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Are YOU Ready , Complete these exercises to review skills you will need Personal. for this module Math Trainer, Online Practice, Graph Ordered Pairs First Quadrant my hrw com and Help. y, EXAMPLE, 10 To graph A 2 7 start at the origin . Move 2 units right , 8, A Then move 7 units up , 6 Graph point A 2 7 . 4, 2, x, O 2 4 6 8 10, Graph each ordered pair on the coordinate plane above .

1 B 9 6 2 C 0 2 3 D 6 10 4 E 3 4 , Write Equivalent Fractions. 14 2 28 Multiply the numerator and denominator by the. EXAMPLE , 21, 14, , 21 2, , 42 same number to find an equivalent fraction . 7 Divide the numerator and denominator by the, 14. , 21, 14, , 21 7, 23, same number to find an equivalent fraction . Write the equivalent fraction , 6 , 5 4 , 6 1 , 7 9 .

8 , 8 32 6 12 8 56 12 4, 5 , 9 25 5 , 10 20 36 , 11 12 20 . 12 10, 9 6 45 36, Multiples Houghton Mifflin Harcourt Publishing Company. EXAMPLE List the first five multiples of 4 , 4 1 4. 4 2 8 Multiply 4 by the numbers 1 2 , 4 3 12 3 4 and 5 . 4 4 16, 4 5 20, List the first five multiples of each number .

13 3 14 7 15 8,170 Unit 3, Reading Start Up Vocabulary. Review Words, Visualize Vocabulary equivalent ratios razones. equivalentes , Use the words to complete the graphic factor factor . Comparing Unit Rates graph gr fica , pattern patr n . Single item, point punto , rate tasa , ratio raz n .

unit unidad , Rate in which the unit rate tasa unitaria . Ratio of two quantities that, second quantity is, have different units. one unit, Preview Words, conversion factor factor. de conversi n , proportion proporci n , Numbers that follow a rule scale escala . scale drawing dibujo a, escala , Understand Vocabulary.

Complete the sentences using the preview words , 1 A is a rate that compares two. equivalent measurements , 2 In a scale drawing the describes how the. dimensions in the actual object compare to the dimensions in the. drawing , Houghton Mifflin Harcourt Publishing Company. Active Reading, Tri Fold Before beginning the module create. a tri fold to help you learn the concepts and, vocabulary in this module Fold the paper into.

three sections Label one column Rates and, Ratios the second column Proportions and. the third column Converting Measurements , Complete the tri fold with important vocabulary . examples and notes as you read the module , Module 7 171. GETTING READY FOR, Applying Ratios and Rates, Understanding the standards and the vocabulary terms in the standards. will help you know exactly what you are expected to learn in this module . 6 RP 3,Use ratio and rate reasoning What It Means to You.

to solve real world and, You will use ratios and rates to solve real world. mathematical problems e g , problems such as those involving proportions . by reasoning about tables of,equivalent ratios tape diagrams EXAMPLE 6 RP 3. double number line diagrams , The distance from Austin to Dallas is about 200 miles How far. or equations 1 in , apart will these cities appear on a map with the scale of .

50 mi,Key Vocabulary 1 inch inches, , 50 miles, , 200 miles. Write the scale as a unit rate ,ratio raz n , A comparison of two quantities. 1 inch 4 inches, by division , 200 is a common denominator . 50 miles 4 200 miles,rate tasa , A ratio that compares two 4. quantities measured in, different units Austin and Dallas are 4 inches apart on the map .

6 RP 3d,Use ratio reasoning to convert, What It Means to You. Houghton Mifflin Harcourt Publishing Company Image Credits Getty Images. measurement units manipulate You will use unit rates to convert measurement units . and transform units appropriately, EXAMPLE 6 RP 3d. when multiplying or dividing,quantities The Washington Monument is about 185. yards tall This height is almost equal to the, Key Vocabulary length of two football fields About how. unit rate tasa unitaria many feet is this , A rate in which the second 3 ft.

quantity in the comparison is 185 yd , 1 yd, one unit 185 yd 3 ft. , 1, , 1 yd, 555 ft, The Washington Monument is about 555 feet tall . Visit my hrw com, to see all CA, Common Core, Standards. explained , my hrw com,172 Unit 3, LESSON, Ratios Rates Tables 6 RP 3a. 7 1 and Graphs, Make tables of equivalent ratios, relating quantities with whole.

number measurements find missing, values in the tables and plot the. pairs of values on the coordinate, plane Use tables to compare. ratios Also 6 RP 3 6 RP 3b, ESSENTIAL QUESTION, How can you represent real world problems involving ratios and. rates with tables and graphs , EXPLORE ACTIVITY 1. 6 RP 3 6 RP 3a, Finding Ratios from Tables, Students in Mr Webster s science classes are doing an experiment that requires.

250 milliliters of distilled water for every 5 milliliters of ammonia The table. shows the amount of distilled water needed for various amounts of ammonia . Ammonia mL 2 3 3 5 5, Distilled water mL 100 200 250. A Use the numbers in the first column of the table to write a ratio of. distilled water to ammonia , B How much distilled water is used for 1 milliliter of ammonia . Use your answer to write another ratio of distilled water to ammonia . C The ratios in A and B are equivalent not equivalent . D How can you use your answer to B to find the amount of distilled Math Talk. Mathematical Practices, water to add to a given amount of ammonia How is the amount of distilled. water in each mixture, related to the amount of, Houghton Mifflin Harcourt Publishing Company. ammonia , E Complete the table What are the equivalent ratios shown in the table .

100 , 250, 200 , 2 3 3 5 5, Reflect, 1 Look for a Pattern For every 1 milliliter of ammonia there are. milliliters of distilled water So for 6 milliliters of. ammonia milliliters of distilled water must be added . Lesson 7 1 173, EXPLORE ACTIVITY 2, 6 RP 3a,Graphing with Ratios. A Copy the table from Explore Activity 1 that shows the amounts of. ammonia and distilled water , Ammonia mL 2 3 3 5 5. Distilled 100 200 250, water mL , B Write the information in the table as ordered pairs Use the. Distilled Water mL , amounts of ammonia as the x coordinates and the amounts of 300 5 250 .

distilled water as the y coordinates 200, 2 3 3 5 200 5 250 100. Graph the ordered pairs Because fractions and decimals can O 2 4 6. represent amounts of chemicals connect the points Ammonia mL . Describe your graph , C For each ordered pair that you graphed write the ratio of the. y coordinate to the x coordinate , D The ratio of distilled water to ammonia is . 1, How are the ratios in, C related to this ratio . E The point 2 5 125 is on the graph but not in the table The ratio of the. y coordinate to the x coordinate is How is this ratio related to. the ratios in C and D , 2 5 milliliters of ammonia requires milliliters of distilled water .

F Conjecture What do you think is true for every point on the graph . Houghton Mifflin Harcourt Publishing Company,Reflect. 2 Communicate Mathematical Ideas How can you use the graph to find. the amount of distilled water to use for 4 5 milliliters of ammonia . 174 Unit 3, Representing Rates with, Tables and Graphs. You can use tables and graphs to represent real world problems involving. equivalent rates Math On the Spot, my hrw com, EXAMPL 1. EXAMPLE 6 RP 3a 6 RP 3b, An express train travels from Webster Webster. to Washington D C at a constant es, mil, speed and makes the trip in 2 hours 120.

A Make a table to show the distance Animated, Math. the train travels in various amounts my hrw com, of time . STEP 1 Write a ratio of distance, Washington D C . to time to find the rate , distance , 60 miles 60 miles per hour. 120 miles , time 2 hours 1 hour, STEP 2 Use the unit rate to make a table .

Time h 1 2 3 4 5, Distance mi 60 120 180 240 300, B Graph the information from the table . y, Write ordered pairs with time as the x coordinate 300. Distance mi , and distance as the y coordinate 240. 1 60 2 120 3 180 4 240 5 300 180, 120 2 120 , Graph the ordered pairs Fractions and decimals 60. x, can represent times and distances so connect, O 1 2 3 4 5.

the points , Time h , C Use the graph to find how long the train takes. Houghton Mifflin Harcourt Publishing Company, to travel 90 miles . The point 1 5 90 is on the graph so the train takes 1 5 hours . YOUR TURN 40, Water used gal , 3 A shower uses 12 gallons of water in 3 minutes 32. Complete the table and the graph Suppose the 24, shower used 32 gallons of water How long did it 16. take 8, Personal, O, Math Trainer, 2 4 6 8 10, Time min 2 3 4 6 Online Practice.

Time min and Help, Water used gal 20 my hrw com, Lesson 7 1 175. Guided Practice, 1 Science The ratio of oxygen atoms to sulfur 2 Use the table in Exercise 1 to graph the. atoms in sulfur dioxide is always the same relationship between sulfur atoms and. The table shows the numbers of atoms oxygen atoms Because numbers of atoms. in different quantities of sulfur dioxide must be whole numbers do not connect the. Complete the table Explore Activity 1 points Explore Activity 2 . Sulfur atoms 6 9 21 60, Oxygen atoms, 48, Oxygen 12 54. atoms 36, 24, What are the equivalent ratios shown in the. 12, table , O 6 12 18 24 30, Sulfur atoms, 3 Stickers are made with the same ratio of 4 Graph the relationship between the width.

length to width A sticker 2 inches wide has and the length of the stickers in Exercise 3 . a length of 4 inches Complete the table Explore Activity 2 . Explore Activity 1 , 20, Width in 2 4 7 Length in 16. 12, Length in 4 16, 8, 4, What are the equivalent ratios shown in the. table O 2 4 6 8 10, Width in , 5 Five boxes of candles contain a total of 60 candles 120. Each box holds the same number of candles Complete. 96, the table and the graph Suppose you have 84 candles . Candles, 72, How many boxes is that Example 1 , 48.

Boxes 5 8 24, Houghton Mifflin Harcourt Publishing Company. Candles 60 120 O 2 4 6 8 10, Boxes, ESSENTIAL QUESTION CHECK IN. 6 How do you represent real world problems involving ratios or rates. visually ,176 Unit 3, Name Class Date, 7 1 Independent Practice Personal. Math Trainer, Online Practice, 6 RP 3 6 RP 3a 6 RP 3b and Help. my hrw com, The table shows information about the number of sweatshirts sold and the.

money collected at a fundraiser for school athletic programs Use the table. for Exercises 7 12 , Sweatshirts sold 3 5 8 12, Money collected 60 180. 7 Find the rate of money collected per sweatshirt sold Show your work . 8 Use the unit rate to complete the table , 9 Explain how to graph information from the table . 10 Write the information in the table as ordered pairs Graph the. relationship from the table 280, Money Collected . 240, 200, 11 What If How much money would be collected if 160. 24 sweatshirts were sold Show your work , Houghton Mifflin Harcourt Publishing Company.

120, 80, 40, O 2 4 6 8 10 12 14, Sweatshirts Sold. 12 Analyze Relationships Does the point 5 5 110 make sense in this. context Explain , Lesson 7 1 177, 13 Communicate Mathematical Ideas The table. Time h 1 2 3 4 5, shows the distance Mindy drove on one day of. her vacation Find the distance Mindy would have Distance mi 55 110 165 220 275. gone if she had driven for one more hour at the, same rate Explain how you solved the problem . Use the graph for Exercises 14 15 , 70, 14 What number of weeks corresponds to 56 days Explain your reasoning 56.

Time days , 42, 28, 15 Represent Real World Problems What is a real life relationship that 14. can be described by the graph , O 2 4 6 8 10, Time weeks . FOCUS ON HIGHER ORDER THINKING Work Area, distance. 16 Make a Conjecture Complete the table Then find the rates . time, and, time, , distance, , Time min 1 2 5 distance. , time, , Distance m 25 100, time, , distance, , time.

a Are the , distance, rates equivalent Explain , b Suppose you graph the points time distance and your friend graphs. distance time How would your graphs be different . Houghton Mifflin Harcourt Publishing Company, 17 Communicate Mathematical Ideas To graph a rate or ratio from a table . how do you determine the scales to use on each axis . 178 Unit 3, LESSON, Applying Ratio and 6 RP 3, 7 2 Rate Reasoning. Use ratio and rate reasoning, to solve real world and. mathematical problems , e g by reasoning about tables of.

equivalent ratios tape diagrams , double number line diagrams or. equations Also 6 RP 3b, ESSENTIAL QUESTION, How can you solve proble. If a chef needs more or less of a dish he can use ratios to scale the recipe up or down Using proportional reasoning the chef keeps the ratios of all ingredients constant LESSON 7 1 Ratios Rates Tables and Graphs 6 RP 3 6 RP 3a 6 RP 3b LESSON 7 2 Applying Ratio and Rate Reasoning 6 RP 3 6 RP 3b LESSON 7 3 Converting Within Measurement

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