UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 19: Student Packet

Transcription

1 Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 19: Student Packet 19.1 Linking Percents and Proportions Use a linear model to solve percent problems. Set up ratios and proportions to represent percent problems. Practice sense-making strategies for solving percent problems Probability: Spinner Puzzles Perform operations with rational numbers. Use fractions, decimals, and percents to represent probabilities. Use logical reasoning to find probabilities of events Dimensional Analysis Add, subtract, multiply, and divide rational numbers. Use measures expressed as rates to solve problems. Check the units of the solutions. Use dimensional analysis. Review math concepts from prior lessons. Demonstrate competency in integers (highlighted review) Week 19 SP

2 FOCUS ON VOCABULARY 19 Find the words in the word search puzzle. Then, choose five words and write their definitions or give examples. F N P U X F R R F I W M F S E M B R T I M A T R I A L F C F H H O K T Q T O S V W K E B N F L B A Q A I U V Y M B C S D B S A R C G O T R P T E C A Q F U B D N A W C E R B J Q M H X T I W I A F O X O N Z V P E T S L G H Y I M P P Y K E L V W E I W I D T E E O B U D E E P V T H O X O Z R R J P U S N S G Y U L F C X I T E P G P T L D N V S A J G M I K N M A S N J O A Y F R K E O C K Z C G Y J I I H A P P N N T H Q E U T W P E R C E N T I M V P D C Word Bank ratio outcome experiment percent sample space trial event probability proportion Week 19 SP

3 19.1 Linking Percents and Proportions LINKING PERCENTS AND PROPORTIONS Ready (Summary) Solve percent problems using a visual model and sense-making strategies. Set (Goals) Use a linear model to solve percent problems. Set up ratios and proportions to represent percent problems. Practice sense-making strategies for solving percent problems. Go (Warmup) Use two methods to solve each problem. Be prepared to share your strategies. Remember to include units in your answer. 1. What is 3% of 1 cm? 2. What is 3% of 5 cm? 3. What is 3% of 2 cm? 4. What is 3% of 1 cm? Week 19 SP1

4 19.1 Linking Percents and Proportions UNDERSTANDING PERCENTS AND PROPORTIONS A B % 8 1 % Complete the chart. Words Proportion (Equation) 1. 3% of 8 is % of 8 is x 1 8 Week 19 SP2

5 19.1 Linking Percents and Proportions FINDING 2% Cut off and use the strip at the bottom of the page to set up proportions to represent each percent problem and find the answers What is 2% of 6? 2. What is 2% of 14? 3. What is 2% of 4? 4. What is 2% of 64? part 2 x whole 1 6 part whole 1 x 1% Week 19 SP3

6 19.1 Linking Percents and Proportions FINDING 85% Cut off and use the strip at the bottom of the page to set up proportions to represent each percent problem and find the answers What is 85% of 6? 2. What is 85% of 14? 3. What is 85% of 4? 4. What is 85% of 64? part 85 x whole 1 6 part whole 1 x 1% Week 19 SP4

7 19.1 Linking Percents and Proportions MORE STRIPS AND PROPORTIONS Cut off and use the strip at the bottom of the page to set up proportions to represent each percent problem and find the answers What percent of 8 is 32? 2. 3% of what amount is 15? 3. What % of 22 is 11? 4. 6% of 18 is what amount? part whole 1 x 1% Week 19 SP5

8 19.1 Linking Percents and Proportions MORE STRIPS AND PROPORTIONS (continued) 5. What is 4% of 5? 6. 5 is 25% of what? 7. What is 15% of 4? 8. 1 is 2% of what? 1% Week 19 SP6

9 19.2 Probability: Spinner Puzzles PROBABILITY: SPINNER PUZZLES Ready (Summary) Review probability concepts using spinners. Use logical reasoning to determine the probability of different events. Set (Goals) Perform operations with rational numbers. Use fractions, decimals, and percents to represent probabilities. Use logical reasoning to find probabilities of events. Go (Warmup) Yellow Red Red Red Red Yellow Write each answer as a fraction. What is the probability of: 1. Landing on red? 2. Landing on yellow? 3. Landing on green? 4. Landing on a primary color? Week 19 SP7

10 19.2 Probability: Spinner Puzzles SPINNER PUZZLES Use the clues provided by your teacher to create each spinners. Spinner Puzzle A Spinner Puzzle B Spinner Puzzle C Spinner Puzzle D Week 19 SP8

11 19.2 Probability: Spinner Puzzles CREATE A SPINNER PUZZLE Draw a spinner with three to five parts. You may want to use a ruler and protractor for accuracy. Label the spinner parts with a theme of your choice. Accurately identify each sector of the spinner with its appropriate fraction, decimal, and percent. Write four to six clues to create a spinner puzzle. Clues: Week 19 SP9

12 19.3 Dimensional Analysis SKILL BUILDER 1A Dimensional analysis is a method of manipulating unit measures algebraically to determine the proper units for a quantity. In the physical world, these units are often units of distance, mass (or weight), and time. You drive 4 hours at a rate of 65 miles per hour. How far will you go? 65 miles 4 hours 65 miles 4 hr 26 miles 1 hours 1 1 hours Draw a ring around the given quantity. Draw a star around the given rate. Underline the units in the answer. Notice that hour hour behaves as a a 1. Solve the rate problems. 1. A car gets 24 miles per gallon. How many gallons would the car need to travel 18 miles? ( ) 2. A worker earns $5 every 4 hours. How much would the worker earn in 42 hours? ( ) Week 19 SP1

13 19.3 Dimensional Analysis SKILL BUILDER 1B Use dimensional analysis to perform each unit conversion. 3. Find the number of years in 1,825 days. ( ) 4. Find the number of yards in 4 miles. (hint: 1 mile 5,28 feet) ( ) 5. Find the number of ounces in 3 gallons. (hints: 8 ounces 1 cup; 4 cups 1 quart; 4 quarts 1 gallon) ( ) Week 19 SP11

14 19.3 Dimensional Analysis SKILL BUILDER 2A Use dimensional analysis to solve each rate problem. 1. A car gets 32 miles per gallon. How many 2. A student earns $28 for 4 hours of work. gallons would the car need to travel 288 How much would the student earn in 3 miles? hours? Perform the unit conversions using dimensional analysis. 3. Find the number of inches in 12 yards. 4. Find the number of minutes in 3 days. 5. It is customary to tip 15% at a restaurant. Represent this relationship for various amounts of restaurant bills with a table, graph, rule, and words. Amount of restaurant bill $1 Tip (15% of bill) $15 $2 $x Rule: y In words: Week 19 SP12

15 19.3 Dimensional Analysis SKILL BUILDER 2B Compute. Show your work using positive symbols (+) and negative symbols(-) (-14) (-3) (-11) Compute without drawing positive or negative symbols (-13) (-5) Solve for x x x 7 3x ( x 2) 4( x+ 1) 16. 2( x 4) Week 19 SP13

16 19.3 Dimensional Analysis SKILL BUILDER 3A Solve the rate problems using dimensional analysis. 1. If 12 pencils cost $1.86, how much money will you need to purchase 6 2. Three fruit smoothies use cups pencils? strawberries. How many fruit smoothies can be made with 12 cups of strawberries? Complete the table. Fraction Decimal Percent % Find the missing number in each proportion. 7 n n n 42 7 Week 19 SP14

17 19.3 Dimensional Analysis SKILL BUILDER 3B Find the final cost for each of the items. 9. The price of a pair of jeans is $55. The sales tax rate is 8%. What is the total cost of the jeans? 1. The regular price of a camera is $25. It is on sale for 15% off. What is the discounted sale price? Compute. 11. (-21) (3 4) (7 5) + (3 5) (-2) Choose the best answer. 15. Which of the following fractions is not a terminating decimal. A B C D Week 19 SP15

18 19.3 Dimensional Analysis TEST PREPARATION 19 Show your work on a separate sheet of paper and choose the best answer. 1. What is 55% of 24? A. 436 B. 132 C. 22 D In the spinner to the right, what is the probability of spinning orange or purple? Green Purple Purple Purple Orange Green E. 2 3 F. 1 2 G. 1 3 H A worker earns $24 in 6 hours. How much would the worker earn in 24 hours? A. $5,769 B. $1,44 C. $96 D. $ List the following integers in numerical order from smallest to largest: -1,, 11, -25, -3 E., -1, -3, 11, -25 F. -1, -3, -25,, 11 G., -1, -3, -25, 11 H. -25, -3, -1,, Which of the following is NOT equivalent to.35? A. 35% B. 35 1, C. 3.5% D If 2 protein bars cost $3, which of the following describes the relationship between the number of protein bars (x) and the cost (y)? E. y 2x F. y 3x G. 2 y x H. 3 y 3 2 x Week 19 SP16

19 19.3 Dimensional Analysis KNOWLEDGE CHECK 19 Show your work on a separate sheet of paper and write your answers on this page Linking Percents and Proportions Use paper strips if needed. Write a proportion to solve each problem. 1. What is 3% of 8? 2. What percent of 9 is 36? 19.2 Probability: Spinner Puzzles Use the spinner to the right to find each probability expressed as a fraction, a decimal, and a percent. 3. What is the probability of landing on orange? Green Purple 4. What is the probability of landing on purple or green? 19.3 Dimensional Analysis Purple Purple Orange Green 5. A car travels 32 miles per gallon of gas. Use dimensional analysis to determine how many miles the car will travel with 7 gallons of gas. 6. Use dimensional analysis to determine the number of minutes in 6 days. Highlighted Review: Integers Revisited Solve the following problems. 7. What must -32 be divided by to get an answer of 4? 8. What must be added to -7 to get 13? Week 19 SP17

20 19.3 Dimensional Analysis Home-School Connection 19 Here are some questions from this week s lessons to review with your young mathematician. 1. What percent of 14 is 7? Green Purple 2. In the spinner to the right, determine the probability of spinning green expressed as a fraction and as a percent. Purple Purple Orange Green 3. A car travels 25 miles per gallon of gas. Use dimensional analysis to determine how many gallons of gas the car would need to travel 35 miles. Parent (or Guardian) signature NS NS Selected California Mathematics Content Standards 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. Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. MG Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). MG Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. SDP Represent probabilities as ratios, proportions, decimals between and 1, and percentages between and 1 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. Week 19 SP18