PMI 6th Grade Ratios & Proportions

Unite Rate Packet.notebook December 02, 2016 www.njctl.org PMI 6th Grade Ratios & Proportions 2016 09 19 www.njctl.org www.njctl.org

Table of Contents Click on the topic to go to that section Writing Ratios Equivalent Ratios Rates & Unit Rates Using Ratios to Convert Measurements Converting Unit Ratios Glossary & Standards Teacher Notes Table of Contents Ratios Ratios can be written three different ways: _ a to b a : b a b Each is read, "the ratio of a to b." Each ratio should be in simplest form.

Ratios The ratio of wings to beaks in the bird house at the zoo was: 2 to 1 This is because for every 2 wings there was 1 beak. wings Math Practice beaks This can also be written as: 2:1 or 2 1 MP 2 Two Types of Ratios There are two types of ratios: Part to Part and Part to Whole

1 Javier has stickers on the front of his folder. Use the stickers to answer the questions. What is the ratio of to? A 6 : 1 B 1 : 6 C 1 : 2 D 6 : 7 2 Dr. Ruiz has 7 snails and 3 fish in his aquarium. What is the ratio of snails to the total number of animals? A 7 to 3 B 7 to 10 C 3 to 7 D 3 to 10 B [This object is a pull tab]

Equivalent Ratios Return to Table of Contents Equivalent Ratios Equivalent Ratios Equivalent ratios have the same value. 1 : 4 is equivalent to 2 : 8 3 to 2 is equivalent to 27 to 18 5 is equivalent to 35 7 49

Equivalent Ratios When two fractions are equal to each other, then the ratios they represent are equivalent. 14 6 = 7 3 35 15 = 7 3 14:6 = 7:3 35:15 = 7:3 May 22 11:40 AM Equivalent Ratios There are two ways to determine if ratios are equivalent. 1. Common Factor 4 12 5 = 15 x 3 4 12 5 = 15 x 3 Since the numerator and denominator were m ultiplied by the same value, the ratios are equivalent.

Equivalent Ratios 2. Cross Products 4 12 = 5 15 Since the cross products are equal, the ratios are equivalent. 4 x 15 = 5 x 12 60 = 60 Equivalent Ratios A carpenter uses a certain amount of nails to install a shelf. The ratio of the number of nails per number of shelves is 4:1. If the carpenter wants to install 20 shelves, how many nails does he need to buy? We can also use common factors to solve: x 20 4 1 =? 20 x 20 4 80 1 = 20 The carpenter needs to buy 80 nails. May 22 12:12 PM

Equivalent Ratios A carpenter uses a certain amount of nails to install a shelf. The ratio of the number of nails per number of shelves is 4:1. If the carpenter wants to install 20 shelves, how many nails does he need to buy? Or we can use cross products to solve: 4 x 1 = 20 4 x 20 = 1x 80 = x 4 80 1 = 20 The carpenter needs to buy 80 nails. May 22 12:12 PM 3 is equivalent to True False

4 is equivalent to True False 5 Which ratio is equivalent to? A B C D

Rates & Unit Rates Return to Table of Contents Rates Rates & Unit Rates A Rate is a ratio that is used to compare measurements with different units. Diet cola was on sale last week; it cost $10 for every 4 pack of diet cola. How much do 2 packs of diet cola cost? How much does 1 pack cost? Pack of Diet Cola 4 2 1 Total Cost 10 Using what you know about equivalent ratios, fill in the rest of the table. From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/integratedalgebra; accessed 17, June, 2011.

6 Wyatt hiked 6 miles in 2 hours. At this same rate, what is the total number of miles Wyatt could hike in 8 hours? A 3 B 8 C 12 D 24 Teacher Notes From NY 2015 released questions NY 2015 released question 7 Mrs. Ucci's class is selling slices of pizza to fundraise for the school dance. Each slice of pizza is $2. At this rate, how much money will the class fundraise if they sell 40 slices of pizza? A $20 B $40 C $80 From NY 2015 released questions NY 2015 released question

Video on Unit Rate Nov 21 12:14 PM Rates & Unit Rates Unit Rate is a rate with a denominator of 1. Rate Unit Rate $32 in 4 hours $8 in 1 hour 36 students at 9 tables 4 students at 1 table 120 miles in 2 hours 60 minutes in 1 hour $5.94 for 6 sodas $0.99 for 1 soda

Expo Marker Problem! Mrs. Ucci bought a pack of expo markers on Amazon. Each pack of 4 markers was $4? How much did each marker cost?? Nov 20 8:57 PM Unit Rate Let's take a pretend trip to Bruno's for pizza. You buy a large pie for $16. Find the unit rate for one slice of pizza.

Eraser Problem! Mrs. Ucci bought the class Halloween erasers. The erasers came in packs of 3 for $6. How much did she pay for each eraser (unit rate)? Nov 20 8:57 PM 8 Margot bought 16 oranges for $4. How much does 1 orange cost? (Read carefully!!) A $0.25 B $0.50 C $2

9 Nahomy bought the new Adele album, "25" on itunes for 8.99. The album features 11 songs. How much was each song? (Round to the hundredths place!) A $0.80 B $0.82 C $1.38 Unit Rate Try these. Find the unit rates. click 20 toys for 5 dogs 4 toys for 1 dog For every 12 laps Evan click Evan runs 3 laps runs Lucas runs Lucas runs 1 Richard read 27 pages Richard read 9 click in 3 hours pages in 1 hour

Instructions Get the "Best Buy" click STORE May 4 10:33 AM Instructions 18 oz box $3.96 24 oz box $4.80 click between the boxes Jul 18 9:51 AM

10 Emily drove 825 miles in 15 hours. How many miles per hour (mph) did she drive? A 815 miles per hour B 60 miles per hour C 55 miles per hour D 15 miles per hour 11 Emily's brother drove 340 miles and used 17 gallons of gas. How many miles per gallon (mpg) did he get?

12 Brian bought 3 pounds of chicken for $10.47. How much was one pound of chicken? 13 A class of 25 students shares a class set of 100 markers. On a day with 5 students absent, which statement is true? A For every 5 students, there is 1 marker. B For every 4 students, there is 1 marker. C For each student, there are 4 markers. D For each student, there are 5 markers. From PARCC EOY sample test non calculator #1 PARCC Sample Question

14 A school band performed a concert on four different days. The band sold tickets and snacks each day of the concert for a fundraiser. The table shows the numbers of snacks sold and the amounts of money collected from snack sales. Part A If each snack costs the same price, what is the price per snack? From PARCC EOY sample test calculator #4 PARCC Sample Question 15 A school band performed a concert on four different days. The band sold tickets and snacks each day of the concert for a fundraiser. The table shows the number of tickers sold and the amounts of money collected from ticket sales. Part B Write an equation that can be used to find y, the amount of money collected for selling x concert tickets. From PARCC EOY sample test calculator #4 PARCC Sample Question

Unit Rate Unit rate is very useful to compare costs of the same item in different quantities. Because the cost cannot be compared by the packaged amount, use the unit rate of each to do a comparison. Compare these products: Sale 1 roll for $.99 Everyday Low Price Sop A Lot Special 9 for $10.44 Math Practice Soake 8 for $7.76 MP8 Dec 1 10:38 AM

Compare Products Everyday Sale 1 roll for $.99 Soake Low Price 8 for $7.76 Sop A Lot Special 9 for $10.44 A B C # of Total Divide Cost Deal Rolls Cost by per roll 1 A 8 B 9 C 16 Which would be the best deal? A 5 candy bars for $6.25 B 8 candy bars for $7.28 C 10 candy bars for $ 9.70 D 12 candy bars for $11.04 B

17 Tim ran 1 mile in 11 minutes, Bob ran 4 miles in 43 minutes, Rosanna ran 15 miles in 158 minutes and Carrie ran 23 miles in 230 minutes. Who ran the fastest? A B C D Tim Bob Rosanna Carrie 18 Who made the most amount of money per hour? A Andrew made $545 for 30 hours of work. B Kyle made $785 for 42 hours of work. C Joshua made $605 for 34 hours of work. D Jamir made $880 for 45 hours of work. D

19 A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch? A 3 cups B cups C 1 cup D cup From NY 2015 released questions NY 2015 Released Question Using Ratios Cory lives 2 miles from her school. What is this distance in yards? 1 mile = 1,760 yards How many yards does Cory live away from school?

20 Kyle's room measures 12.5 feet long. What is this measurement in inches? 1 feet = 12 inches 21 How many inches are in 10 feet?

22 How many feet are in 2 miles? 1 mile = 5,280 feet 23 How many yards are in 2 miles? 1 mile = 1,760 yards

24 How many feet are in 60 yards? A 30 feet B 100 feet C 120 feet D 180 feet 25 Kelly needed 2.5 feet of ribbon. How many inches of ribbon is this? A 12 inches B 24 inches C 30 inches D 32 inches

26 Maria had 30 inches of fabric. How much is this in feet? A 1 foot B 2 feet C D 2 feet 6 inches 3 feet Using Ratios You can use ratios to convert US Customary Units into Metric Units. Some common conversions you should know: 1 in = 2.54 cm 1 ft = 0.3 m 1 mi = 1.6 km 1 lb = 0.45 kg 1 gal = 3.79 l (liters) 1 kg

Using Ratios How many centimeters are in a standard ruler? (1 foot) We know that there are 12 inches in 1 foot, and 1 inch = 2.54 cm Glossary & Standards Teacher Notes Return to Table of Contents Glossary

Conversion Factor A number used to multiply or divide a quantity to convert from one system of measurement to another. 21 days = 3 weeks Qts Pts To convert days into weeks, divide by 7. Divide by 2 9 qts = 8.5 pts 16in 1.5 ft 12 Back to Instruction Conversion Factor Ratio Language A pair of numbers that represent a relationship between two quantities, never the pair of quantities themselves. "3 cups to 4 cups" 3:4 "5 girls to 2 boys" 5:2 "12 miles to 1 hour" 12:1 Back to Instruction Ratio Language

Ratio Relationship Descriptions A pair of quantities that represents a relationship and describes the units measured. 3:4 "3 cups to 4 cups" 5:2 "5 girls to 2 boys" 12:1 "12 miles to 1 hour" Back to Instruction Ratio Relationship Description Equivalent Ratios Two ratios that have the same value, even though they represent different amounts. 4 12 4 = 1 4 3 10 to 25 is equivalent to = 2 to 5 3 out of is equivalent to 1out of 9 3 Back to Instruction Equivalent Ratios

Part to Part Ratio A comparison of part of a whole to the rest of the whole. red:white red white 3:5 3 5 Back to Instruction Part to Part Ratio Part to Whole Ratio A comparison of part of a whole the total. red:total 3:8 red total 3 8 Back to Instruction Part to Whole Ratio

Rate A ratio that compares quantities in different units. One minute for every 60 seconds. min 1 2 3 sec 60 120 180 $8 per adult movie ticket. adults 1 2 3 $ 8 16 24 Expect to drive 35 miles for every hour you drive. Back to Instruction Rate Ratio A comparison of two or more values. Can be written as a fraction, decimal, percent, or with a colon, the word "to" or the words "out of". Dr. Opinions Agree 4 out of 5 4 5.8 4 to 1 4:1 80% Disagree 1 out of 5 1 5.2 1 to 4 1:4 20% Back to Instruction Ratio

Simplest Form When the GCF of both parts of a ratio is one. 4 12 4 = 1 4 3 10 to 25 Both are divisible by 5 = 2 to 5 3 out of is the same as 1out of 9 3 Back to Instruction Simplest Form Unit Rate A comparison of two measurements when one of the terms has a value of 1. One minute for every 60 seconds. 1 min:60 sec $8 per adult movie ticket. $8 1 adult 35 miles per 1 hour Back to Instruction Unit Rate

Tape Diagram A visual model that uses rectangles to represent the parts of a ratio. 0 1 2 3 4 5 0% 20% 40% 60% 80% 100% 2 1/ 2 miles 4 = 80% $14 + $14 + $14 = $42 5 Back to Instruction Tape Diagram Standards for Mathematical Practices MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit. Math Practices