Chapter 8 Algebra: Ratios and Functions

Chapter 8 Algebra: Ratios and Functions
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Lesson 8-1 Ratios and Rates
Algebra: Ratios and Functions 8 Lesson 8-1 Ratios and Rates Lesson 8-2 Problem-Solving Strategy: Look for a Pattern Lesson 8-3 Ratio Tables Lesson 8-4 Equivalent Ratios Lesson 8-5 Problem-Solving Investigation: Choose the Best Strategy Lesson 8-6 Algebra: Ratios and Equations Lesson 8-7 Algebra: Sequences and Expressions Lesson 8-8 Algebra: Equations and Graphs Chapter Menu

Five-Minute Check (over Chapter 7) Main Idea and Vocabulary
8-1 Ratios and Rates Five-Minute Check (over Chapter 7) Main Idea and Vocabulary California Standards Example 1: Write a Ratio in Simplest Form Example 2: Use Ratios to Compare Parts to a Whole Example 3: Find a Unit Rate Ratios and Tangrams Lesson 1 Menu

I will express ratios and rates in fraction form.
8-1 Ratios and Rates I will express ratios and rates in fraction form. ratio rate unit rate Lesson 1 MI/Vocab

8-1 Ratios and Rates Preparation for Standard 6NS1.2 Interpret 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

8-1 Ratios and Rates Write the ratio in simplest form that compares the number of scooters to the number of unicycles. scooters 4 10 2 5 = unicycles Lesson 1 Ex1

8-1 Ratios and Rates Answer: The ratio of scooters to unicycles is , 2 to 5, or 2:5. This means that for every 2 scooters there are 5 unicycles. 2 5 Lesson 1 Ex1

8-1 Ratios and Rates Write the ratio in simplest form that compares the number of singers in a duet to the number in an octet. A. 1 4 B. 2 8 C. 1 8 D. 2 4 Lesson 1 CYP1

8-1 Ratios and Rates 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 or 25 responses. Lesson 1 Ex2

8-1 Ratios and Rates sports responses 7 25 total responses 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. 7 25 Lesson 1 Ex2

8-1 Ratios and Rates 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. 12:18 2:3 2:15 12:30 Lesson 1 CYP2

Find the cost per ounce of a 16-ounce jar of salsa that costs $2.88.
8-1 Ratios and Rates Find the cost per ounce of a 16-ounce jar of salsa that costs $2.88. $2.88 16 ounces $0.18 1 ounce = Answer: So, the salsa costs $0.18 per ounce. Lesson 1 Ex3

8-1 Ratios and Rates 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

End of Lesson 1

Five-Minute Check (over Lesson 8-1) Main Idea California Standards
8-2 Problem-Solving Strategy: Look for a Pattern Five-Minute Check (over Lesson 8-1) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 2 Menu

I will solve problems by looking for a pattern.
8-2 Problem-Solving Strategy: Look for a Pattern I will solve problems by looking for a pattern. Lesson 2 MI/Vocab

8-2 Problem-Solving Strategy: Look for a Pattern Standard 5MR1.1 Analyze problems by identifying 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

8-2 Problem-Solving Strategy: Look for a Pattern 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

Understand What facts do you know? It is now 1:15 P.M.
8-2 Problem-Solving Strategy: Look for a Pattern 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

Plan Start with the time the first bus arrives and look for a pattern.
8-2 Problem-Solving Strategy: Look for a Pattern Plan Start with the time the first bus arrives and look for a pattern. Lesson 2 Ex1

8-2 Problem-Solving Strategy: Look for a Pattern 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

8-2 Problem-Solving Strategy: Look for a Pattern 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

End of Lesson 2

Five-Minute Check (over Lesson 8-2) Main Idea and Vocabulary
8-3 Ratio Tables Five-Minute Check (over Lesson 8-2) Main Idea and Vocabulary California Standards Example 1: Equivalent Ratios of Larger Quantities Example 2: Equivalent Ratios of Smaller Quantities Example 3: Use Scaling Example 4: Use a Ratio Table Lesson 3 Menu

8-3 Ratio Tables I will use ratio tables to represent and solve problems involving equivalent ratios. ratio table equivalent ratio scaling Lesson 3 MI/Vocab

8-3 Ratio Tables Standard 5MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Preparation for Standard 5AF1.5 Solve 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

8-3 Ratio Tables 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

One Way: Find a pattern and extend it.
8-3 Ratio Tables One Way: Find a pattern and extend it. For 4 cups of beans, you would need a total of or 20 cups of water. 2 3 10 15 20 Lesson 3 Ex1

Another Way: Multiply each quantity by the same number.
8-3 Ratio Tables 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

8-3 Ratio Tables 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

Answer: So, a spider has 8 legs.
8-3 Ratio Tables 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

8-3 Ratio Tables 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

Answer: So, with 24 yards of fabric, Coco could make 18 blouses.
8-3 Ratio Tables 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

8-3 Ratio Tables Mrs. Stine can grade 48 papers in 96 minutes. How many can she grade in 24 minutes? 6 papers 12 papers 24 papers 96 papers Lesson 3 CYP3

Answer: So, a worker can pack 24 cartons in 14 minutes.
8-3 Ratio Tables 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. 60 24 35 Answer: So, a worker can pack 24 cartons in 14 minutes. Lesson 3 Ex4

8-3 Ratio Tables 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

End of Lesson 3

8-4 Equivalent Ratios Five-Minute Check (over Lesson 8-3) Main Idea California Standards Example 1: Use Unit Rates Example 2: Use Unit Rates Example 3: Real-World Example Example 4: Use Equivalent Fractions Example 5: Use Equivalent Fractions Lesson 4 Menu

I will determine if two quantities are equivalent.
8-4 Equivalent Ratios I will determine if two quantities are equivalent. Lesson 4 MI/Vocab

8-4 Equivalent Ratios Preparation for Standard 5AF1.5 Solve 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

Determine if the pair of rates is equivalent. Explain your reasoning.
8-4 Equivalent Ratios Determine if the pair of rates is equivalent. Explain your reasoning. 42 people on 7 teams; 64 people on 8 teams Write each rate as a fraction. Then find its unit rate. 42 people 6 people = 7 teams 1 team Lesson 4 Ex1

64 people 8 people = 8 teams 1 team
8-4 Equivalent Ratios 64 people 8 people = 8 teams 1 team Answer: Since the rates do not have the same unit rate, they are not equivalent. Lesson 4 Ex1

not enough information to solve
8-4 Equivalent Ratios Determine if the pair of rates is 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

Determine if the pair of rates is equivalent. Explain your reasoning.
8-4 Equivalent Ratios Determine if the pair of rates is equivalent. Explain your reasoning. 20 rolls for $5; 48 rolls for $12 Write each rate as a fraction. Then find its unit rate. 20 rolls 4 rolls = $5 $1 Lesson 4 Ex2

Answer: Since the rates have the same unit rate, they are equivalent.
8-4 Equivalent Ratios 48 rolls 4 rolls = $12 $1 Answer: Since the rates have the same unit rate, they are equivalent. Lesson 4 Ex2

No; they are not the same. not enough information
8-4 Equivalent Ratios 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

Write each rate as a fraction. Then find its unit rate.
8-4 Equivalent Ratios 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

21 pizzas 7 pizzas = 3 hours 1 hour 35 pizzas 7 pizzas = 5 hours
8-4 Equivalent Ratios 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

9 magazines per hour, 9 magazines per hour; yes
8-4 Equivalent Ratios 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 magazines per hour, 9 magazines per hour; yes 9 magazines per hour, 8 magazines per hour; no 8 magazines per hour, 8 magazines per hour; yes 8 magazines per hour, 9 magazines per hour; no Lesson 4 CYP3

Determine if the pair of ratios is equivalent. Explain your reasoning.
8-4 Equivalent Ratios 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

D. not enough information
8-4 Equivalent Ratios Determine if the pair of ratios is equivalent. 15 pages read in 30 minutes; 22 pages read in 40 minutes Yes; they are both . 1 2 B. no C. Yes; they are both . 2 3 D. not enough information Lesson 4 CYP4

Determine if the pair of ratios is equivalent. Explain your reasoning.
8-4 Equivalent Ratios Determine if the pair of ratios is equivalent. Explain your reasoning. 8 corrals with 56 horses; 4 corrals with 28 horses 8 corrals 4 corrals = ? 56 horses 28 horses Answer: Since the fractions are equivalent, the rates are equivalent. Lesson 4 Ex5

Yes; both are 1 barnyard per 7 cows.
8-4 Equivalent Ratios Determine if the pair of ratios is equivalent. 7 barnyards with 49 cows; 9 barnyards with 63 cows Yes; both are 1 barnyard per 7 cows. Yes; both are 7 barnyards per 1 cow. Yes; both are 1 barnyard per 9 cows. no Lesson 4 CYP5

End of Lesson 4

8-5 Problem-Solving Investigation: Choose the Best Strategy Five-Minute Check (over Lesson 8-4) Main Idea California Standards Example 1: Problem-Solving Investigation Lesson 5 Menu

I will choose the best strategy to solve a problem.
8-5 Problem-Solving Investigation: Choose the Best Strategy I will choose the best strategy to solve a problem. Lesson 5 MI/Vocab

8-5 Problem-Solving Investigation: Choose the Best Strategy Standard 5MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Standard 5SDAP1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ. Lesson 5 Standard 1

8-5 Problem-Solving Investigation: Choose the Best Strategy AJAY: I took my dog to the veterinarian’s office. While waiting, I noticed that there were more dogs than cats in the waiting room. The vet said that for about every 5 dogs he sees, he sees cats. YOUR MISSION: Find about how many dogs the vet will see if 21 total pets come into the office. Lesson 5 Ex1

Understand What facts do you know?
8-5 Problem-Solving Investigation: Choose the Best Strategy Understand What facts do you know? You know that the ratio of dogs to cats is about 5:2. What do you need to find? You need to find about how many dogs the vet will see. Lesson 5 Ex1

Plan Use counters to act out how many dogs the vet will see. 8-5
Problem-Solving Investigation: Choose the Best Strategy Plan Use counters to act out how many dogs the vet will see. Lesson 5 Ex1

8-5 Problem-Solving Investigation: Choose the Best Strategy Solve Use red counters to represent the dogs and yellow counters to represent the cats. Since the ratio of dogs to cats is 5:2, place 5 red counters and 2 yellow counters in a group. Make groups of 7 counters until you have 21 counters total. Lesson 5 Ex1

8-5 Problem-Solving Investigation: Choose the Best Strategy Solve After three groups there are 21 counters, so you can stop making groups. Find the number of red counters to find how many dogs the vet will see = 15. Answer: So, if the vet sees 21 pets, about 15 of them will be dogs. Lesson 5 Ex1

8-5 Problem-Solving Investigation: Choose the Best Strategy Check Find the ratio of red counters to yellow counters. If the ratio is equivalent to the original ratio, 5:2, then the answer is correct. Lesson 5 Ex1

End of Lesson 5

8-6 Algebra: Ratios and Equations Five-Minute Check (over Lesson 8-5) Main Idea California Standards Example 1: Solve Using Equivalent Fractions Example 2: Solve Using Equivalent Fractions Example 3: Solve Using Equivalent Fractions Example 4: Solve Using Equivalent Fractions Example 5: Make Predictions Example 6: Solve Using Unit Rates Lesson 6 Menu

Lesson 6 MI/Vocab/Standard 1
8-6 Algebra: Ratios and Equations I will solve equations using equivalent fractions. Lesson 6 MI/Vocab/Standard 1

8-6 Algebra: Ratios and Equations Standard 5AF1.1 Use information taken from a graph or equation to answer questions about a problem situation. Standard 5AF1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. Lesson 6 Standard 1

Since 4 × 7 = 28, multiply the numerator and denominator by 7. 4 28 =
8-6 Algebra: Ratios and Equations Solve = 4 5 28 x Since 4 × 7 = 28, multiply the numerator and denominator by 7. 4 28 = 5 x 4 5 28 35 = 5 × 7 = 35 Answer: So, x = 35. Lesson 6 Ex1

Solve = . 5 8 20 x A. x = 36 B. x = 32 C. x = 40 D. x = 2 8-6
Algebra: Ratios and Equations Solve = 5 8 20 x A. x = 36 B. x = 32 C. x = 40 D. x = 2 Lesson 6 CYP1

Since 5 × 4 = 20, multiply the numerator and denominator by 4. b 16 =
8-6 Algebra: Ratios and Equations Solve = b 5 16 20 Since 5 × 4 = 20, multiply the numerator and denominator by 4. b 16 = 5 20 4 16 THINK What number multiplied by 4 equals 16? The answer is 4. = 5 20 Answer: So, b = 4. Lesson 6 Ex2

Solve = . h 6 36 A. h = 12 B. h = 5 C. h = 6 D. h = 1 8-6
Algebra: Ratios and Equations Solve = h 6 36 A. h = 12 B. h = 5 C. h = 6 D. h = 1 Lesson 6 CYP2

Since = , then n = 11, because is the same as . 19 38 1 2 11 22
8-6 Algebra: Ratios and Equations Solve = 19 38 n 22 Since = , then n = 11, because is the same as . 19 38 1 2 11 22 Answer: So, n = 11. Lesson 6 Ex3

Solve = . 18 45 m 5 A. m = 2 B. m = 9 C. m = 3 D. m = 7 8-6
Algebra: Ratios and Equations Solve = . 18 45 m 5 A. m = 2 B. m = 9 C. m = 3 D. m = 7 Lesson 6 CYP3

Since 7 × 4 = 28, multiply the numerator and denominator by 4. 7 28 =
8-6 Algebra: Ratios and Equations Solve = 28 60 7 t Since 7 × 4 = 28, multiply the numerator and denominator by 4. 7 28 = t 60 7 28 THINK What number multiplied by 4 equals 60? The answer is 15. = 15 60 Answer: So, t = 15. Lesson 6 Ex4

4 64 Solve = . y 80 A. y = 3 B. y = 6 C. y = 5 D. y = 4 8-6
Algebra: Ratios and Equations Solve = 64 80 4 y A. y = 3 B. y = 6 C. y = 5 D. y = 4 Lesson 6 CYP4

8-6 Algebra: Ratios and Equations Out of the 40 students in a gym class, 12 say soccer is their favorite sport. Based on this result, predict how many of the 4,200 students in the community would rate soccer as their favorite sport. Write and solve an equation. Let s represent the number of students who can be expected to prefer soccer. Lesson 6 Ex5

8-6 Algebra: Ratios and Equations Class School prefer soccer 12 s prefer soccer = total students 40 4,200 total students The denominators 40 and 4,200 are not easily related by multiplication, so simplify the ratio 12 out of 40. Then solve using equivalent fractions. Lesson 6 Ex5

8-6 Algebra: Ratios and Equations 12 3 s Since 10 × 420 = 4,200, multiply the numerator and denominator by 420. = = 40 10 4,200 Answer: So, about 1,260 out of 4,200 students in the school can be expected to prefer soccer. Lesson 6 Ex5

8-6 Algebra: Ratios and Equations Out of the 30 kids in Mrs. Ankrum’s class, are girls. Based on this result, predict how may of the 660 students in the school are girls. 264 girls 300 girls 260 girls 284 girls Lesson 6 CYP5

8-6 Algebra: Ratios and Equations Cedric earned $184 for 8 hours of work. At this rate, how much will he earn for 15 hours of work? Step 1 Set up the equation. Let a represent the amount of money to be earned. 184 dollars a dollars = 8 hours 15 hours Lesson 6 Ex6

Answer: So, Cedric will earn $345 for working for 15 hours.
8-6 Algebra: Ratios and Equations Step 2 Find the unit rate. 184 dollars 23 $345 = = 8 hours 1 15 hours Answer: So, Cedric will earn $345 for working for 15 hours. Lesson 6 Ex6

8-6 Algebra: Ratios and Equations Julio earned $145 for mowing 5 lawns. At this rate, how much will he earn for 30 lawns? $174 $870 $850 $445 Lesson 6 CYP6

End of Lesson 6

Five-Minute Check (over Lesson 8-6) Main Idea and Vocabulary
8-7 Algebra: Sequences and Expressions Five-Minute Check (over Lesson 8-6) Main Idea and Vocabulary California Standards Example 1: Describe Sequences Example 2: Describe Sequences Example 3: Make a Table Example 4: Real-World Example Lesson 7 Menu

8-7 Algebra: Sequences and Expressions I will extend and describe arithmetic sequences using algebraic expressions. sequence term arithmetic sequence Lesson 7 MI/Vocab

8-7 Algebra: Sequences and Expressions Standard 5AF1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. Standard 5AF1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. Lesson 7 Standard 1

8-7 Algebra: Sequences and Expressions Use the words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence. Notice that the value of each term is 7 times its position number. So the value of the term in position n is 7n. Lesson 7 Ex1

Now find the value of the tenth term.
8-7 Algebra: Sequences and Expressions Now find the value of the tenth term. 7n = 7 × 10 Replace n with 10. = 70 Multiply. Answer: So, the value of the tenth term in the sequence is 70. Lesson 7 Ex1

7 times its position number; 7n; 35
8-7 Algebra: Sequences and Expressions Use the words and symbols to describe the value of each term as a function of its position. Then find the value of the fifth term in the sequence. 7 times its position number; 7n; 35 6 times its position number; 6 + n; 11 6 times its position number; 6n; 30 3 times its position number; 3n; 15 Lesson 7 CYP1

8-7 Algebra: Sequences and Expressions Use the words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence. Notice that the value of each term is 2 more than its position number, so the rule is n + 2. Lesson 7 Ex2

Now find the value of the tenth term.
8-7 Algebra: Sequences and Expressions Now find the value of the tenth term. n + 2 = Replace n with 10. = 12 Add. Answer: So, the value of the tenth term in the sequence is 12. Lesson 7 Ex2

2 less than its position number; 2 – n; 8
8-7 Algebra: Sequences and Expressions Use the words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence. 2 less than its position number; 2 – n; 8 2 less than its position number; n – 2; 8 3 less than its position number; 3 – n; 7 3 less than its position number; n – 3; 7 Lesson 7 CYP2

8-7 Algebra: Sequences and Expressions MEASUREMENT There are 60 seconds in minute. It takes Panya minutes to walk to school. Make a table, and then write an algebraic expression relating the number of seconds to the number of minutes. Find how many seconds it takes Panya to walk to school. Lesson 7 Ex3

Notice that the number of seconds is 60 times the number of minutes.
8-7 Algebra: Sequences and Expressions Notice that the number of seconds is 60 times the number of minutes. Lesson 7 Ex3

Answer: So, it will take Panya 540 seconds to walk to school.
8-7 Algebra: Sequences and Expressions Now find the ninth term. 60n = 60 × 9 Replace n with 9. = 540 Multiply. Answer: So, it will take Panya 540 seconds to walk to school. Lesson 7 Ex3

8-7 Algebra: Sequences and Expressions There are 60 minutes in an hour. It takes Mr. Daugherty 5 hours each week to grade all of his fifth graders’ papers. Choose an expression and correct answer that represents the amount of minutes Mr. Daugherty spends grading papers each week. A. 60h; 300 C – h; 55 B ; 12 60 h D = h; 5 Lesson 7 CYP3

8-7 Algebra: Sequences and Expressions The table to the right shows the number of plants in a garden, based on the number of rows. Write an expression to find the number of plants in n rows. Lesson 7 Ex4

rows multiplied by 3 gives the number of plants.
8-7 Algebra: Sequences and Expressions The number of plants increases by 3, so the rule contains 3n. If the rule were simply 3n, then the value for 1 row would be 3. Notice that adding to the number of rows multiplied by 3 gives the number of plants. Answer: So, 3n + 1 gives the number of flowers in n rows. Lesson 7 Ex4

Choose the expression to find the number of cars in each row.
8-7 Algebra: Sequences and Expressions Choose the expression to find the number of cars in each row. A. n + 7 B. n × 8 C. 3n × 8 D. 6n + 2 Lesson 7 CYP4

End of Lesson 7

8-8 Algebra: Equations and Graphs Five-Minute Check (over Lesson 8-7) Main Idea California Standards Example 1: Write an Equation for a Function Example 2: Real-World Example Example 3: Real-World Example Example 4: Real-World Example Example 5: Real-World Example Example 6: Real-World Example Lesson 8 Menu

I will write an equation to describe a linear situation.
8-8 Algebra: Equations and Graphs I will write an equation to describe a linear situation. Lesson 8 MI/Vocab

8-8 Algebra: Equations and Graphs Standard 5AF1.1 Use the information taken from a graph or an equation to answer questions about a problem situation. Standard 5AF1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. Lesson 8 Standard 1

Write an equation to represent the function displayed in the table.
8-8 Algebra: Equations and Graphs Write an equation to represent the function displayed in the table. Each output y is equal to 5 times the input x. Lesson 8 Ex1

Answer: So, the equation that represents the function is y = 5x.
8-8 Algebra: Equations and Graphs Answer: So, the equation that represents the function is y = 5x. Lesson 8 Ex1

8-8 Algebra: Equations and Graphs Choose the equation that represents the function displayed in the table. A. x = 6y B. y = 3y + 3 C. y = 6x D. y = x + 6 Lesson 8 CYP1

8-8 Algebra: Equations and Graphs Javier sells handmade notebooks. He charges $25 for each book. Make a table to show the relationship between the number of b books sold and the total amount Javier earns t. The total earned (output) is equal to $25 times the number of books made (input). Lesson 8 Ex2

8-8 Algebra: Equations and Graphs Answer: Lesson 8 Ex2

8-8 Algebra: Equations and Graphs Jean sells dream catchers. She charges $15 for each one. Which table correctly shows the relationship between the number of b dream catchers and the total amount Jean earned? A. Lesson 8 CYP2

8-8 Algebra: Equations and Graphs B. Lesson 8 CYP2

8-8 Algebra: Equations and Graphs C. Lesson 8 CYP2

8-8 Algebra: Equations and Graphs D. Lesson 8 CYP2

8-8 Algebra: Equations and Graphs Answer: A. Lesson 8 CYP2

8-8 Algebra: Equations and Graphs Javier sells handmade notebooks. He charges $25 for each book. Write an equation to find the total amount earned t for selling b books. Study the table. Lesson 8 Ex3

The total earned equals $25 times the number of books Javier sells.
8-8 Algebra: Equations and Graphs The total earned equals $25 times the number of books Javier sells. Answer: So, the equation is t = 25b. Lesson 8 Ex3

8-8 Algebra: Equations and Graphs Jean sells dream catchers. She charges $15 for each one. Choose the equation to find the total amount t Jean earned. Lesson 8 CYP3

8-8 Algebra: Equations and Graphs A. 15t = b B = b 15 t C. t + 15 = b D × 5 = b Lesson 8 CYP3

Answer: So, Javier will earn $175.
8-8 Algebra: Equations and Graphs Javier sells handmade notebooks. He charges $25 for each book. How much will Javier earn if he sells 7 books using the equation t = 25b? t = 25b Write the equation. t = 25(7) Replace b with 7. t = 175 Simplify. Answer: So, Javier will earn $175. Lesson 8 Ex4

8-8 Algebra: Equations and Graphs Jean sells dream catchers. She charges $15 for each one. How much will Jean earn if she sells dream catchers? Use the equation t = 15b. A. $140 B. $135 C. $160 D. $155 Lesson 8 CYP4

8-8 Algebra: Equations and Graphs The table below shows the amount that a kennel charges for grooming a dog. Write a sentence and an equation to describe the data. Then find the total cost of grooming 11 dogs, dogs, and 13 dogs. Lesson 8 Ex5

8-8 Algebra: Equations and Graphs The cost of getting a dog groomed is $12 for each dog. The total cost t is $12 times the number of dogs d. Therefore, t = 12d. Answer: $132, $144, $156 Lesson 8 Ex5

8-8 Algebra: Equations and Graphs The table below shows the amount that a Girl Scout troop charges for a box of cookies. Choose the correct equation to describe the data. Then find the total cost for 12, 13, and boxes of cookies. Lesson 8 CYP5

8-8 Algebra: Equations and Graphs A. 3t = c; $30, $40, $50 B. 3c = t; $30, $40, $50 C. c + 3 = t; $36, $39, $42 D. 3c = t; $36, $39, $42 Lesson 8 CYP5

Graph the results from Example 5 on a coordinate plane.
8-8 Algebra: Equations and Graphs Graph the results from Example 5 on a coordinate plane. Lesson 8 Ex6

8-8 Algebra: Equations and Graphs Step 1 Make a coordinate place with the d values along the x-axis and the t values along the y-axis. Step 2 Using the (d, t) values from Example 5, plot the coordinate plane. Lesson 8 Ex6

8-8 Algebra: Equations and Graphs Use the information in the table to write a set of ordered pairs in the form (c, t). Lesson 8 CYP6

8-8 Algebra: Equations and Graphs (1, 2), (3, 4), (3, 6), (9, 12) B. (1, 3), (2, 6), (3, 9), (4, 12) C. (3, 1), (6, 2), (9, 3), (12, 4) D. (1, 3), (3, 9) Lesson 8 CYP6

End of Lesson 8

8 Five-Minute Checks Math Tool Chest Image Bank Ratios and Tangrams
Algebra: Ratios and Functions 8 Five-Minute Checks Math Tool Chest Image Bank Ratios and Tangrams CR Menu

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Lesson 8-1 (over Chapter 7) Lesson 8-2 (over Lesson 8-1)
Algebra: Ratios and Functions 8 Lesson 8-1 (over Chapter 7) Lesson 8-2 (over Lesson 8-1) Lesson 8-3 (over Lesson 8-2) Lesson 8-4 (over Lesson 8-3) Lesson 8-5 (over Lesson 8-4) Lesson 8-6 (over Lesson 8-5) Lesson 8-7 (over Lesson 8-6) Lesson 8-8 (over Lesson 8-7) 5Min Menu

(over Chapter 7) Solve 8p = 56. 8 7 12 9 5Min 1-1

(over Chapter 7) Solve 30 = 3f. 10 3 12 15 5Min 1-2

(over Chapter 7) Solve –15v = –45. 5 4 3 6 5Min 1-3

(over Chapter 7) Solve 7y = –70. –7 10 7 –10 5Min 1-4

Write the ratio as a fraction in simplest form.
(over Lesson 8-1) Write the ratio as a fraction in simplest form. 16 apples out of 24 pieces of fruit A. 4 6 B. 2 8 C. 2 3 D. 8 6 5Min 2-1

Write the ratio as a fraction in simplest form.
(over Lesson 8-1) Write the ratio as a fraction in simplest form. 18 dogs out of 90 pets A. 4 5 B. 8 10 C. 1 5 D. 9 10 5Min 2-2

1 folder 1 folder 1 folder $2.00 1 folder
(over Lesson 8-1) Write the following as a unit rate. $5 for 10 folders A. $0.50 1 folder B. $0.10 1 folder C. $5.00 1 folder D. $2.00 1 folder 5Min 2-3

12 chairs 1 row 8 chairs 1 row 16 chairs 1 row 15 chairs 1 row
(over Lesson 8-1) Write the following as a unit rate. 48 chairs for 3 rows A. 12 chairs 1 row B. 8 chairs 1 row C. 16 chairs 1 row D. 15 chairs 1 row 5Min 2-4

(over Lesson 8-2) Solve. Luis saw the numbers below in a science report. Describe the pattern. Then find the next numbers in the pattern. 6, 18, 54, 162, 486, __, __, __ A. Multiply by 3; 1,548; 4,747; 13,122 B. Multiply by 3; 1,458; 4,374; 13,122 C. Multiply by 3; 972, 1,844; 3,688 5Min 3-1

(over Lesson 8-3) Use the ratio table to solve the problem. A dozen roses sell for $18. How much will 16 roses cost? $26 $32 $20 $24 5Min 4-1

Use the ratio table to solve the problem. How much will 24 roses cost?
(over Lesson 8-3) Use the ratio table to solve the problem. How much will 24 roses cost? $30 $36 $12 $18 5Min 4-2

Determine if the pair of rates is equivalent.
(over Lesson 8-4) Determine if the pair of rates is equivalent. $18 in 3 days; $42 in 6 days no yes 5Min 5-1

Determine if the pair of ratios is equivalent.
(over Lesson 8-4) Determine if the pair of ratios is equivalent. 50 desks in 2 rooms; 75 desks in 3 rooms no yes 5Min 5-2

Determine if the pair of rates is equivalent.
(over Lesson 8-4) Determine if the pair of rates is equivalent. 8 fruit drinks for $20; 9 fruit drinks for $24 no yes 5Min 5-3

Determine if the pair of ratios is equivalent.
(over Lesson 8-4) Determine if the pair of ratios is equivalent. 12 dogs out of 18 pets; 10 dogs out of 15 pets no yes 5Min 5-4

(over Lesson 8-5) Solve. Maria is building chains. She uses 1 ring on the first chain, 6 rings on the second, 11 rings on the third, and 16 rings on the fourth. If she continues the pattern, how many rings will be on the next chain? 35 rings 19 rings 34 rings 21 rings 5Min 6-1

(over Lesson 8-6) Solve. w 40 5 8 = 15 25 100 30 5Min 7-1

(over Lesson 8-6) Solve. 6 11 n 33 = 18 20 15 25 5Min 7-2

(over Lesson 8-6) Solve. 300 a 50 3 = 18 22 60 15 5Min 7-3

(over Lesson 8-6) Solve. 15 11 x 66 = 90 88 15 45 5Min 7-4

(over Lesson 8-7) Use words and symbols to describe the value of each term as a function of its position. Then find the value of the ninth term in the sequence. 5n + 5; 45 15n + 5; 60 15n + 10; 80 5Min 8-1

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Chapter 8 Algebra: Ratios and Functions

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Chapter 8 Algebra: Ratios and Functions

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Presentation on theme: "Chapter 8 Algebra: Ratios and Functions"— Presentation transcript:

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