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Chapter 3 Ratios and Rates (Part 2) Day….. 1. Introducing Rates 2. Graphing Rate of Change 3. Unit Rates 4. Pop Quiz Day 1 Bell Work Walt can mow 500ft2 in10 minutes. If he does not slow down, how long will it take him to mow his parents lawn that measures 3,500ft2? Justify your Response Vocabulary • Rate – A ratio comparing two quantities with different kinds of units. (Example: 4 tires: 1 car) • Unit Rate – a rate that is simplified so that it has a denominator of one. (Example: 5 1 ℎ ) • Ratio – A comparison of two quantities by division. (Example: a:b, a to b, ) • Equivalent Ratio – ratios the express the same relationship between two quantities. (Example: 10:15 is equivalent to 2:3 and 20:30) • Scaling – to multiply or divide two related quantities by the same number. (Example: 4 20 x 2 20 = 80 40 ) • Ratio Table – a table with columns filled with pairs of numbers that have the same ratio. Nails Used 5 10 15 Example: Shelves Hung 1 2 3 I Can…. Identify and determine equivalent rates. Introducing Rates Essential Understanding: • A rate is a ratio that compares two quantities with different kinds of units. Examples: 1) Driving 120 miles in two hours. 2) Paying $2.49 per gallon. 3) Reading 15 pages in 20 minutes. 4) Making $15 an hour. • Because rates compare quantities with different units, the units must be included when writing or solving rates. Example: • Just like before we must be careful to write the units (labels) in the order they are given or answer the question in the order the units are asked. Example: Introducing Rates Essential Understanding: • Because rates are ratios (just like fractions are ratios) all the rules and procedures for ratios apply. Such as….. Rates can be written in three forms Example: Rates can be scaled up and down to generate equivalent rates or determine an unknown variable. Example: You can also determined if rates are equivalent by finding their cross products, unit rates, or simplest form. Example: Watch This • http://learnzillion.com/lessons/839understand-rates-as-a-type-of-ratio (6 minutes) • http://learnzillion.com/lessons/614-solve-rateproblems-using-multiplicative-reasoning (7 minutes) Practice Clear your desk of everything except for a pencil and a calculator. Wrap it Up • Review • Questions • Exit Tickets Day 2 Bell Work Mark works in a factory where he is paid buy the piece to put together roof vents. He clocked himself one day and found he could make one roof vent in 20 minutes. If he works an 8 hour shift, how many roofs vents can he make in one day? How many vents can he make it two days? A week? Homework Check Vocabulary • Rate – A ratio comparing two quantities with different kinds of units. (Example: 4 tires: 1 car) • Unit Rate – a rate that is simplified so that it has a denominator of one. (Example: 5 1 ℎ ) • Ratio – A comparison of two quantities by division. (Example: a:b, a to b, ) • Equivalent Ratio – ratios the express the same relationship between two quantities. (Example: 10:15 is equivalent to 2:3 and 20:30) • Scaling – to multiply or divide two related quantities by the same number. (Example: 4 20 x 2 20 = 80 40 ) • Ratio Table – a table with columns filled with pairs of numbers that have the same ratio. Nails Used 5 10 15 Example: Shelves Hung 1 2 3 I Can…. Determine unit rates and plot the rate of change on a graph to determine an unknown variable. Unit Rates Essential Understanding: • A unit rate is a rate that has been simplified to a denominator of 1. Example: • Remember a rate is a ratio and it must be scaled down by division (not subtraction) to find its simplest form. Example: • However, the quickest way to determine a unit rate is to divide the numerator by the denominator and place the quotient over a 1. Example: Watch This • http://learnzillion.com/lessons/840-createunit-rate-using-diagram (5 Minutes) • http://learnzillion.com/lessons/841-create-unitrate-using-tape-diagram (5 minutes) Rate of Change Essential Understanding: • A line graph can be used to organize and illustrate equivalent rates. This is preferable to a ratio table, when illustrating rate of change. Such as changes over time, speed, distance, and profit/loss ($). Please open your book to page 162 Watch This • http://learnzillion.com/lessons/615-graphingrate-problems-using-a-table (7 minutes) Practice Take out your white boards. Wrap it Up • Review • Questions • Exit Tickets Day 3 Bell Work A store sold 255 DVDs in 5 days. If sales continue at this rate, how many DVDs can the expect to sell by the 10th day? 15th day? 30th day? Graph the rate of change for each day given on the provided graph card. Homework Check Vocabulary • Rate – A ratio comparing two quantities with different kinds of units. (Example: 4 tires: 1 car) • Unit Rate – a rate that is simplified so that it has a denominator of one. (Example: 5 1 ℎ ) • Ratio – A comparison of two quantities by division. (Example: a:b, a to b, ) • Equivalent Ratio – ratios the express the same relationship between two quantities. (Example: 10:15 is equivalent to 2:3 and 20:30) • Scaling – to multiply or divide two related quantities by the same number. (Example: 4 20 x 2 20 = 80 40 ) • Ratio Table – a table with columns filled with pairs of numbers that have the same ratio. Nails Used 5 10 15 Example: Shelves Hung 1 2 3 I Can…. Solve unit rate problems including those involving unit pricing and constant speed. Station Rotations 1. Write your exit ticket. 2. Pack up everything but a pencil and a calculator. 3. You will have 15 minutes per station 1st Rotation 2nd Rotation 3rd Rotation 4th Rotation Computer Station • http://learnzillion.com/lessons/842-define-unitrate-using-double-number-line • http://learnzillion.com/lessons/613-solve-rateproblems-using-double-number-lines • http://learnzillion.com/lessons/612-solve-formissing-values-in-rate-problems-using-a-table (6 minutes per video) Wrap it Up • Review • Questions • Exit Tickets Day 4 Bell Work 1. A 5lb sack of potatoes cost $4.32. An 8lb sack of potatoes cost $6.78. Which is the better deal? 1. Jessie says she will charge Jim $45.00 for 3 hours of tutoring. Mark says he will charge Jim $90.00 for 5 hours of tutoring. Who offers Jim the better hourly rate of pay? Homework Check Vocabulary • Rate – A ratio comparing two quantities with different kinds of units. (Example: 4 tires: 1 car) • Unit Rate – a rate that is simplified so that it has a denominator of one. (Example: 5 1 ℎ ) • Ratio – A comparison of two quantities by division. (Example: a:b, a to b, ) • Equivalent Ratio – ratios the express the same relationship between two quantities. (Example: 10:15 is equivalent to 2:3 and 20:30) • Scaling – to multiply or divide two related quantities by the same number. (Example: 4 20 x 2 20 = 80 40 ) • Ratio Table – a table with columns filled with pairs of numbers that have the same ratio. Nails Used 5 10 15 Example: Shelves Hung 1 2 3 I Can…. • Relate ratios and rates to the multiplication and division of fractions. • Look at my answer to check that I answered what was asked and see if my answer makes sense. pOp Quiz • Take out a pencil and a calculator. • Clear your desk of everything else. Let’s Review Complete Chapter Study Guide Wrap it Up • Review • Questions • Exit Tickets Day 5 No School I Can…. Use ratio and rate reasoning to solve realworld and mathematical problems Bell Work 1. Mr. Vanderson drove 110 miles in 2 hours. How fast did Mr. Vanderson drive? 2. Nikki can bounce a basket ball 900 times in 20 minutes. How may times can Nikki bounce a basketball in one minute. 3. Dakota walked 12 blocks to his uncle’s house in 30 minutes. How many minutes did it take Dakota to walk 1 block? Vocabulary • Rate – A ratio comparing two quantities with different kinds of units. (Example: 4 tires: 1 car) • Unit Rate – a rate that is simplified so that it has a denominator of one. (Example: 5 1 ℎ ) • Ratio – A comparison of two quantities by division. (Example: a:b, a to b, ) • Equivalent Ratio – ratios the express the same relationship between two quantities. (Example: 10:15 is equivalent to 2:3 and 20:30) • Scaling – to multiply or divide two related quantities by the same number. (Example: 4 20 x 2 20 = 80 40 ) • Ratio Table – a table with columns filled with pairs of numbers that have the same ratio. Nails Used 5 10 15 Example: Shelves Hung 1 2 3