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9 Percent Lesson 9 -1 Lesson 9 -2 Lesson 9 -3 Lesson 9 -4 9 Percent Lesson 9 -1 Lesson 9 -2 Lesson 9 -3 Lesson 9 -4 Lesson 9 -5 Lesson 9 -6 Lesson 9 -7 Lesson 9 -8 Lesson 9 -9 Lesson 9 -10 Percents and Fractions Circle Graphs Percents and Decimals Problem-Solving Strategy: Solve a Simpler Problem Estimating with Percents Percent of a Number Problem-Solving Investigation: Choose the Best Strategy Probability Sample Spaces Making Predictions

9 -1 Percents and Fractions Five-Minute Check (over Chapter 8) Main Idea and Vocabulary 9 -1 Percents and Fractions Five-Minute Check (over Chapter 8) Main Idea and Vocabulary California Standards Key Concept: Percent Example 1 Example 2 Example 3 Example 4 Example 5

9 -1 Percents and Fractions • I will express percents as fractions and fractions 9 -1 Percents and Fractions • I will express percents as fractions and fractions as percents. • percent

9 -1 Percents and Fractions Standard 5 NS 1. 2 Interpret percents as a 9 -1 Percents and Fractions Standard 5 NS 1. 2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Standard 5 SDAP 1. 3 Use fractions and percentages to compare data sets of different sizes.

9 -1 Percents and Fractions 9 -1 Percents and Fractions

Percents and Fractions 9 -1 Write 60% as a fraction in simplest form. 60% Percents and Fractions 9 -1 Write 60% as a fraction in simplest form. 60% means 60 out of 100. 60 60% = 100 3 60 or 3 100 5 5 Definition of percent Simplify. Divide the numerator and the denominator by the GCF, 20.

9 -1 Percents and Fractions Choose the fraction in simplest form that represents 75%. 9 -1 Percents and Fractions Choose the fraction in simplest form that represents 75%. A. 3 4 B. 1 2 C. 75 100 D. 15 20

9 -1 Percents and Fractions Write 140% as a mixed number in simplest form. 9 -1 Percents and Fractions Write 140% as a mixed number in simplest form. 140% means 140 for every 100. 140% = 140 100 =1 40 100 Definition of percent Write as a mixed number.

9 -1 Percents and Fractions 2 40 2 =1 or 1 100 5 5 9 -1 Percents and Fractions 2 40 2 =1 or 1 100 5 5 Divide the numerator and denominator by the GCF, 20.

9 -1 Percents and Fractions Choose 160% as a mixed number in simplest form. 9 -1 Percents and Fractions Choose 160% as a mixed number in simplest form. 60 A. 1 100 B. 1 30 50 C. 1 D. 2 3 5

9 -1 Percents and Fractions Use the table below. What fraction of the class 9 -1 Percents and Fractions Use the table below. What fraction of the class members preferred spaghetti for the school lunch? The table shows that 25% of those surveyed prefer spaghetti.

9 -1 Percents and Fractions 25% = = 25 100 1 4 Definition of 9 -1 Percents and Fractions 25% = = 25 100 1 4 Definition of percent Simplify. Answer: So, 1 of those surveyed prefer spaghetti. 4

9 -1 Percents and Fractions Use the table below. What fraction of the fifth 9 -1 Percents and Fractions Use the table below. What fraction of the fifth graders preferred football? 20 A. 100 B. 1 5 C. 1 2 D. 1 20

9 -1 Percents and Fractions Write 7 as a percent. 10 7 n = 9 -1 Percents and Fractions Write 7 as a percent. 10 7 n = 10 100 Write an equation using ratios. One ratio is the fraction. The other is an unknown value compared to 100. 7 70 = 10 100 Since 10 × 10 = 100, multiply 7 by 10 to find n. Answer: So, 7 70 = or 70%. 10 100

9 -1 Percents and Fractions Write 14 as a percent. 25 A. 50% B. 9 -1 Percents and Fractions Write 14 as a percent. 25 A. 50% B. 60% C. 56% D. 14%

9 -1 Percents and Fractions 42 At Boulder Middle School, of the students 600 9 -1 Percents and Fractions 42 At Boulder Middle School, of the students 600 24 study Spanish. At Foothills Middle School, 480 of the students study Spanish. Which school has the greater percent of students that study Spanish? Write each fraction as a percent. Then compare.

9 -1 Percents and Fractions Boulder MS Foothills MS 42 n = 600 100 9 -1 Percents and Fractions Boulder MS Foothills MS 42 n = 600 100 28 n = 480 100 42 7 = or 7% 600 100 28 5 = or 5% 480 100 Answer: Since 7% > 5%, Boulder MS has the greater percent of students that study Spanish.

9 -1 Percents and Fractions 45 At Franklin Heights High School, of the students 9 -1 Percents and Fractions 45 At Franklin Heights High School, of the students 300 has their driver’s license. At Grove City High School, 36 of the students has their driver’s license. Which 360 school has the greater percent of students with their driver’s license and with what percent? A. Franklin Heights HS; 15% > 10% B. Franklin Heights HS; 20% > 15% C. Grove City HS; 15% > 10% D. Grove City HS; 20% > 15%

9 -2 Circle Graphs Five-Minute Check (over Lesson 9 -1) Main Idea and Vocabulary 9 -2 Circle Graphs Five-Minute Check (over Lesson 9 -1) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Example 4 Circle Graphs

9 -2 Circle Graphs • I will sketch and analyze circle graphs. • circle 9 -2 Circle Graphs • I will sketch and analyze circle graphs. • circle graph

9 -2 Circle Graphs Standard 5 SDAP 1. 2 Organize and display single-variable data 9 -2 Circle Graphs Standard 5 SDAP 1. 2 Organize and display single-variable data in appropriate graphs and representations (e. g. , histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. Standard 5 SDAP 1. 3 Use fractions and percentages to compare data sets of different sizes.

9 -2 Circle Graphs The table shows how many hours a group of teenagers 9 -2 Circle Graphs The table shows how many hours a group of teenagers spent playing video games in one week. Sketch a circle graph to display the data.

9 -2 Circle Graphs • Write a fraction for each percent. 7 35 35% 9 -2 Circle Graphs • Write a fraction for each percent. 7 35 35% = or 20 100 1 10 10% = or 10 100 1 25 25% = or 4 100 3 30 30% = or 10 100 • Use a compass to draw a circle with at least a 1 -inch radius.

9 -2 Circle Graphs 1 • Since 30% is about 3 of the circle, 9 -2 Circle Graphs 1 • Since 30% is about 3 of the circle, shade about a third of the circle for 3 or more. 1 1 • Since 25% is of the circle, shade of the 4 4 circle for 2– 3. 1 • Since 35% is a little more than , shade a little 3 1 more than of the circle for 0– 1. 3 • Shade the remaining small piece or 10% for 1– 2.

9 -2 Circle Graphs • Label each section of the circle graph. Then give 9 -2 Circle Graphs • Label each section of the circle graph. Then give the graph a title.

9 -2 Circle Graphs Choose the circle graph that represents the data in the 9 -2 Circle Graphs Choose the circle graph that represents the data in the table. A. B.

9 -2 Circle Graphs Choose the circle graph that represents the data in the 9 -2 Circle Graphs Choose the circle graph that represents the data in the table. C. D.

9 -2 Circle Graphs Choose the circle graph that represents the data in the 9 -2 Circle Graphs Choose the circle graph that represents the data in the table. C.

9 -2 Circle Graphs Use the circle graph to the right that shows the 9 -2 Circle Graphs Use the circle graph to the right that shows the method of transportation students use to get to Martin Luther King, Jr. , Middle School. Which method of transportation do most students use? Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs The largest section of the graph is the section that 9 -2 Circle Graphs The largest section of the graph is the section that represents taking the bus. Answer: So, most students arrive at school by bus. Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs Use the graph to the right that shows the favorite 9 -2 Circle Graphs Use the graph to the right that shows the favorite fruit of students in Ms. Bradley’s fifth grade class to determine the fruit most students prefer. A. orange B. banana C. mango D. apple Favorite Fruits

9 -2 Circle Graphs Use the circle graph to the right that shows the 9 -2 Circle Graphs Use the circle graph to the right that shows the method of transportation students use to get to Martin Luther King, Jr. , Middle School. Which two methods of transportation are used by the least amount of students? Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs The smallest section of the graph represents riding a moped. 9 -2 Circle Graphs The smallest section of the graph represents riding a moped. The next smallest section of the graph represents walking to school. Answer: So, the least amount of students arrive at school by moped and by walking. Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs Use the graph to the right that shows the favorite 9 -2 Circle Graphs Use the graph to the right that shows the favorite fruit of students in Ms. Bradley’s fifth grade class to determine the fruit the fewest students prefer. A. orange B. banana C. mango D. apple Favorite Fruits

9 -2 Circle Graphs Use the circle graph to the right that shows the 9 -2 Circle Graphs Use the circle graph to the right that shows the method of transportation students use to get to Martin Luther King, Jr. , Middle School. How does the number of students who ride mopeds compare to the number of students who take the bus? Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs The section representing taking the bus is about 5 times 9 -2 Circle Graphs The section representing taking the bus is about 5 times larger than the section representing riding a moped. Answer: So, 5 times as many students take the bus. Method of Transportation Used by Students to Arrive at School

9 -2 Circle Graphs Use the graph to the right that shows the favorite 9 -2 Circle Graphs Use the graph to the right that shows the favorite fruit of students in Ms. Bradley’s fifth grade class to compare the number of students who preferred mango to the number of students who preferred apple. Favorite Fruits

9 -2 Circle Graphs Use the graph on the previous slide that shows compare 9 -2 Circle Graphs Use the graph on the previous slide that shows compare the number of students who preferred mango to the number of students who preferred apple. A. 4 times as many students prefer apples. B. 4 times as many students prefer mangoes. C. 3 times as many students prefer apples. D. 3 times as many students prefer mangoes.

9 -3 Percents and Decimals Five-Minute Check (over Lesson 9 -2) Main Idea California 9 -3 Percents and Decimals Five-Minute Check (over Lesson 9 -2) Main Idea California Standards Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7

9 -3 Percents and Decimals • I will express percents as decimals and decimals 9 -3 Percents and Decimals • I will express percents as decimals and decimals as percents.

9 -3 Percents and Decimals Standard 5 NS 1. 2 Interpret percents as a 9 -3 Percents and Decimals Standard 5 NS 1. 2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

9 -3 Percents and Decimals Write 86% as a decimal. 86 86% = 100 9 -3 Percents and Decimals Write 86% as a decimal. 86 86% = 100 = 0. 86 Rewrite the percent as a fraction with a denominator of 100. Write 86 hundredths as a decimal.

9 -3 Percents and Decimals Write 75% as a decimal. A. 7. 5 B. 9 -3 Percents and Decimals Write 75% as a decimal. A. 7. 5 B. 0. 075 C. 0. 75 D. 7. 05

9 -3 Percents and Decimals Write 1% as a decimal. 1 1% = 100 9 -3 Percents and Decimals Write 1% as a decimal. 1 1% = 100 = 0. 01 Rewrite the percent as a fraction with a denominator of 100. Write 1 hundredths as a decimal.

9 -3 Percents and Decimals Write 7% as a decimal. A. 0. 7 B. 9 -3 Percents and Decimals Write 7% as a decimal. A. 0. 7 B. 0. 007 C. 7. 0 D. 0. 07

9 -3 Percents and Decimals Write 110% as a decimal. 110% = 100 Rewrite 9 -3 Percents and Decimals Write 110% as a decimal. 110% = 100 Rewrite the percent as a fraction with a denominator of 100. 10 = 1 100 Write as a mixed number. = 1. 10 Write 1 and 10 hundredths as a decimal. = 1. 1

9 -3 Percents and Decimals Write 130% as a decimal. A. 1. 3 B. 9 -3 Percents and Decimals Write 130% as a decimal. A. 1. 3 B. 13. 0 C. 0. 113 D. 1. 13

9 -3 Percents and Decimals Write 0. 44 as a percent. 44 0. 44 9 -3 Percents and Decimals Write 0. 44 as a percent. 44 0. 44 = 100 = 44% Write 44 hundredths as a fraction. Write the fraction as a percent.

9 -3 Percents and Decimals Write 0. 65 as a percent. A. 65% B. 9 -3 Percents and Decimals Write 0. 65 as a percent. A. 65% B. 6. 5% C. 650% D. 0. 65%

9 -3 Percents and Decimals Write 1. 81 as a percent. 81 1. 81 9 -3 Percents and Decimals Write 1. 81 as a percent. 81 1. 81 = 1 100 Write 1 and 81 hundredths as a mixed number. 181 100 Write the mixed number as an improper fraction. = 181% Write the fraction as a percent. =

9 -3 Percents and Decimals Write 2. 37 as a percent. A. 2. 37% 9 -3 Percents and Decimals Write 2. 37 as a percent. A. 2. 37% B. 23. 7% C. 237% D. 23%

9 -3 Percents and Decimals Write 0. 09 as a percent. 0. 09 = 9 -3 Percents and Decimals Write 0. 09 as a percent. 0. 09 = 9 100 = 9% Write 9 hundredths as a fraction. Write the fraction as a percent.

9 -3 Percents and Decimals Write 0. 03 as a percent. A. 30% B. 9 -3 Percents and Decimals Write 0. 03 as a percent. A. 30% B. 300% C. 3% D. 0. 3%

9 -3 Percents and Decimals During a particularly rainy June in Boston, it rained 9 -3 Percents and Decimals During a particularly rainy June in Boston, it rained 0. 8 of the days in the month. Write 0. 8 as a percent. 0. 8 = 8 10 8 × 10 = 10 × 10 = 80 100 = 80% Write 8 tenths as a fraction. Multiply the numerator and denominator by 10 so that the denominator is 100. Simplify. Write the fraction as a percent.

9 -3 Percents and Decimals Write 0. 5 as a percent. A. 5% B. 9 -3 Percents and Decimals Write 0. 5 as a percent. A. 5% B. 50% C. 0. 5% D. 500%

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Five-Minute Check (over Lesson 9 -3) 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Five-Minute Check (over Lesson 9 -3) Main Idea California Standards Example 1: Problem-Solving Strategy

9 -4 Problem-Solving Strategy: Solve a Simpler Problem • I will solve problems by 9 -4 Problem-Solving Strategy: Solve a Simpler Problem • I will solve problems by solving a simpler problem.

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Standard 5 MR 2. 2 Apply 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Standard 5 MR 2. 2 Apply strategies and results from simpler problems to more complex problems. Standard 5 NS 1. 2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

9 -4 Problem-Solving Strategy: Solve a Simpler Problem A total of 400 students at 9 -4 Problem-Solving Strategy: Solve a Simpler Problem A total of 400 students at Liberty Elementary voted on whether a tiger or a dolphin should be the new school’s mascot. The circle graph shows the results. How many students voted for the tiger for the school mascot?

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Understand What facts do you know? 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Understand What facts do you know? • 400 students voted. • 70% of the students voted for the tiger. What do you need to find? • How many students voted for the tiger for the school mascot?

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Plan Solve a simpler problem by 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Plan Solve a simpler problem by finding 10% of the number of students that voted. Then use that result to find 70% of the number of students that voted.

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Solve Since 10% = or , 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Solve Since 10% = or , 1 out of every 10 students voted for the tiger. 400 ÷ 10 = 40 students. Since 70% is equal to 7 times 10%, multiply 40 by 7. 40 × 7 = 280 students. Answer: So, 280 students voted for the tiger.

9 -4 Problem-Solving Strategy: Solve a Simpler Problem Check Look back at the problem. 9 -4 Problem-Solving Strategy: Solve a Simpler Problem Check Look back at the problem. You know that 70% is close to 75%, which is . Since of 400 is 100, 300. So, 280 is a reasonable answer. of 400 is

9 -5 Estimating with Percents Five-Minute Check (over Lesson 9 -4) Main Idea California 9 -5 Estimating with Percents Five-Minute Check (over Lesson 9 -4) Main Idea California Standards Key Concept: Percent-Fraction Equivalents Example 1 Example 2 Example 3 Example 4 Estimating with Percents

9 -5 Estimating with Percents • I will estimate the percent of a number. 9 -5 Estimating with Percents • I will estimate the percent of a number.

9 -5 Estimating with Percents Standard 5 MR 2. 2 Apply strategies and results 9 -5 Estimating with Percents Standard 5 MR 2. 2 Apply strategies and results from simpler problems to more complex problems. Standard 5 NS 2. 5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

9 -5 Estimating with Percents 9 -5 Estimating with Percents

9 -5 Estimating with Percents Estimate 49% of 302. 49% is close to 50% 9 -5 Estimating with Percents Estimate 49% of 302. 49% is close to 50% or 1. Round 302 to 300. 2 1 of 300 is 150. 2 1 or half means to divide by 2. 2 Answer: So, 49% of 302 is about 150.

9 -5 Estimating with Percents Estimate 51% of 599. A. 300 B. 250 C. 9 -5 Estimating with Percents Estimate 51% of 599. A. 300 B. 250 C. 350 D. 200

9 -5 Estimating with Percents Estimate 80% of 42. 80% is 4. Round 42 9 -5 Estimating with Percents Estimate 80% of 42. 80% is 4. Round 42 to 40 since it is divisible by 5. 5 4 4 of 40 = × 40 or 32 5 5 Answer: Thus, 80% of 42 is about 32.

9 -5 Estimating with Percents Estimate 75% of 41. A. 40 B. 35 C. 9 -5 Estimating with Percents Estimate 75% of 41. A. 40 B. 35 C. 30 D. 32

9 -5 Estimating with Percents A CD that originally cost $11. 90 is on 9 -5 Estimating with Percents A CD that originally cost $11. 90 is on sale for 30% off. If you have $7, would you have enough money to buy the CD? To determine whether you have enough money to buy the CD, you need to estimate 30% of $11. 90.

9 -5 Estimating with Percents One Way: Use an equation. 1 30% is about 9 -5 Estimating with Percents One Way: Use an equation. 1 30% is about and $11. 90 is about $12. 3 x 1 = 12 3 Write the equation. x 1 = 12 3 Since 3 × 4 = 12, multiply 1 by 4. x=4

9 -5 Estimating with Percents Another Way: Use mental math. 1 30% is about 9 -5 Estimating with Percents Another Way: Use mental math. 1 30% is about and $11. 90 is about $12. 3 1 of $12 is about $4. 3 Answer: Since 30% off or $11. 90 – $4. 00 = $7. 90, you would not have enough money for the CD.

9 -5 Estimating with Percents Admission to theme park was originally $50. Lou has 9 -5 Estimating with Percents Admission to theme park was originally $50. Lou has a coupon for 25% off. His mom gave him $40. Does he have enough money to buy the ticket? A. Yes B. No C. Maybe D. Not enough information

9 -5 Estimating with Percents Claire surveyed her classmates about their favorite national park 9 -5 Estimating with Percents Claire surveyed her classmates about their favorite national park in California. Predict the number of students out of 234 who prefer the Redwood National Forest.

9 -5 Estimating with Percents You need to estimate the number of students out 9 -5 Estimating with Percents You need to estimate the number of students out of 234 that preferred Redwood National Forest. 26% of the students surveyed chose Redwood National Forest. 26% is about 25% or 1. 4 Round 234 to 240 since it is divisible by 4. 1 1 4 of 240 = 4 × 240 or 60. Answer: So, about 60 students would prefer Redwood National Forest.

9 -5 Estimating with Percents Claire surveyed her classmates about their favorite national park 9 -5 Estimating with Percents Claire surveyed her classmates about their favorite national park in California. Predict the number of students out of 234 who prefer the Yosemite National Park. A. 80 students B. 75 students C. 60 students D. 85 students

9 -6 Percent of a Number Five-Minute Check (over Lesson 9 -5) Main Idea 9 -6 Percent of a Number Five-Minute Check (over Lesson 9 -5) Main Idea California Standards Example 1 Example 2 Example 3

9 -6 Percent of a Number • I will find the percent of a 9 -6 Percent of a Number • I will find the percent of a number.

9 -6 Percent of a Number Standard 5 NS 1. 2 Interpret percents as 9 -6 Percent of a Number Standard 5 NS 1. 2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

9 -6 Percent of a Number Find 7% of 400. To find 7% of 9 -6 Percent of a Number Find 7% of 400. To find 7% of 400, you can use either method. One Way: Write the percent as a fraction. 7% = 7 100 7 7 of 400 = × 400 or 28 100

9 -6 Percent of a Number Another Way: Write the percent as a decimal. 9 -6 Percent of a Number Another Way: Write the percent as a decimal. 7% = 7 or 0. 07 100 0. 07 of 400 = 0. 07 × 400 or 28 Answer: So, 7% of 400 is 28.

9 -6 Percent of a Number Find 5% of 400. A. 20 B. 25 9 -6 Percent of a Number Find 5% of 400. A. 20 B. 25 C. 22 D. 30

9 -6 Percent of a Number Find 130% of 80. 9 -6 Percent of a Number Find 130% of 80.

9 -6 Percent of a Number One Way: Write the percent as a fraction. 9 -6 Percent of a Number One Way: Write the percent as a fraction. 130% = 130 or 13 100 10 13 13 of 80 = × 80 10 10 13 80 × or 104 10 1

9 -6 Percent of a Number Another Way: Write the percent as a decimal. 9 -6 Percent of a Number Another Way: Write the percent as a decimal. 130% = 130 or 1. 3 100 1. 3 of 80 = 1. 3 × 80 or 104 Answer: So, 130% of 80 is 104.

9 -6 Percent of a Number Find 140% of 20. A. 30 B. 28 9 -6 Percent of a Number Find 140% of 20. A. 30 B. 28 C. 70 D. 15

9 -6 Percent of a Number The Adams School raised money for a field 9 -6 Percent of a Number The Adams School raised money for a field trip by selling the items shown in the circle graph. If the school collected $596, how much did the school raise with the book sale?

9 -6 Percent of a Number You need to find 28% of $596. 28% 9 -6 Percent of a Number You need to find 28% of $596. 28% = 28 100 = 0. 28 Definition of a percent Write 28 hundredths as a decimal. 0. 28 of $596 = 0. 28 × 596 = 166. 88 Multiply. Answer: So, the school raised $166. 88 with the book sale.

9 -6 Percent of a Number If the school raised $455, how much did 9 -6 Percent of a Number If the school raised $455, how much did the school raise with the baked goods sale? A. $109. 20 B. $110 C. $108. 98 D. $111. 15

9 -7 Problem-Solving Investigation: Choose the Best Strategy Five-Minute Check (over Lesson 9 -6) 9 -7 Problem-Solving Investigation: Choose the Best Strategy Five-Minute Check (over Lesson 9 -6) Main Idea California Standards Example 1: Problem-Solving Investigation

9 -7 Problem-Solving Investigation: Choose the Best Strategy • I will choose the best 9 -7 Problem-Solving Investigation: Choose the Best Strategy • I will choose the best strategy to solve a problem.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Standard 5 MR 1. 1 Analyze 9 -7 Problem-Solving Investigation: Choose the Best Strategy Standard 5 MR 1. 1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Standard 5 NS 1. 2 Interpret percents as a part of a hundred; . . . compute a given percent of a whole number.

9 -7 Problem-Solving Investigation: Choose the Best Strategy TYRA: I’m going to the mall 9 -7 Problem-Solving Investigation: Choose the Best Strategy TYRA: I’m going to the mall with $75 to buy a shirt, a pair of jeans, and a hat. The hat costs $15, which is 50% of the cost of one shirt. The shirt costs $10 less than the jeans. If I spend more than $50, I get a 15% discount off of the total price. YOUR MISSION: Determine if Tyra has enough money to buy all three items.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Understand What facts do you know? 9 -7 Problem-Solving Investigation: Choose the Best Strategy Understand What facts do you know? • Tyra has $75 to spend. What do you need to find? • You need to determine if Tyra has enough money to buy all three items.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Plan You can work backward to 9 -7 Problem-Solving Investigation: Choose the Best Strategy Plan You can work backward to find the amount that each item costs. Then find out how much she spent.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Solve The hat is 50% of 9 -7 Problem-Solving Investigation: Choose the Best Strategy Solve The hat is 50% of the cost of one shirt. So, one shirt costs $15 × 2 or $30. The cost of the jeans is $10 more than the cost of the shirt. So, the jeans cost $30 + $10 or $40. So, Tyra spent $15 + $30 + $40 or $85. Since she spent a total of $85, she gets a 15% discount. 85 × 15% → 85 × 0. 15 = $12. 75 The discount is $12. 75.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Solve Answer: So, Tyra spent $85 9 -7 Problem-Solving Investigation: Choose the Best Strategy Solve Answer: So, Tyra spent $85 – $12. 75 or $72. 25. Since $72. 25 is less than $75, Tyra has enough money.

9 -7 Problem-Solving Investigation: Choose the Best Strategy Check Start with the cost of 9 -7 Problem-Solving Investigation: Choose the Best Strategy Check Start with the cost of the jeans. The jeans cost $40. The shirt costs are $40 – $10 or $30. The hat is 50% of the cost of the shirt, so the hat is $30 ÷ 2 or $15.

9 -8 Probability Five-Minute Check (over Lesson 9 -7) Main Idea and Vocabulary California 9 -8 Probability Five-Minute Check (over Lesson 9 -7) Main Idea and Vocabulary California Standards Key Concept: Probability Example 1 Example 2 Example 3 Example 4

9 -8 Probability • I will find and interpret the probability of a simple 9 -8 Probability • I will find and interpret the probability of a simple event. • outcomes • random • simple event • complementary events • probability

9 -8 Probability Preparation for Standard 6 SDAP 3. 3 Represent probabilities as ratios, 9 -8 Probability Preparation for Standard 6 SDAP 3. 3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 – P is the probability of an event not occurring.

9 -8 Probability 9 -8 Probability

9 -8 Probability There are six equally likely outcomes on the spinner to the 9 -8 Probability There are six equally likely outcomes on the spinner to the right. Find the probability of landing on 1. There is one section of the spinner labeled 1.

9 -8 Probability P(1) = = number of favorable outcomes number of possible outcomes 9 -8 Probability P(1) = = number of favorable outcomes number of possible outcomes 1 6 1 Answer: The probability of landing on 1 is , 6 0. 167, or 16. 7%.

9 -8 Probability There are six equally likely outcomes on the spinner below. Find 9 -8 Probability There are six equally likely outcomes on the spinner below. Find the probability of landing on an even number. A. 50% B. 40% C. 25% D. 75%

9 -8 Probability There are six equally likely outcomes on the spinner to the 9 -8 Probability There are six equally likely outcomes on the spinner to the right. Find the probability of landing on 2 or 4. The word or indicates that the favorable outcomes are the 2 and 4 sections. There is one section of the spinner that is a 2 and one section that is a 4.

9 -8 Probability P(2 or 4) = number of favorable outcomes number of possible 9 -8 Probability P(2 or 4) = number of favorable outcomes number of possible outcomes 2 = 6 1 = 3 Simplify. 1 Answer: The probability of landing on 2 or 4 is , 3 0. 33, or 33%.

9 -8 Probability There are six equally likely outcomes on the spinner below. Find 9 -8 Probability There are six equally likely outcomes on the spinner below. Find the probability of landing on a number greater than 2. 3 A. 4 1 A. 4 3 A. 6 2 A. 3

9 -8 Probability The spinner is spun once. Find the probability of not landing 9 -8 Probability The spinner is spun once. Find the probability of not landing on a 6. The probability of not landing on a 6 and the probability of landing on a 6 are complementary.

9 -8 Probability P(6) + P(not 6) = 1 The sum of the probabilities 9 -8 Probability P(6) + P(not 6) = 1 The sum of the probabilities is 1. 1 + P(not 6) = 6 1 Replace P(6) with – 1 6 = – 1 6 5 P(not 6) = 6 Subtract 1. 6 1 from each side. 6 5 Answer: So, the probability of not landing on 6 is , 6 0. 8333…, or 83. 33%.

9 -8 Probability The spinner is spun once. Find the probability of not landing 9 -8 Probability The spinner is spun once. Find the probability of not landing on an even number. A. 30% B. 50% C. 40% D. 25%

9 -8 Probability A sportscaster predicted that the Tigers have a 75% chance of 9 -8 Probability A sportscaster predicted that the Tigers have a 75% chance of winning tonight. Describe the complement of the event and find its probability. The complement of winning is not winning. The sum of the probabilities is 100%.

9 -8 Probability P(winning) + P(not winning) = 100% 75% + P(not winning) = 9 -8 Probability P(winning) + P(not winning) = 100% 75% + P(not winning) = 100% – 75% = – 75% P(not winning) = 25% Replace P(winning) with 75%. Subtract 75% from each side. Answer: So, the probability that the Tigers will not win 1 is 25%, , or 0. 25. 4

9 -8 Probability The weathercaster reported a 40% chance of thunderstorms. Identify the complement. 9 -8 Probability The weathercaster reported a 40% chance of thunderstorms. Identify the complement. Then find its probability. A. 60% chance of not storming B. 40% chance of not storming C. 50% chance of not storming D. 45% chance of not storming

9 -9 Sample Spaces Five-Minute Check (over Lesson 9 -8) Main Idea and Vocabulary 9 -9 Sample Spaces Five-Minute Check (over Lesson 9 -8) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3

9 -9 Sample Spaces • I will construct sample spaces using tree diagrams or 9 -9 Sample Spaces • I will construct sample spaces using tree diagrams or lists. • sample space • tree diagram

9 -9 Sample Spaces Preparation for Standard 6 SDAP 3. 1 Represent all possible 9 -9 Sample Spaces Preparation for Standard 6 SDAP 3. 1 Represent all possible outcomes for compound events in an organized way (e. g. tables, grids, tree diagrams) and express theoretical probability of each outcome.

9 -9 Sample Spaces While on vacation, Carlos can snorkel, boat, and paraglide. In 9 -9 Sample Spaces While on vacation, Carlos can snorkel, boat, and paraglide. In how many ways can Carlos do the three activities? Make an organized list to show the sample space. Let S = snorkel, B = boat, and P = paraglide. SBP BPS PBS SPB BSP PSB Answer: So, there are 6 ways to do the three activities.

9 -9 Sample Spaces While shopping at the store, Louisa must get toilet paper, 9 -9 Sample Spaces While shopping at the store, Louisa must get toilet paper, milk, bread, and cat food. How many different ways can she collect these items? A. 16 B. 64 C. 24 D. 30

9 -9 Sample Spaces A car can be purchased with either two doors or 9 -9 Sample Spaces A car can be purchased with either two doors or four doors. You may also choose leather, fabric, or vinyl seats. Use a tree diagram to find all the buying options. List each door choice. Then pair each door choice with each seat choice.

9 -9 Sample Spaces Car Seat Outcome leather (L) 2 F 2 V leather 9 -9 Sample Spaces Car Seat Outcome leather (L) 2 F 2 V leather (L) 4 L fabric (F) 4 F vinyl (V) 4 -door (4) fabric (F) vinyl (V) 2 -door (2) 2 L 4 V Answer: There are 6 possible combinations.

9 -9 Sample Spaces At the ice cream store, you can order either a 9 -9 Sample Spaces At the ice cream store, you can order either a sugar cone or a cake cone. You may also choose from chocolate, strawberry, vanilla, or orange sherbet ice cream flavors. How many combinations of cone and ice cream can I get? A. 6 B. 8 C. 10 D. 16

9 -9 Sample Spaces Dayo rolls two number cubes. What is the probability that 9 -9 Sample Spaces Dayo rolls two number cubes. What is the probability that she will roll a 5 on the first cube and a 2 on the second cube? Use a tree diagram to find all of the possible outcomes.

Sample Spaces 9 -9 1 2 3 4 5 6 123456 123456 Notice there Sample Spaces 9 -9 1 2 3 4 5 6 123456 123456 Notice there is only one combination of 5 first then 2. Answer: Since there are 36 possible outcomes and only one favorable outcome, the probability of rolling a 5 on the first cube and a 2 on the 1 second is. 36

9 -9 Sample Spaces Joy rolls two number cubes. What is the probability that 9 -9 Sample Spaces Joy rolls two number cubes. What is the probability that she will roll a 3 and a 4? 1 A. 36 1 B. 18 2 C. 36 1 D. 63

9 -10 Making Predictions Five-Minute Check (over Lesson 9 -9) Main Idea and Vocabulary 9 -10 Making Predictions Five-Minute Check (over Lesson 9 -9) Main Idea and Vocabulary California Standards Example 1 Example 2

9 -10 Making Predictions • I will predict the actions of a larger group 9 -10 Making Predictions • I will predict the actions of a larger group using a sample. • survey • population • sample

9 -10 Making Predictions Standard 5 AF 1. 2 Use a letter to represent 9 -10 Making Predictions Standard 5 AF 1. 2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

9 -10 Making Predictions Bonne asked every sixth person in the school cafeteria to 9 -10 Making Predictions Bonne asked every sixth person in the school cafeteria to name the kind of activity he or she would like to do for the school’s spring outing. What is the probability that a student will prefer an amusement park?

9 -10 Making Predictions P(amusement park) = = number of students that prefer the 9 -10 Making Predictions P(amusement park) = = number of students that prefer the amusement park number of students surveyed 15 40 15 Answer: So, 15 out of 40 or , 0. 375, or 37. 5% 40 will prefer the amusement park.

9 -10 Making Predictions Use the table below to answer the following question. What 9 -10 Making Predictions Use the table below to answer the following question. What is the probability that a student prefers chocolate ice cream? 22 A. 55 2 B. 5 11 C. 25 22 D. 50

9 -10 Making Predictions There are 400 students at Julia’s school. Predict how many 9 -10 Making Predictions There are 400 students at Julia’s school. Predict how many students prefer going to an amusement park. Let s represent the number of students that prefer going to an amusement park.

9 -10 Making Predictions s 400 15 40 = 15 40 s = 400 9 -10 Making Predictions s 400 15 40 = 15 40 s = 400 Since 40 × 10 = 400, multiply 15 by 10 to find s. 15 40 150 = 400 s = 150 Write an equation. Answer: Of 400 students, about 150 will prefer the amusement park.

9 -10 Making Predictions There are 550 students at Corbin’s school. Predict how many 9 -10 Making Predictions There are 550 students at Corbin’s school. Predict how many of the students will prefer strawberry. A. 170 students B. 55 students C. 130 students D. 155 students

9 Percent Five-Minute Checks Circle Graphs Estimating with Percents 9 Percent Five-Minute Checks Circle Graphs Estimating with Percents

9 Percent Lesson 9 -1 (over Chapter 8) Lesson 9 -2 (over Lesson 9 9 Percent Lesson 9 -1 (over Chapter 8) Lesson 9 -2 (over Lesson 9 -1) Lesson 9 -3 (over Lesson 9 -2) Lesson 9 -4 (over Lesson 9 -3) Lesson 9 -5 (over Lesson 9 -4) Lesson 9 -6 (over Lesson 9 -5) Lesson 9 -7 (over Lesson 9 -6) Lesson 9 -8 (over Lesson 9 -7) Lesson 9 -9 (over Lesson 9 -8) Lesson 9 -10 (over Lesson 9 -9)

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Make a table to show the relationship between the total distance d the family traveled in h hours. A.

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Make a table to show the relationship between the total distance d the family traveled in h hours. B.

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Make a table to show the relationship between the total distance d the family traveled in h hours. C.

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Make a table to show the relationship between the total distance d the family traveled in h hours. D.

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Make a table to show the relationship between the total distance d the family traveled in h hours. D.

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. Write an equation to find the total distance d that the Nguyen family traveled in h hours. A. d = 30 h 2 B. d = 60 h C. d = 20 h 3

9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled 9 Percent (over Chapter 8) While driving on a vacation, the Nguyen family traveled at an average speed of 60 miles per hour. How many miles did the Nguyen family travel in 4 hours? A. 120 miles B. 100 miles C. 240 miles

9 Percent (over Lesson 9 -1) Write 35% as a fraction or a mixed 9 Percent (over Lesson 9 -1) Write 35% as a fraction or a mixed number in simplest form. A. 7 20 B. 3 5 1 C. 3 D. 1 3 4

9 Percent (over Lesson 9 -1) Write 4% as a fraction or a mixed 9 Percent (over Lesson 9 -1) Write 4% as a fraction or a mixed number in simplest form. A. 4 10 B. 40 100 C. 1 D. 3 5 1 25

9 Percent (over Lesson 9 -1) Write 175% as a fraction or a mixed 9 Percent (over Lesson 9 -1) Write 175% as a fraction or a mixed number in simplest form. A. 1 B. 3 4 17 150 C. 1 D. 2 3 5 6

9 Percent (over Lesson 9 -1) Write 2 as a percent. 5 A. 25% 9 Percent (over Lesson 9 -1) Write 2 as a percent. 5 A. 25% B. 40% C. 35% 2 D. 1 5

9 Percent (over Lesson 9 -1) Write 3 as a percent. 25 A. 15% 9 Percent (over Lesson 9 -1) Write 3 as a percent. 25 A. 15% B. 2 3 5 C. 40% D. 12%

9 Percent (over Lesson 9 -1) Write 2 3 as a percent. 5 A. 9 Percent (over Lesson 9 -1) Write 2 3 as a percent. 5 A. 260% B. 35% C. 125% 3 D. 2 5

9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In 9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In a survey of preferences of four careers, 14% of students chose teacher, 25% chose doctor, 25% chose lawyer, and 36% chose musician. A.

9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In 9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In a survey of preferences of four careers, 14% of students chose teacher, 25% chose doctor, 25% chose lawyer, and 36% chose musician. B.

9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In 9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In a survey of preferences of four careers, 14% of students chose teacher, 25% chose doctor, 25% chose lawyer, and 36% chose musician. C.

9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In 9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In a survey of preferences of four careers, 14% of students chose teacher, 25% chose doctor, 25% chose lawyer, and 36% chose musician. D.

9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In 9 Percent (over Lesson 9 -2) Sketch a circle graph of this data: In a survey of preferences of four careers, 14% of students chose teacher, 25% chose doctor, 25% chose lawyer, and 36% chose musician. B.

9 Percent (over Lesson 9 -3) Write 98% as a decimal. A. 0. 98 9 Percent (over Lesson 9 -3) Write 98% as a decimal. A. 0. 98 B. 1. 98 C. 0. 02 D. 0. 20

9 Percent (over Lesson 9 -3) Write 7% as a decimal. A. 0. 70 9 Percent (over Lesson 9 -3) Write 7% as a decimal. A. 0. 70 B. 1. 03 C. 0. 07 D. 0. 93

9 Percent (over Lesson 9 -3) Write 135% as a decimal. A. 13. 5 9 Percent (over Lesson 9 -3) Write 135% as a decimal. A. 13. 5 B. 1. 035 C. 1. 35 D. 0. 65

9 Percent (over Lesson 9 -3) Write 0. 79 as a percent. A. 21% 9 Percent (over Lesson 9 -3) Write 0. 79 as a percent. A. 21% B. 79% C. 7. 9% D. 0. 79%

9 Percent (over Lesson 9 -3) Write 0. 03 as a percent. A. 3% 9 Percent (over Lesson 9 -3) Write 0. 03 as a percent. A. 3% B. 93% C. 30% D. 1. 3%

9 Percent (over Lesson 9 -3) Write 1. 09 as a percent. A. 1. 9 Percent (over Lesson 9 -3) Write 1. 09 as a percent. A. 1. 9% B. 19% C. 0. 19% D. 109%

9 Percent (over Lesson 9 -4) Use the solve a simpler problem strategy to 9 Percent (over Lesson 9 -4) Use the solve a simpler problem strategy to solve this problem. A team needs to assemble 1, 200 boxes. They can assemble 45 boxes every 30 minutes. If they work 8 hours a day, can they assemble all the boxes in one day? Explain. A. No; they can make only 720 boxes in one day. B. Yes; they can make 1, 200 boxes.

9 Percent (over Lesson 9 -5) Estimate 19% of $78. A. 1 of $80; 9 Percent (over Lesson 9 -5) Estimate 19% of $78. A. 1 of $80; $16 5 B. 1 of $70; $15 6 C. 2 of $90; $20 8

9 Percent (over Lesson 9 -5) Estimate 53% of 220. 2 A. of 200; 9 Percent (over Lesson 9 -5) Estimate 53% of 220. 2 A. of 200; 150 5 B. 3 of 250; 225 5 C. 1 of 200; 100 2

9 Percent (over Lesson 9 -5) Estimate 69% of 20. 7 A. of 20; 9 Percent (over Lesson 9 -5) Estimate 69% of 20. 7 A. of 20; 14 10 B. 6 of 20; 16 10 C. 8 of 20; 8 10

9 Percent (over Lesson 9 -5) Estimate 4% of 20. 1 A. of 20; 9 Percent (over Lesson 9 -5) Estimate 4% of 20. 1 A. of 20; 1 20 B. 4 of 20; 16 5 C. 1 of 20; 6 4

9 Percent (over Lesson 9 -6) Find 50% of 786. A. 409 B. 343 9 Percent (over Lesson 9 -6) Find 50% of 786. A. 409 B. 343 C. 410 D. 393

9 Percent (over Lesson 9 -6) Find 100% of 150. A. 75 B. 150 9 Percent (over Lesson 9 -6) Find 100% of 150. A. 75 B. 150 C. 100 D. 1, 500

9 Percent (over Lesson 9 -6) Find 8% of 25. A. 2 B. 12 9 Percent (over Lesson 9 -6) Find 8% of 25. A. 2 B. 12 C. 4 D. 20

9 Percent (over Lesson 9 -6) Find 75% of 84. A. 75 B. 24 9 Percent (over Lesson 9 -6) Find 75% of 84. A. 75 B. 24 C. 63 D. 76

9 Percent (over Lesson 9 -6) Find 105% of 40. A. 42 B. 65 9 Percent (over Lesson 9 -6) Find 105% of 40. A. 42 B. 65 C. 60 D. 105

9 Percent (over Lesson 9 -7) Use any strategy to solve this problem. Explain 9 Percent (over Lesson 9 -7) Use any strategy to solve this problem. Explain how you used the strategy. Tickets for a town fair cost $25 for adults and $10 for students. The town collected $2, 045 for 107 tickets. How many student tickets were sold? A. 107 student tickets B. 2, 045 student tickets C. 42 student tickets D. 35 student tickets

9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 sections that are marked 1, 2, 3, 4, 5, 6, 7, and 8. P(even number) A. 1 3 B. 1 7 1 C. 8 D. 1 2

9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 sections that are marked 1, 2, 3, 4, 5, 6, 7, and 8. P(number > 3) A. 1 9 B. 3 8 5 C. 8 D. 6 8

9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 sections that are marked 1, 2, 3, 4, 5, 6, 7, and 8. P(not an even number) A. 3 8 B. 3 5 1 C. 2 D. 3 7

9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 9 Percent (over Lesson 9 -8) Find each probability for a spinner with 8 sections that are marked 1, 2, 3, 4, 5, 6, 7, and 8. P(number not > 3) A. 3 8 B. 1 2 3 C. 8 D. 1 3

9 Percent (over Lesson 9 -9) An ice cream wagon offers chocolate, strawberry, and 9 Percent (over Lesson 9 -9) An ice cream wagon offers chocolate, strawberry, and vanilla ice cream cones. You can have a waffle cone or a sugar cone with one scoop of ice cream. Find the sample space and tell how many outcomes are possible. A. 3 outcomes: WC, WS, WV B. 3 outcomes: SC, SS, SV C. 6 outcomes: WC, WS, WV, SC, SS, SV

9 Percent (over Lesson 9 -9) You roll a number cube twice. You record 9 Percent (over Lesson 9 -9) You roll a number cube twice. You record one number from the first roll and another number from the second roll. Tell how many outcomes are possible. A. 24 outcomes B. 36 outcomes C. 12 outcomes

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