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**Chapter 8**Algebra: Ratios and Functions Click the mouse or press the space bar to continue. Splash Screen**Algebra: Ratios and Functions**8 Lesson 8-1Ratios and Rates Lesson 8-2Problem-Solving Strategy: Look for a Pattern Lesson 8-3Ratio Tables Lesson 8-4Equivalent Ratios Lesson 8-5Problem-Solving Investigation: Choose the Best Strategy Lesson 8-6Algebra: Ratios and Equations Lesson 8-7Algebra: Sequences and Expressions Lesson 8-8Algebra: Equations and Graphs Chapter Menu**Ratios and Rates**8-1 Five-Minute Check (over Chapter 7) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Ratios and Tangrams Lesson 1 Menu**Ratios and Rates**8-1 • I will express ratios and rates in fraction form. • ratio • rate • unit rate Lesson 1 MI/Vocab**Ratios and Rates**8-1 Preparation for Standard 6NS1.2Interpret and use ratios in different contexts(e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations . Lesson 1 Standard 1**Ratios and Rates**8-1 unicycles 4 2 10 5 scooters Write the ratio in simplest form that compares the number of scooters to the number of unicycles. = Lesson 1 Ex1**Ratios and Rates**8-1 Answer:The ratio of unicycles to scooters is , 2 to 5, or 2:5. This means that for every 2 unicycles there are 5 scooters. 2 5 Lesson 1 Ex1**Ratios and Rates**8-1 A. 1 2 1 2 4 4 8 8 B. C. D. Write the ratio in simplest form that compares the number of singers in a duet to the number in an octet. Lesson 1 CYP1**Ratios and Rates**8-1 Several students were asked to name their favorite kind of book. Write the ratio that compares the number of people who chose sports books to the total number of responses. 7 students preferred sports out of a total of 7 + 9 + 4 + 5 or 25 responses. Lesson 1 Ex2**Ratios and Rates**8-1 7 25 Answer:The ratio in simplest form of the number of students who chose sports to the total number of responses is , 7 to 25, or 7:25. So, seven out of every 25 students preferred sports. sports responses 7 25 total responses Lesson 1 Ex2**Ratios and Rates**8-1 Several students were asked to name their favorite kind of movie. Choose the ratio that compares the number of people who chose thriller movies to the total number of responses in simplest form. • 2:5 • 12:30 • 12:18 • 2:3 Lesson 1 CYP2**Ratios and Rates**8-1 $2.88 $0.18 16 ounce 1 ounce Find the cost per ounce of a 16-ounce jar of salsa that costs $2.88. = Answer: So, the salsa costs $0.18 per ounce. Lesson 1 Ex3**Ratios and Rates**8-1 A 4 pound package of ground beef costs $3.56. What is the cost per pound? • $0.99 • $0.88 • $0.98 • $0.89 Lesson 1 CYP3**Problem-Solving Strategy: Look for a Pattern**8-2 Five-Minute Check (over Lesson 8-1) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 2 Menu**Problem-Solving Strategy: Look for a Pattern**8-2 • I will solve problems by looking for a pattern. Lesson 2 MI/Vocab**Problem-Solving Strategy: Look for a Pattern**8-2 Standard 5MR1.1Analyze problems byidentifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Standard 5NS2.1 Add,subtract, multiply, and divide with decimals; … and verify the reasonableness of results. Lesson 2 Standard 1**Problem-Solving Strategy: Look for a Pattern**8-2 Emelia is waiting for her friend Casey to arrive. It is 1:15 P.M. now, and Casey said that he would be on the first bus to arrive after 6:00 P.M. Emelia knows that buses arrive every 30 minutes, starting at 1:45 P.M. How much longer will it be before Casey arrives? Lesson 2 Ex 1**Problem-Solving Strategy: Look for a Pattern**8-2 Understand What facts do you know? • It is now 1:15 P.M. • The first bus arrives at 1:45 P.M. • Casey will be on the first bus after 6 P.M. What do you need to find? • How much longer will it be before Casey arrives? Lesson 2 Ex1**Problem-Solving Strategy: Look for a Pattern**8-2 Plan Start with the time the first bus arrives and look for a pattern. Lesson 2 Ex1**Problem-Solving Strategy: Look for a Pattern**8-2 Solve Answer: So, the first bus to arrive after 6:00 P.M. is the 6:15 P.M. bus. Since it is now 1:15 P.M., Casey will not arrive for another 5 hours. Lesson 2 Ex1**Problem-Solving Strategy: Look for a Pattern**8-2 Check Look back at the problem. Continue adding 30 minutes to the previous arrival time until you reach 6:15 P.M. Then add up the 30-minute periods. Lesson 2 Ex1**Ratio Tables**8-3 Five-Minute Check (over Lesson 8-2) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Example 4 Lesson 3 Menu**Ratio Tables**8-3 • I will use ratio tables to represent and solve problems involving equivalent ratios. • ratio table • equivalent ratio • scaling Lesson 3 MI/Vocab**Ratio Tables**8-3 Standard 5MR2.3Use a variety of methods, such aswords, numbers, symbols, charts, graphs, tables,diagrams, and models, to explain mathematical reasoning. Preparation for Standard 5AF1.5Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. Lesson 3 Standard 1**Ratio Tables**8-3 A recipe calls for 5 cups of water for each cup of pinto beans. Use the ratio table to find how many cups of water should be used for 4 cups of pinto beans. Lesson 3 Ex1**Ratio Tables**8-3 One Way: Find a pattern and extend it. For 4 cups of beans, you would need a total of 5 + 5 + 5 + 5 or 20 cups of water. 2 3 20 10 15 Lesson 3 Ex1**Ratio Tables**8-3 Another Way: Multiply each quantity by the same number. 20 Answer: So, for 4 cups of pinto beans, you will need 20 cups of water. Lesson 3 Ex1**Ratio Tables**8-3 The recipe for rice calls for 3 cups of water for each cup of rice. How many cups of water should be used for 6 cups of rice? • 18 cups • 9 cups • 12 cups • 16 cups Lesson 3 CYP1**Ratio Tables**8-3 There are over 50,000 species of spiders. Use the ratio table below to find how many legs a spider has. 2 8 16 Answer: So, a spider has 8 legs. Lesson 3 Ex2**Ratio Tables**8-3 A marathon runner can run 24 miles in 3 hours. How many miles can he run in 1 hour? • 16 miles • 8 miles • 12 miles • 4 miles Lesson 3 CYP2**Ratio Tables**8-3 Coco used 12 yards of fabric to make 9 blouses. Use the ratio table to find the number of blouses she could make with 24 yards of fabric. 18 13.5 18 Answer: So, with 24 yards of fabric, Coco could make 18 blouses. Lesson 3 Ex3**Ratio Tables**8-3 Mrs. Stine can grade 48 papers in 96 minutes. How many can she grade in 24 minutes? • 6 • 12 • 24 • 96 Lesson 3 CYP3**Ratio Tables**8-3 It takes a worker 70 minutes to pack 120 cartons of books. The worker has 14 minutes of work left. Use a ratio table to find how many cartons of books the worker can pack in 14 minutes. 24 Answer: So, a worker can pack 24 cartons in 14 minutes. Lesson 3 Ex4**Ratio Tables**8-3 It takes Sarah 60 minutes to walk 4 miles. How far will she have walked after 30 minutes? • 1 mile • 2 miles • 3 miles • 4 miles Lesson 3 CYP4**Equivalent Ratios**8-4 Five-Minute Check (over Lesson 8-3) Main Idea California Standards Example 1 Example 2 Example 3 Example 4 Example 5 Lesson 4 Menu**Equivalent Ratios**8-4 • I will determine if two quantities are equivalent. Lesson 4 MI/Vocab**Equivalent Ratios**8-4 Preparation for Standard 5AF1.5Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. Lesson 4 Standard 1**Equivalent Ratios**8-4 Determine if the pair of rates is equivalent. Explain your reasoning. 42 people on 7 teams; 64 people on 8 teams 42 people = 6 people per team 7 teams 64 people = 8 people per team 8 teams Answer: These rates are not equivalent since they are not the same. Lesson 4 Ex1**Equivalent Ratios**8-4 Determine if the pair of rates are equivalent.2 chapters in one day; 18 chapters in 9 days • Yes, both are 2:1. • Yes, both are 18:9. • No. • not enough information to solve Lesson 4 CYP1**Equivalent Ratios**8-4 Determine if the pair of rates is equivalent. Explain your reasoning. 20 rolls for $5; 48 rolls for $12 20 rolls = $4 per roll $5 48 rolls = $4 per roll $12 Answer: These are equivalent because the rates are the same. Lesson 4 Ex2**Equivalent Ratios**8-4 Determine if the pair of rates is equivalent. $12 for 3 hours; $15 for 5 hours • Yes, both are $4 an hour. • Yes, both are $5 an hour. • No, they are not the same. • not enough information Lesson 4 CYP2**Equivalent Ratios**8-4 One day Jafar sold 21 pizzas in 3 hours. The next day he sold 35 pizzas in 5 hours. Are these selling rates equivalent? Explain your reasoning. Write each rate as a fraction. Then find its unit rate. Lesson 4 Ex3**Equivalent Ratios**8-4 21 pizzas 7 pizzas = 3 hours 1 hour 35 pizzas 7 pizzas = 5 hours 1 hour Answer: Since the rates have the same unit rate, they are equivalent. So, Jafar’s selling rates are equivalent. Lesson 4 Ex3**Equivalent Ratios**8-4 Paella sold 27 magazine subscriptions in 3 hours. The next day she sold 32 magazine subscriptions in 4 hours. What are the selling rates for each day? Are they equivalent? • 9, 9; yes • 9, 8; no • 8, 8; yes • 8, 9; no Lesson 4 CYP3**Equivalent Ratios**8-4 ? = Determine if the pair of ratios is equivalent. Explain your reasoning. 5 laps swam in 8 minutes; 11 laps swam in 16 minutes Write each ratio as a fraction. The numerator and denominator do not multiply by the same number. So, they are not equivalent. 5 laps 11 laps 8 minutes 16 minutes Answer: Since the fractions are not equivalent the ratios are not equivalent. Lesson 4 Ex4**Equivalent Ratios**8-4 1 2 • Yes, they are both . 2 3 C. Yes, they are both . Determine if the pair of ratios is equivalent.15 pages read in 30 minutes; 22 pages read in 40 minutes B. No. D. not enough information Lesson 4 CYP4**Equivalent Ratios**8-4 ? = Determine if the pair of ratios is equivalent. Explain your reasoning. 8 corrals with 56 horses; 4 corrals with 28 horses Write each ratio as a fraction. 8 corrals 1 corral 56 horses 7 horses Lesson 4 Ex5