7:5, _ , 7 to 5 5 1 8) 1:2, _ , 1 to 2 2 5 9) 5:9, _ , 5 to 9 9 5 10) 5:9, _ , 5 to 9 9 11) Possible answers: squash to cucumbers 5 8:3 total fruit to total vegetables 5 23:11 cucumbers to total produce 5 3:34 peaches to total fruit 5 19:46 squash to total vegetables 5 8:11 PowerTeaching Math 3rdMath Edition 38 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 1 1 quick check Name Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 9 Jenna wrote the ratio _ to compare the number of questions she got correct on her test with the 1 number of questions she got wrong. © 2015 Success for All Foundation PowerTeaching Math 3rd Edition quick check Name Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 9 Jenna wrote the ratio _ to compare the number of questions she got correct on her test with the 1 number of questions she got wrong. © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 39 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 61 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 homework Quick Look Vocabulary words introduced in this cycle: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern Today we learned to write ratios. A ratio is a comparison of two related quantities with the same or different units of measure. Let’s write a ratio for this problem: There are 35 cars and 5 trucks in the parking lot. Compare the number of cars with the number of trucks in the parking lot. 35 7 We can write the ratio three ways: _ , 35:5, and 35 to 5. We can also write it in simplest form: _ , 7:1, and 5 1 7 to 1. So for every 7 cars in the parking lot, there is 1 truck. This is a part‑to‑part comparison because it compares a part of the vehicles, the cars, to another part of the vehicles, the trucks. Directions for questions 1–4: Write a ratio in simplest form three different ways. 1) Billy’s store sells ice cream. He sold 25 vanilla cones and 50 chocolate cones. Compare the number of vanilla cones sold with the number of cones sold in all. 2) Crystal collects shells. She has 14 pink shells and 36 white shells. Compare the number of pink shells with the number of white shells. 3) Mrs. Richardson gave a math test to her students. There were 12 addition problems and 9 subtraction problems. Compare the number of subtraction problems with the total amount of problems. 4) There are 16 flowers in a vase. Some are red, and 6 are white. Compare the number of red flowers with the total flowers in the vase. Directions for questions 5–8: Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 5) Missy wrote the ratio 5 to 30 to compare the number of oranges with the total amount of fruit. Explain your thinking. 6) Rose wrote the ratio 2:3 to compare the number of boys with the number of girls in her homeroom. 6 7) John wrote the ratio _ to compare the number of chapter books with the number of picture books on 21 his bookshelf. 8) Louise wrote the ratio 5:20 to compare the number of pigs on her farm with the number of pigs on her neighbor’s farm. © for All Foundation 402015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 6 1| Unit 5: Introduction to Ratios and Rates | Cycle 1 Homework Lesson 1 Mixed Practice 2 9) What is an equivalent fraction for _ ? 10 10) What is the GCF of 20 and 50? 10 2 11) _ 4_ 5 7 3 12) Use , , or 5 to compare. |– 14| ________ 13 Word Problem 13) Sarah surveyed 100 students at her school. She found that 64 of them prefer the new chocolate pudding in the cafeteria over the old. Write her findings as a ratio in simplest terms. Describe your ratio in words. For the Guide on the Side Today your student learned to write ratios. A ratio is a comparison of two related quantities. They can have the same or different units of measure. They can also express different types of relationships: part to whole, part to part, and whole to whole. We write ratios in words, with a colon, or as fractions. Fractions are a special kind of ratio that compares parts to wholes. Your student should be able to answer these questions about ratios: 1) How do you read this ratio? 2) What does this ratio mean? 3) Does this number represent a part or the whole? How do you know? 4) This is a part‑to‑part ratio. What part‑to‑whole ratio could you write to represent the same information? Here are some ideas to work on writing ratios with your student: 1) Write ratios to describe items around your home (fruits to vegetables, males to females, minutes of a TV show to minutes of commercials, etc.). 2) Survey family and friends about their likes and dislikes, and write ratios to describe your findings. For example, 7 out of 10 of my classmates like the new school mascot better than the old one. 3) Use Khan Academy to review ratios. www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/introduction‑to‑ratios‑new‑hd‑version 4) Use Khan Academy to practice writing ratios. www.khanacademy.org/math/cc‑sixth‑grade‑math/cc‑6th‑ratios‑prop‑topic/cc‑6th‑describing‑ratios/v/ ratios‑as‑fractions PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 41 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 61 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 1 homework answers 1 1) 1:3, _ , 1 to 3 3 7 2) 7:18, _ , 7 to 18 18 3 3) 3:7, _ , 3 to 7 7 5 4) 5:8, _ , 5 to 8 8 5) Possible explanation: The ratio means that 5 pieces of fruit out of all 30 pieces of fruit are oranges. This is a part‑to‑whole comparison because it compares the oranges with all the fruit. I used TLM #2 to translate the ratio into words. I had to pay attention to what each number represents and think about the relationship between the numbers. Here the number of oranges is part of the whole number of pieces of fruit. 6) Possible explanation: The ratio means that for every 2 boys, there are 3 girls in her homeroom. This is a part‑to‑part comparison. It compares the number of boys with the number of girls. The number 2 describes the boys because it is written first in the ratio. 7) Possible explanation: The ratio means that for every 6 chapter books, there are 21 picture books. This is a part‑to‑part comparison. It compares the number of chapter books with the number of picture books. The number 6 describes the chapter books because it is written first in the ratio. 8) Possible explanation: The ratio means that for every 5 pigs on Louise’s farm, there are 20 on her neighbor’s farm. This is a whole‑to‑whole comparison. It compares the number of pigs on two different farms. The number 5 describes the pigs at Louise’s farm because it is written first in the ratio. Mixed Practice 4 9) Possible answer: _ 20 10) 10 1 11) 2 _ 7 12) |– 14| 13 Word Problem 16 13) _ , 16:25, or 16 to 25. 16 classmates out of every 25 classmates prefer the new chocolate pudding over 25 the old chocolate pudding. © for All Foundation 422015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 2 2 teamwork Directions for questions 1–4: Use the tables to answer each question. 1) Fill in the information missing from the table for Patty’s fruit dip. Patty’s Fruit Dip cream cheese (ounces) Tina’s Fruit Dip marshmallow crème (ounces) cream cheese (ounces) marshmallow crème (ounces) 2 5 30 4 10 60 12 30 75 16 40 8 16 2) If Patty uses 32 ounces of cream cheese, how many ounces of fruit dip will she make in all? 3) If both Patty and Tina make 56 ounces of fruit dip, who will use more cream cheese? 4) If both Patty and Tina use 30 ounces of marshmallow crème, who will make less fruit dip in all? Explain your thinking. Directions for questions 5–8: Use the tables to answer each question. 5) Fill in the information missing from the table for Aisha’s purple dye mix. Aisha’s purple dye mix red (drops) blue (drops) 6 12 Reese’s purple dye mix red (drops) blue (drops) 2 6 18 3 9 36 4 12 5 15 30 6) If Aisha uses 24 drops of red, how many more drops of blue than red does she need? 7) If both Aisha and Reese make 30 drops of purple dye, who will use less blue? Explain your answer. 8) If both Aisha and Reese use 3 drops of red, who will make more purple dye? © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 43 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 2 2 Teamwork Challenge 3 9) Manju mixed in 1_ cups of milk for every 1 cup of oatmeal. How much milk does he need if he is using 4 1 _ cup of oatmeal? 2 Manju’s oatmeal oatmeal (cups) milk (cups) 1 _ ? 1 3 1_ 2 1 3_ 4 7 10 1 17_ 2 4 2 2 PowerTeaching Math 3rdMath Edition 44 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 2 2 teamwork answers 1) Patty’s Fruit Dip cream cheese (ounces) marshmallow crème (ounces) 8 15 16 30 32 60 40 75 2) Patty will make 92 ounces of fruit dip. 3) Patty will use more cream cheese. 4) Tina will make less fruit dip. Possible explanation: I used the ratio information in the table and added the cream cheese and marshmallow crème to find the total ounces of fruit dip. I made sense of the ratio information in the table before I solved the problem (TLM #1). I saw that Tina and Patty use different ratios for their dips because 8:15 doesn’t simplify to 2:5. So I had to look at where both Tina and Patty used 30 ounces of marshmallow crème to find how many ounces of dip they each made in all. 5) Aisha’s purple dye mix red (drops) blue (drops) 6 9 12 18 24 36 30 45 6) Aisha will need 12 more drops of blue. 7) Aisha will use less blue dye. Possible explanation: If both Aisha and Reese use 9 drops of blue, Aisha will make 15 drops of purple, and Reese will make 12 drops of purple. Reese will need to use more than 9 drops of blue dye to make more than 12 drops of purple dye. 8) Reese will make more purple dye. 7 9) Manju will need _ cup of milk. 8 © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 45 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 62 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 2 quick check Name If both Ms. Anderson and Ms. Kraft have 20 students in their classes, which teacher will need fewer folders? Ms. Anderson’s School Supplies Ms. Kraft’s School Supplies number of students number of folders number of students number of folders 4 3 5 4 8 6 10 8 © 2015 Success for All Foundation PowerTeaching Math 3rd Edition quick check Name If both Ms. Anderson and Ms. Kraft have 20 students in their classes, which teacher will need fewer folders? Ms. Anderson’s School Supplies Ms. Kraft’s School Supplies number of students number of folders number of students number of folders 4 3 5 4 8 6 10 8 © for All Foundation 462015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 2 2 homework Quick Look Vocabulary words introduced in this cycle: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern Today we learned to find equivalent ratios. Equivalent ratios are two or more ratios that describe the same comparison. You can find equivalent ratios the same way you find equivalent fractions—multiply or divide both parts of the ratio by the same number. One way to find equivalent ratios is to use a ratio table. Watermelons for Picnic How many guests would be at the picnic if there are 8 watermelons? 2 number of guests [ When there are 4 3 2 5 8 watermelons, then there are 10 3 2 5 20 guests. number of watermelons 5 2 10 4 ] 2 8 Ratio tables are also helpful to compare two ratios: Watermelons for Picnic Watermelons for Brunch number of guests number of watermelons number of guests number of watermelons 5 2 4 1 10 4 8 2 20 8 20 5 By looking at the table, we can see that if there are 20 guests, you will need more watermelons for the picnic than for the brunch. You can also see that if there are 2 watermelons, you will feed more guests with it at the brunch than at the picnic. Directions for questions 1–4: Use the tables to answer each question. 1) Fill in the missing information from the table for Ms. Lin’s class. Geoboards for Ms. Lin’s class Geoboards for Mr. Mark’s class number of students number of geoboards number of students number of geoboards 4 3 6 3 8 6 18 9 24 12 30 15 16 18 2) If Ms. Lin has 12 students, how many geoboards does she need? © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 47 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 2 2 Homework 3) If both Ms. Lin and Mr. Mark have 48 students in their classes, which teacher needs more geoboards? 4) If Ms. Lin and Mr. Mark have 12 geoboards each, how many students do they have in all? Directions for questions 5–8: Use the tables to answer each question. 5) Fill in the missing information from the table showing Jerry’s punch recipe. Jerry’s Punch Della’s Punch raspberry juice (ounces) lemonade (ounces) raspberry juice (ounces) lemonade (ounces) 1 15 2 10 30 3 15 10 4 20 20 6 30 6) If Jerry uses 45 ounces of lemonade, how much raspberry juice will he use? 7) If both Jerry and Della use 2 ounces of raspberry juice, who will make more punch? 8) If both Jerry and Della use 90 ounces of lemonade, who will use more raspberry juice? Explain your thinking. Mixed Practice 9) Divide. 6.512 4 1.44 5 13 1 10) Is _ closest to 0, _ , or 1? 79 2 11) Nicki wrote the ratio 12:42 to compare the number of minutes she ran with the number of minutes she walked during her workout. Explain in your own words what the ratio means. 12) Order the numbers from least to greatest. 4 1.501, 1.055, 1_ 9 Word Problem 13) The ratio of girls to boys at Park Middle School is 8:9. How many boys are in the school if there are 340 students in total? PowerTeaching Math 3rdMath Edition 48 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation Homework Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 2 2 For the Guide on the Side Today your student learned to find equivalent ratios. Equivalent ratios are two or more ratios that describe the same comparison. We found equivalent ratios the same way we found equivalent fractions—by multiplying or dividing both parts of the ratio by the same number. Making ratio tables is a useful tool to organize equivalent ratios. This way, we can also compare different quantities in two different ratios. Your student should be able to answer these questions about finding equivalent ratios: 1) How do you know the ratios are equivalent? 2) How did you find the number(s) missing from the table? 3) If the whole/part of this ratio is x, what do you estimate the whole/part of this equivalent ratio to be? 4) What do you notice when you compare these two ratios? Here are some ideas to work with finding equivalent ratios: 1) Select a recipe, and find how much of each ingredient you need to make different amounts of the recipe. For example, how much sugar do you need to make half a batch of cookies? How much do you need for three batches of cookies? 2) Find the price for two different brands of one product. Create a ratio table to compare how much different amounts of the products cost. If you compare the same amount of product, which brand is cheaper? If you spend the same amount of money, which brand gives you more product? 3) Use Khan Academy to review equivalent ratios: www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/introduction‑to‑ratios‑new‑hd‑version © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 49 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 2 2 homework answers 1) Geoboards for Ms. Lin’s class number of students number of geoboards 4 3 8 6 16 12 24 18 2) Ms. Lin needs 9 geoboards. 3) Ms. Lin needs more geoboards. 4) Ms. Lin and Mr. Mark have 40 students in all. 5) Jerry’s Punch raspberry juice (ounces) lemonade (ounces) 1 15 2 30 10 150 20 300 6) Jerry will use 3 ounces of raspberry juice. 7) Jerry will make more punch. 8) Della will need more raspberry juice. Possible explanation: Jerry uses 2 ounces of raspberry juice for every 30 ounces of lemonade. If he uses 2 3 30 5 60 ounces of lemonade, he will need 2 3 2 5 4 ounces of raspberry juice. Della uses 6 ounces of raspberry juice for every 30 ounces of lemonade. If she makes 2 3 30 5 60 ounces of lemonade, she will need 2 3 6 5 12 ounces of raspberry juice. I used TLM practice #4 and used the table as a math model to help me find equivalent ratios. Mixed Practice 13 10) _ is closest to 0. 9) 4.52 79 11) Possible answer: This ratio means for every 12 minutes that Nicki ran during her workout, she walked for 42 minutes. The number 12 describes the number of minutes Nicki ran because it is the first number in the ratio. 4 12) 1.055, 1 _ , 1.501 9 Word Problem 13) There are 180 boys in Park Middle School. PowerTeaching Math 3rdMath Edition 50 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 3 3 teamwork 1) It cost Rosemary $6.68 for 4 pounds of apples. a. What is the rate that Rosemary paid for the apples? Write the rate in words and as a ratio. b. Write a unit price to describe the price Rosemary paid for 1 pound of apples. 2) Nico was paid $47 for mowing 4 lawns. a. At what rate was Nico paid to mow the lawns? Write the rate in words and as a ratio. b. Write a unit rate to describe how much Nico was paid for mowing 1 lawn. 3) Deepa drove 910 miles in 14 hours. a. What is Deepa’s driving rate? Write the rate in words and as a ratio. b. Write a unit rate to describe how far Deepa drove in 1 hour. 4) Orisa bought a 12 pack of soda for $5.76. a. What is the rate Orisa paid for 12 sodas? Write the rate in words and as a ratio. b. Write a unit price to describe how much Orisa paid for one soda. 5) Phillip drove his truck 340 miles on 20 gallons of gas. a. At what rate did Phillip’s truck use gas? Write the rate in words and as a ratio. b. Write a unit rate to describe how far Phillip’s truck can go on 1 gallon of gas. 6) Daniel read a 125‑page book in 75 minutes. a. Write a rate that describes how many pages Daniel read. Write the rate in words and as a ratio. b. Write a unit rate describes the number of pages Daniel read in 1 minute. 15 sit‑ups 1 minute 7) Michaela does sit‑ups at a rate of __. Explain how many sit‑ups Michaela will do in 2 minutes and 3 minutes and what the rate means in words. 8) Cory bought 22 baseball cards for $4.18. Explain what the rate means in words. Challenge 9) Yen bought a 4‑pack of yogurt for $3.68. Each of the 4 containers has 4.6 ounces of yogurt. Write the unit price to describe the price per ounce of yogurt. © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 51 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 3 3 teamwork answers 1) a. $6.68 4 pounds $6.68 per 4 pounds; __ $1.67 pound b. $1.67 per pound, or __ 2) a. $47 4 lawns $47 per 4 lawns; __ $11.75 lawn b. $11.75 per lawn, or __ 3) a. 910 miles 910 miles per 14 hours; __ 14 hours 65 miles b. 65 miles per hour, or __ hour 4) a. $5.76 12 sodas $5.76 per 12 sodas; __ $0.48 soda b. $0.48 per soda, or _ 5) a. 340 miles 340 miles per 20 gallons; __ 20 gallons 17 miles b. 17 miles per gallon, or __ gallon 6) a. 125 pages 75 minutes 125 pages per 75 minutes; or __ 1.667 pages minute b. 1.667 pages per minute, or __ 7) Possible explanation: This is a unit rate, so for every 1 minute, Michaela does 15 sit‑ups. In 2 minutes, she will do 30 sit‑ups. In 3 minutes, she will do 45 sit‑ups. 8) Possible explanation: Cory paid $4.18 for every 22 baseball cards. If he bought 11 baseball cards, he would pay $2.09, and if he bought 66 baseball cards, he would pay $12.54. $0.20 9) The yogurt cost $0.20 per ounce, or _ ounce . PowerTeaching Math 3rdMath Edition 52 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation quick check Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 3 3 Name JD was paid $45 for babysitting for 5 hours. What was JD’s rate of pay? Write a unit rate to describe how much JD made in 1 hour. © 2015 Success for All Foundation quick check PowerTeaching Math 3rd Edition Name JD was paid $45 for babysitting for 5 hours. What was JD’s rate of pay? Write a unit rate to describe how much JD made in 1 hour. © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 53 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 63 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 homework Quick Look Vocabulary words introduced in this cycle: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern Today we learned to write rates and unit rates. Rates are a type of ratio that compares two different units of measure. Unit rates are a type of rate that compares a quantity to 1 unit of another measure. For example: Leslie pays $2.68 for every 4 pounds of bananas. $2.68 4 pounds The rate: __, or $2.68 for every 4 pounds. To find the unit rate, or the cost for 1 pound, we divide the parts of the rate by 4: $2.68 _ $0.67 44 __ 5 __, or $0.67 per pound. 4 pounds 4 4 pound 1) Mr. Jay paid $99 for 10 hours of work. a. At what rate did Mr. Jay pay for work? Write the rate in words and as a ratio. b. Write a unit rate to describe how much Mr. Jay paid for 1 hour of work. 2) It took Regina 4 minutes to complete 2 homework problems. a. At what rate does Regina complete homework problems? Write the rate in words and as a ratio. b. Write a unit rate to describe how long it takes Regina to do 1 homework problem. 3) Simon ran 13 miles in 104 minutes. a. At what rate did Simon run? Write the rate in words and as a ratio. b. Write the unit rate to describe how far Simon ran in 1 minute. 4) It took Adia 27 minutes to read 2 chapters. Use a ratio to describe her rate. How long would it take her to read 4 chapters? Explain your thinking. 5) Antonio paid $3.18 for 1 gallon of milk. Explain what the rate means in words. Mixed Practice 6) Write an integer to describe a withdrawal of $50 from a bank account. 7) Multiply. 5 6 _ 3_ 5 12 10 8) Find the least common multiple of 8 and 14. © for All Foundation 542015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 6 3| Unit 5: Introduction to Ratios and Rates | Cycle 1 Homework Lesson 3 9) Use mental math to find the product. 940 3 8 Word Problem 10) It cost Abby $345 to stay in a hotel for 3 nights. Write a unit rate to describe how much it cost her per night. Explain your thinking. For the Guide on the Side Today your student learned to write rates and unit rates. Rates are a type of ratio that compares two different units of measure. Unit rates are a type of rate that compares a quantity to 1 unit of another measure. Rates and unit rates can be written as a ratio or in words using per (meaning for each or for every). To find a unit rate, of miles per hour for example, divide both the number of miles and the number of hours by the number of hours to get the number of miles per 1 hour. Because we are dividing both parts of the rate by the same number, we are finding an equivalent rate. Later in the cycle, we will find unit rates to solve more complex problems. Your student should be able to answer the following questions about writing rates and unit rates: 1) What does this rate/unit rate mean? 2) How can you tell that this is a rate/unit rate? 3) How do you write the rate/unit rate? Why? 4) How did you find this rate/unit rate? Here are some ideas to work with solving unit rate problems: 1) Time your student or another person doing some task. Write a rate to describe what was done and how long it took to do it. Then, find a unit rate to describe the task. For example, I washed 15 dishes in 5 minutes, so I wash 15 dishes per 5 minutes, or 5 dishes per minute. 2) Look at a grocery store flier. Write a rate to describe the price for a certain amount of one item. Then, find a unit price for that item. For example, orange marmalade costs $4.49 for 13 ounces, so it costs $4.49 per 13 ounces, or $0.35 per ounce. 3) Use Khan Academy to review finding unit rates and unit prices: www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/finding‑unit‑prices www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/finding‑unit‑rates PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 55 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 63 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 3 homework answers 1) a. $99 10 hours $99 per 10 hours; __ $9.90 hour b. $9.90 per hour, or _ 2) a. 4 minutes 4 minutes per 2 problems; __ 2 problems 2 minutes b. 2 minutes per problem, or __ problem 3) a. 13 miles 13 miles per 104 minutes; __ 104 minutes 0.125 mile b. 0.125 mile per minute, or __ minute 4) Adia’s rate is 2 chapters:27 minutes, and it would take her 54 minutes to read 4 chapters. To find how long it would take Adia to read 4 chapters, I doubled her rate. I used TLM #6 to accurately and precisely determine her reading rate and how long it would take to read 4 chapters. 5) Possible explanation: Every 1 gallon of milk costs $3.18. At that rate, it costs $6.36 for 2 gallons of milk. 6) – $50 1 7) _ 4 8) 56 9) 7,520 $115 night 10) It costs Abby $115 per night, or _, to stay in the hotel. Possible explanation: Abby paid $345 for 3 nights in a hotel. To find out how much she paid for 1 night, I divided both parts of the ratio by 3. $345 _ $115 43 __ 5_ 3 nights 43 night © for All Foundation 562015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 4 4 teamwork 1) Mason rode his bike 13 miles in 80 minutes. Olivia rode her bike 15 miles in 120 minutes. Who travels at a slower rate? Explain your thinking. 2) Tyler is buying frozen treats for the school picnic. He is choosing between Sam’s Grocery, where the treats are 15 for $1.65, and the Jewel Market, where they are 25 for $2.25. Which store has the better price? 3) Henry reads 20 pages in 10 minutes. Rotha reads 30 pages in 12 minutes. Who reads at a quicker rate? 4) A 4‑ounce strawberry yogurt contains 80 calories, and a 6‑ounce peach yogurt contains 130 calories. Which flavor has fewer calories per ounce? Explain your thinking. 5) The cost of ribbon at Yarn World is $0.83 for 3 yards. The same ribbon is $2.64 for 12 yards at Deals. Which store has a higher price for the ribbon? 6) It takes Hasanna 23 days to knit 3 sweaters and Luther 64 days to knit 9 sweaters. Who knits sweaters at a quicker rate? 7) Joseph answered 10 multiplication problems in 80 seconds, and Khristina answered 8 multiplication problems in 48 seconds. Who completes problems at a faster rate? 8) Jim drove 1,700 miles in 29 hours, and Kara drove 3,400 miles in 56 hours. Who drives at a slower rate? Challenge 9) Contestant A swam 7.5 laps in 12 minutes, contestant B swam 10.5 laps in 17 minutes, and contestant C swam 5 laps in 9 minutes. Who had the fastest swimming rate? © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 57 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 4 4 teamwork answers 1) Olivia travels at a slower rate. Possible explanation: I knew that I couldn’t compare the rates as written because the miles and minutes were all different. So I multiplied to find equivalent rates that I could compare (TLM #2). I chose to find how far they each travel in 240 minutes, which made it clear that Olivia goes slower. 13 miles 39 miles 3 Mason: __ 3_ 5 __ 80 minutes 3 240 minutes 15 miles 2 30 miles Olivia: __ 3_ 5 __ 120 minutes 2 240 minutes Then, I compared the distances traveled in 240 minutes for both rates. 39 miles __ 30 miles __ 240 minutes 240 minutes So Olivia traveled at a slower rate. 2) Jewel Market has the better price. 3) Rotha reads at a quicker rate. 4) The strawberry yogurt has fewer calories per ounce. Possible explanation: I found how many calories are in 2 ounces of each yogurt because 2 is the GCF of 4 and 6. 80 calories 40 calories 2 strawberry yogurt: __ 4_ 5 __ 4 ounces 2 2 ounces 130 calories 43.3 calories 3 peach yogurt: __ 4_ 5 __ 6 ounces 3 2 ounces I knew that I couldn’t compare the rates as written because the ounces and calories were all different. So I divided to get the GCF to find equivalent rates that I could compare (TLM #2). I chose to find the number of calories in 2 ounces of each kind of yogurt. That made it clear that strawberry has fewer calories per ounce. 5) Yarn World has a higher price. 6) Luther knits at a quicker rate. 7) Khristina completes problems at a faster rate. 8) Jim drives at a slower rate. 9) Contestant A had the fastest swimming rate. PowerTeaching Math 3rdMath Edition 58 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation quick check Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 4 4 Name Ethan and Emma check their heartbeats. Ethan’s heart beats at a rate of 26 beats per 20 seconds, and Emma’s beats at a rate of 42 beats per 30 seconds. Whose heart beats faster? © 2015 Success for All Foundation quick check PowerTeaching Math 3rd Edition Name Ethan and Emma check their heartbeats. Ethan’s heart beats at a rate of 26 beats per 20 seconds, and Emma’s beats at a rate of 42 beats per 30 seconds. Whose heart beats faster? © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 59 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 64 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 homework Quick Look Vocabulary words introduced in this cycle: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern Today we learned how to compare rates. For example: It costs $5.60 for a 28‑ounce container of peanut butter, but it costs Jen $0.60 to make 4 ounces of peanut butter. Which peanut butter is cheaper? To compare rates, find an equivalent rate so one of the units in both of the rates has the same quantity. You can use common factors and common multiples to compare. In this example, 4 is the GCF of 4 and 28. Store‑bought 47 [ $0.80 4 ounces $5.80 28 ounces Homemade ] 47 $0.60 4 ounces $0.80 for 4 ounces $0.60 for 4 ounces. Jen can make her own peanut butter for less than she can buy the store‑bought kind. You can always use unit rates to compare because one of the units will have a quantity of 1. Let’s find how much 1 ounce of peanut butter costs for each type. Store‑bought Homemade $5.60 $0.20 28 __ 4_5_ ounce 28 ounces 28 $0.60 $0.15 4 __ 4_5_ ounce 4 ounces 4 $0.20 per ounce $0.15 an ounce. We got the same answer either way. Directions for questions 1–6: Compare the two rates. 1) Ade and Rachel checked their heartbeats. Ade’s heart beat 37 times in 15 seconds, and Rachel’s beat 124 times in 1 minute. Who had a faster heartbeat? 2) Team Cure ran 27 miles in 261 minutes. Team Speedster ran 13.5 miles in 117 minutes. Which team ran at a faster speed? 3) Betty makes 80 donuts in one hour. Andre makes 64 donuts in 40 minutes. Who can make donuts at a quicker rate? Explain your thinking. 4) A red game spinner makes 32 revolutions in 19 seconds. A blue game spinner makes 24 revolutions in 13 seconds. Which color spinner is faster? 5) A 6‑ounce steak costs $5.58, and a 10‑ounce steak costs $8.90. Which steak is the better buy? Explain your thinking. © for All Foundation 602015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 6 4| Unit 5: Introduction to Ratios and Rates | Cycle 1 Homework Lesson 4 6) 3 slices of sausage pizza cost $3.90, and 4 slices of vegetable pizza cost $4.50. Which type of pizza costs less per slice? Mixed Practice 7) Subtract. 8.209 4.13 5 8) Convert to an improper fraction: 4 2_ 5 6 9) Divide. 5 8 _ 4_5 24 15 10) Order these numbers from least to greatest: 6 2_ , 2.09, 2.538 15 Word Problem 11) Harper’s family eats 5 boxes of cereal in 3 days. Owen’s family eats 9 boxes of cereal in 5 days. Which family will need to buy more cereal in one month? Explain your thinking. PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 61 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Homework Level 64 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 For the Guide on the Side Today we learned how to compare rates. To compare rates, one of the units in both of the rates needs to have the same quantity. If Selena drives 10 miles in 25 minutes and Avis drives 15 miles in 30 minutes, it is difficult to see who travels at a faster speed. If we find equivalent rates, we can see that it takes Avis a shorter amount of time to travel the same distance as Selena, so Avis travels at a faster speed. 10 miles 30 miles Selena: __ 5 __ 25 minutes 75 minutes 15 miles 30 miles Avis: __ 5 __ 30 minutes 60 minutes Students can use what they already know about equivalent ratios to compare. This is similar to finding common denominators to compare fractions. Your student should be able to answer these questions about comparing rates: 1) How did you compare these rates? 2) How do you know these rates are equivalent? 3) Is there another way you could have compared these rates? Here are some ideas to work with comparing rates with your student: 1) Sometimes, grocery and convenience stores do not give you the unit price to help you compare the price of their products. Compare products that do not give the unit prices to find which one is cheaper per volume and/or weight. 2) Guess how fast your heart beats in 60 seconds. Then, place two fingers on your wrist or neck, and count how many beats you feel in 10 seconds. Was your guess faster or slower than the heartbeat you measured? 3) Use Khan Academy to review finding the unit price and unit rate. www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/finding‑unit‑rates www.khanacademy.org/math/arithmetic/basic‑ratios‑proportions/v/finding‑unit‑prices © for All Foundation 622015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 6 4| Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 4 homework answers 1) Ade has a faster heartbeat. 2) Team Speedster ran faster. 3) Andre can make donuts at a quicker rate. Possible explanation: 10 is a factor of 60 and 40, so I used it to compare the rates. 80 donuts 13.3 donuts 6 Betty: __ 4 _ 5 __ 60 minutes 6 10 minutes 64 donuts 16 donuts 4 Andre: __ 4 _ 5 __ 40 minutes 4 10 minutes 16 donuts 13.3 donuts, so Andre makes donuts faster. I knew that I couldn’t compare the rates as written because the donuts and minutes were all different. So I used TLM practice #2 and divided to get the GCF to find equivalent rates that I could compare. 4) The blue spinner is faster. 5) The 10‑ounce steak is the better buy. 6) The vegetable pizza costs less per slice. Possible explanation: I found the unit cost of 1 slice of pizza to compare the rates. $3.90 3 slices $1.30 slice $4.50 4 slices 3 sausage: __ 4 _ 5_ 3 $1.13 slice 4 vegetable: __ 4 _ 5_ 4 $1.13 $1.30, so the vegetable pizza costs less per slice. I knew that I couldn’t compare the rates as written because the cost and number of slices were all different. So I used TLM practice #2 and divided to get the GCF to find equivalent rates that I could compare. Mixed Practice 7) 4.079 8 8) _ 25 9) _ 6 10) 2.09, 2_ , 2.538 3 15 64 Word Problem 11) Owen’s family will need to buy more cereal in one month. First I made equivalent rates with 15 in the denominator because it is the LCM of 3 and 5. 5 boxes 25 boxes 5 Harper’s family: __ 3 _ 5 __ 3 days 5 15 days 9 boxes 27 boxes 3 Owen’s family: __ 3 _ 5 __ 5 days 3 15 days Then, I compared the number of boxes eaten in 15 days. 27 boxes is more cereal eaten than 25 boxes, so Owen’s family eats boxes of cereal at a faster rate. If his family eats more cereal than Harper’s family in 15 days, his family will still eat more than Harper’s in a month. I knew that I couldn’t compare the rates as written because the boxes and number of days were all different. So I used TLM practice #2 and multiplied to get the LCM to find equivalent rates that I could compare. PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 63 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 65 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 teamwork 1) Evan is building a tower with plastic cups. The first layer has 36 cups, the second layer has 32 cups, and the third layer has 28 cups. If his tower continues like this, how many layers of cups will Evan have? 2) Eli walks his dog for 2.75 minutes on Sunday, 5.5 minutes on Monday, and 11 minutes on Tuesday. If he continues walking his dog like this, how many minutes will they walk on Friday? 3) Jill is trying to get her baby to go to sleep earlier at night. She puts her to bed at 8:30 p.m. on Monday, 8:15 p.m. on Tuesday, and 8:00 p.m. on Wednesday. If she continues like this, how much earlier will the baby go to bed on Saturday than on Monday? 4) A fisherman goes crabbing at the end of the crab season. The first morning he catches 128 crabs, the second morning he catches 64 crabs, and the third morning he catches 32 crabs. If the crabbing continues this way, how many crabs will he catch on the sixth morning? 5) A zoo watched its attendance each month. In January, it had 1,126 visitors, in February, it had 1,251 visitors, and in March, it had 1,376 visitors. How many more visitors will the zoo have in May than in January? 6) Michelle’s charity raised $1,300 in the first year, $1,450 in the second year, and $1,600 in the third year. If her charity continues to raise money like this, how much money will she raise in all by the fifth year? 1 1 7) Zaki is studying for his math test that is Friday morning. He studied _ hour on Monday night, _ hour on 4 2 3 Tuesday night, and _ hour on Wednesday night. If he continues to study like this, how many hours total 4 will he study for the test? 8) Mr. Adams washed 42 cars on Monday, 35 cars on Tuesday, and 28 cars on Wednesday. If he continues like this, when will Mr. Adams have a day that he won’t have any cars to wash? Challenge 9) Create a word problem that can be solved by finding a pattern. Create a table, and solve the problem. Then, have your teammates solve the problem you created. © for All Foundation 642015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 6 5| Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 teamwork answers 1) Evan will have 9 layers of cups. 2) They will walk for 88 minutes on Friday. 3) The baby will go to bed 1 hour and 15 minutes earlier. 4) On the sixth morning, he will catch only 4 crabs. 5) The zoo will have 500 more visitors in May than January. 6) The charity will raise $8,000 in all. 7) Zaki will study for a total of 2 hours and 30 minutes. 8) Mr. Adams will not have to wash any cars on Sunday. 9) Answers will vary. PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 65 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson Level 65 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Lesson 5 quick check Name Zahra’s website had 14 visitors on day 1, 26 visitors on day 2, and 38 visitors on day 3. If she keeps getting visitors this way, how many more visitors will she have on day 8 than on day 1? © 2015 Success for All Foundation quick check PowerTeaching Math 3rd Edition Name Zahra’s website had 14 visitors on day 1, 26 visitors on day 2, and 38 visitors on day 3. If she keeps getting visitors this way, how many more visitors will she have on day 8 than on day 1? © for All Foundation 662015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 5 5 homework Quick Look Vocabulary words introduced in this cycle: ratio, equivalent ratios, rate, per, unit rate, unit price, pattern Today we learned to look for patterns to solve word problems. For example: Ameen is trying to shorten the time it takes to do his chores. In week one, he finished them in 194 minutes. In week two, he finished them in 190 minutes. In week three, he finished them in 186 minutes. If he keeps going like this, by how many fewer minutes will it take him to do chores in week seven than in week one? Week one two three four five six seven Minutes to do Chores 194 190 186 182 178 174 170 If the problem looks like it has a pattern, create a table for the given information. At least 3 pieces of information are needed to determine a pattern. In this problem, the pattern is that Ameen shortens his time each week by 4 minutes. Next, fill in the table to find how long it takes Ameen to do his chores in week seven, 170 minutes. Finally, solve. It took him 194 minutes to do his chores on week one. The difference in time between these two weeks is 194 170 5 24 minutes. So Ameen takes 24 fewer minutes to complete his chores in week seven than week one. Directions for questions 1–6: Solve. 1) In Ramblebrook, it snowed 91.8 inches in December, 30.6 inches in January, and 10.2 inches in February. If it continues snowing like this, how many inches total will the town get between the months of December and March? 2) Rhonda does 5 sit‑ups on day one, 10 sit‑ups on day two, and 20 sit‑ups on day three. If she keeps doing sit‑ups like this, how many will she do on day seven? 3) The height of Mrs. Robbin’s tree was 5.23 inches the first year. It was 8.36 inches tall the second year, and 11.49 inches tall the third year. If it continues to grow like this, how much taller will it be in the seventh year than in the first year? 4) A pancake house served 250 pancakes on Sunday, 235 pancakes on Monday, and 220 pancakes on Tuesday. If the restaurant continues to serve pancakes like this, on what day will it serve 160 pancakes? 5) Leah’s garden grew 21 tomatoes the first summer, 42 tomatoes the second summer, and 84 tomatoes the third summer. If her garden continues to produce like this, how many tomatoes will grow the sixth summer? 6) Will hiked 48 minutes on day one, 56 minutes on day two, and 1 hour and 4 minutes on day three. If he continues like this, how many minutes in all will he hike for seven days? © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 67 Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates || Cycle 1 1 Lesson Lesson 5 5 Teamwork Mixed Practice 7) Divide. 21 5,258 5 8) Multiply. 2.25 3 6.9 5 9) Write a ratio in three ways. Be sure to write the ratio in simplest form. Alisha wrote the ratio 5 to 25 to compare the number of pennies in her pocket with the number of pennies in her piggy bank. 10) Ferdinand ran 2 miles in 19.5 minutes. Felicia ran 3 miles in 27.25 minutes. Who ran at a faster rate? Word Problem 11) Alex set up a phone tree to let people know when baseball games are rained out. During the first round, 3 people are called. During the second round, 9 people are called, and during the third round, 27 people are called. How many people total are called after 5 rounds of the phone tree? Explain your thinking. For the Guide on the Side Today your student learned to solve problems by looking for a pattern. Sometimes there is a pattern we can use to solve a word problem. Patterns can be used to organize the data in the problem and to make predictions about future data. First, we organize the data into a table to determine the pattern. (At least three pieces of data are needed to establish a pattern.) Then, we fill out the table and use the information in it to solve the problem. Your student should be able to answer these questions when looking for patterns: 1) What is the question asking? 2) What pattern did you find? How did you find the pattern? 3) How did you use your table to find the answer? 4) Does this pattern continue forever? Why do you think that? 5) Where do we find patterns in our schools, homes, or town? Here’s an idea to look for patterns at home with your student: Where do we find patterns in our homes, schools, or towns? Record your pattern. Can you use this information to predict an event that will happen in the future? PowerTeaching Math 3rdMath Edition 68 PowerTeaching 3rd Edition | Unit Guide © 2015 Success for All Foundation Level 6 6 || Unit 5: Introduction to Ratios and Rates Rates | | Cycle 1 1 Lesson Lesson 5 5 homework answers 1) It will snow 136 inches. 2) Rhonda will do 320 sit‑ups on day seven. 3) It will be 18.78 inches taller in year seven than in year one. 4) The restaurant will serve 160 pancakes on Saturday. 5) The garden will produce 672 tomatoes in the sixth summer. 6) He will hike for 504 minutes. Mixed Practice 7) 250.381 or 250 R8 8) 15.525 1 9) 1:5, 1 to 5, _ 5 10) Felicia ran at a faster rate. Word Problem 11) 363 people are called after 5 rounds. Possible explanation: I used TLM practice #7 and found a pattern in the problem, which helped me determine how many people would be called in each round. The pattern is that in each subsequent round, 3 times more people are called. So I found the number called in each round and then added together the numbers for rounds 1–5 to answer the question. © 2015 Success for All Foundation Foundation Math 3rd Edition PowerTeaching Math PowerTeaching 3rd Edition | Unit Guide 69 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 AssessmentLevel Day 6 | Unit 5: Introduction to Ratios and Rates Cycle 1 unit check Directions for questions 1 and 2: Write a ratio in simplest form in three different ways. 1) 61 out of the 81 sixth graders take the bus to school. Compare the sixth graders who take the bus with the sixth graders who do not take the bus. 2) Jack’s Furniture Store sold 84 chairs and 34 beds last month. Compare the chairs sold with the total number of items sold. Directions for questions 3 and 4: Explain what the ratio means in words. Write whether the ratio is a part‑to‑part, part‑to‑whole, or whole‑to‑whole comparison. 3) Marty compared the dogs with all the pets in the store: 5:12. 4) June compared the number of slices of mushroom pizza with the number of slices of pepperoni pizza: 37:12. Directions for questions 5–7: Use the ratio tables to answer the following questions. Marie’s Fruit Punch cups of cranberry juice Sal’s Fruit Punch cups of pineapple juice cups of cranberry juice 5 1 4 6 cups of pineapple juice 2 15 25 6 12 5 5) Fill in the information missing from the tables. 6) If both Sal and Marie use 4 cups of cranberry juice, who will have less juice in all? 7) If both Sal and Marie make 56 cups of fruit punch, who will use more pineapple juice? Explain your thinking. 8) Sue drove 180 miles in 3 hours. a. What was Sue’s driving rate? Write the rate in words and as a ratio. b. Write a unit rate to describe how far Sue could drive in 1 hour. Directions for questions 9 and 10: Explain what the rate means in words. 9) 528 calories per 4 servings of blueberry oatmeal 10) Gina types at a rate of 36 words/minute. © for All Foundation 702015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates Cycle Level 1 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 Assessment Unit Check Day Directions for questions 11–13: Solve. 11) There are 3 loaves of bread at a table with 12 people and 6 loaves at a table with 29 people. At which table does each person get more bread? 12) A bag of Krazy Cat Food costs $10.00 for 4 pounds. A bag of Best Cat Food costs $12.00 for 5 pounds. Which is the better deal? Explain your thinking. 13) Nick is doing push‑ups. The first day he does 10, the next day he does 14, and the day after that, he does 18. If he continues his workout this way, how many push‑ups will he do on the tenth day? After the tenth day, how many push‑ups will Nick have done in all? PowerTeaching Math Edition © 2015 Success for All3rd Foundation 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 71 Level 6 | Unit 5: Introduction to Ratios and Rates | Cycle 1 AssessmentLevel Day 6 | Unit 5: Introduction to Ratios and Rates Cycle 1 unit check answers Lesson 1: Write ratios in three ways, and use ratio language. [20 pts] 61 1) 61:20, 61 to 20, _ [5 pts] 20 42 2) 42:59, 42 to 59, _ [5 pts] 59 3) Possible answer: This ratio means that 5 out of every 12 pets are dogs. This is a part‑to‑whole comparison. It compares the number of dogs with the total number of pets in the stores. The number 5 describes the number of dogs because it is the first number in the ratio. [5 pts] 4) Possible answer: This ratio means that for every 37 slices of mushroom pizza, there are 12 slices of pepperoni pizza. This is a part‑to‑part comparison. It compares part of the pizza with another part of the pizza. The number 37 describes the mushroom slices because that is the first number in the ratio. [5 pts] Lesson 2: Use tables to find equivalent ratios. [20 pts] 5) Marie’s Fruit Punch Sal’s Fruit Punch cups of cranberry juice cups of pineapple juice cups of cranberry juice cups of pineapple juice 2 5 1 3 4 10 2 6 6 15 4 12 10 25 5 15 [7 pts] 6) Marie will have less juice in all. [6 pts] 7) Sal will use more pineapple juice. Possible explanation: Marie uses 5 cups of pineapple juice for every 7 cups of fruit punch. To make 56 cups of fruit punch (7 3 8), she will use 5 3 8, or 40, cups of pineapple juice. Sal uses 3 cups of pineapple juice for every 4 cups of fruit punch. To make 56 cups of fruit punch (4 3 14), he will use 3 3 14, or 42, cups of pineapple juice. 42 40, so Sal will use more pineapple juice. [7 pts] Lesson 3: Identify and write rates, and find unit rates. [20 pts] 8) a. 180 miles 180 miles per 3 hours; __ [4 pts] 3 hours 60 miles b. 60 miles per hour; __ [4 pts] hour 9) Possible explanation: For every 4 servings of oatmeal, there are 528 calories, so 2 servings would have 264 calories, and 8 servings would have 1,056 calories. [6 pts] 10) Possible explanation: This is a unit rate, so for every one minute, Gina types 36 words. If she types for 2 minutes, she can type 72 words. If she types for 3 minutes, she can type 108 words. [6 pts] © for All Foundation 722015 Success PowerTeaching Math 3rd Edition | Unit Guide Math 3rd Edition ©PowerTeaching 2015 Success for All Foundation Level 6 | Unit 5: Introduction to Ratios and Rates Cycle Level 1 6 | Unit 5: Introduction to Ratios and Rates | CycleUnit 1 Assessment Check Answers Day Lesson 4: Compare rates in the context of real-world problems. [20 pts] 11) The 12‑person table gets more bread per person. [10 pts] 12) Best Cat Food is the better deal. [10 pts] Possible explanation: I used the LCM of 4 and 5 to compare the cat food brands. $10.00 4 pounds $50.00 20 pounds $12.00 5 pounds 5 Krazy Cat Food: __ 3 _ 5 __ 5 $48.00 20 pounds 4 Best Cat Food: __ 3 _ 5 __ 4 $48.00 for 20 pounds is cheaper than $50.00 for 20 pounds, so Best Cat Food is the better deal. Lesson 5: Find a pattern to solve problems. [20 pts] 13) Nick will do 46 push‑ups on the tenth day. He will have done 280 push‑ups in all after the tenth day. Day 1 2 3 4 5 6 7 8 9 10 # of Push‑ups 10 14 18 22 26 30 34 38 42 46 Prep Points Analysis Team Scores (out of 20 points) Question Number Core Objective 3 Write ratios in three ways, and use ratio language. 7 Use tables to find equivalent ratios. 9 Identify and write rates, and find unit rates. 11 Compare rates in the context of real‑world problems. 13 Find a pattern to solve problems. PowerTeaching Math Edition © 2015 Success for All3rd Foundation 1 2 3 4 5 Class Results (check if 16 out of 20 points or better) 2015 Success for Guide All Foundation PowerTeaching Math©3rd Edition | Unit 73
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