Slide 1 / 82 Slide 2 / 82 Algebra I Relationships Between Quantities 2015-11-02 www.njctl.org Slide 3 / 82 Slide 4 / 82 Table of Contents Click on the topic to go to that section Relationships Between Relationships Between Different Units of Measurement. · Different Units of Picking the Appropriate Unit of Measurement · Measurement Choosing the Appropriate Level of Accuracy · Glossary · Return to Table of Contents Slide 5 / 82 Slide 6 / 82 Units Word Problems As with all word problems, we will follow the 4 step process: You have probably seen a word problem like the following: Step 1 - Read the problem thoroughly, UNDERSTAND While traveling in England, Sonia noticed that the price of gas was 1.4 pounds (£) per liter. She wondered how that compared to what it is they want you to find out. the price of gas in Atlanta, where she lives. On that day, the exchange rate was £1 = $1.56. Set up and evaluate a Step 2 - PLAN how you will solve the problem. conversion expression to find the equivalent price in dollars per gallon. Step 3 - SOLVE it! Use the conversion factor 1 L = 0.26 gal. Step 4 - CHECK your answer. Is it reasonable, does it make sense? UPS
Slide 7 / 82 Slide 8 / 82 Units Units While traveling in England, Sonia noticed that the price of gas was While traveling in England, Sonia noticed that the price of gas was 1.4 pounds (£) per liter. She wondered how that compared to the 1.4 pounds (£) per liter. She wondered how that compared to the price of gas in Atlanta, where she lives. On that day, the exchange price of gas in Atlanta, where she lives. On that day, the exchange rate was £1 = $1.56. Set up and evaluate a conversion expression rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. factor 1 L = 0.26 gal. Sonia wants to find out how the price of gas compares from England to the U.S. We will also need to convert the currency since England uses pounds and the U.S. uses dollars so we can use the In order to find this out we will need to convert units. $1.56 ratio of England uses metric measurement. £1 The US uses a system called the Customary System. (Outside of the US it is referred to as the US Measurement System). Slide 9 / 82 Slide 10 / 82 Units Units While traveling in England, Sonia noticed that the price of gas was While traveling in England, Sonia noticed that the price of gas was 1.4 pounds (£) per liter. She wondered how that compared to the 1.4 pounds (£) per liter. She wondered how that compared to the price of gas in Atlanta, where she lives. On that day, the exchange price of gas in Atlanta, where she lives. On that day, the exchange rate was £1 = $1.56. Set up and evaluate a conversion expression rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. factor 1 L = 0.26 gal. Use a proportion to solve this problem. Remember, we want to change to dollars per gallon but that First we have to create a ratio out of our initial value. means we have to change both the top and the bottom. £1.4 That also means we need two more ratios. $1.56 1L 1L and £1 .26gal Slide 11 / 82 Slide 12 / 82 Units Units While traveling in England, Sonia noticed that the price of gas was While traveling in England, Sonia noticed that the price of gas was 1.4 pounds (£) per liter. She wondered how that compared to the 1.4 pounds (£) per liter. She wondered how that compared to the price of gas in Atlanta, where she lives. On that day, the exchange price of gas in Atlanta, where she lives. On that day, the exchange rate was £1 = $1.56. Set up and evaluate a conversion expression rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. factor 1 L = 0.26 gal. £1.4 1L $1.56 x x = ? Next multiply all three ratios together. .26gal £1 1L £1.4 1L $1.56 1.4 x 1 x 1.56 x 2.184 x = ? = = $8.40 per gallon .26gal £1 1L .26 1 x .26 x 1 Notice that they are set up so that the labels that are not needed Notice that all of the unwanted labels have been cancelled out. are diagonal from each other.
Slide 13 / 82 Slide 14 / 82 Units Proportion Try this! While traveling in England, Sonia noticed that the price of gas was A cupcake shop sells an average of 14 dozen cupcakes a day to 1.4 pounds (£) per liter. She wondered how that compared to the about 50 customers What is their average sales rate, in cupcakes price of gas in Atlanta, where she lives. On that day, the exchange per customer? rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion **HINT: There are 12 units in a dozen. factor 1 L = 0.26 gal. $8.40 per gallon 12 x 14 168 12 14 doz. x = = = 3.36 50 1 doz. 50 customers 1 x 50 Does your answer make sense? Liters are a much smaller = 3.36 cupcakes per customer quantity than gallons, .26 to be exact. The exchange rate of the Click to reveal proportion and answer pound is £1 for every $1.56, so it does make sense that the price per gallon should be more than it is per liter. About 4 times more. Slide 15 / 82 Slide 16 / 82 2 Which expression correctly shows how to convert 1 Is this the correct conversion to convert 13 pints to 50 liters per minute into milliliters per second? gallons? (There are 8 pints in a gallon.) 1 min 1 min 1000 ml Remember that A x x Hint unwanted units 50 liters 60 sec 1 liter 8 pts. 13 pts. should cancel x 1 gal. x 50 liters 1 min 1000 ml B x x True 1 min 60 sec 1 liter False 50 liters 60 sec 1000 ml C x x 1 min 1 min 1 liter Slide 17 / 82 Slide 18 / 82 4 A police officer saw a car traveling at 1800 feet in 30 3 A car burns .85 gallons of gas per hour while idling. seconds. The speed limit is 55 mph. Was the person Express this rate in quarts per minute. Round your speeding? answer to the hundredths place. Remember to check to see if your answer is reasonable. Yes No
Slide 19 / 82 Slide 20 / 82 Graphs Graphs Let's try one! Another important skill with units is being able to graph a Click on the house below situation with the appropriate scale and labels. On the following slides, we will look at some real life examples and examine the thought process behind creating graphs that are correct and meaningful. Stop the video after 1:08 Slide 21 / 82 Slide 22 / 82 Graphs Graphs Now watch the video again but this time ask yourself the Now we are ready to graph. following questions: Why do we need to know his height at the beginning? "How high do you think he was at the top of the stairs? How did you estimate that elevation?" We need to come up with a scale and we need to know where to start our graph. "Were there intervals of time when his elevation wasn't Click to reveal. changing? Was he still moving?" Let's use a scale of 0 to 40 feet with intervals of 10 feet for the y Click on the house below axis. What about the x axis? That should be the time it took him to come down the stairs. Let's use a scale of 0 to 15 with intervals of one. Click to reveal. Stop the video after 1:08 Slide 23 / 82 Slide 24 / 82 Graphs Graphs Good, now what's next? Now we need to label the axes. feet time (in seconds)
Slide 25 / 82 Slide 26 / 82 Graphs Graphs Now it's time to plot our data. So, let's compare our graph to the one in the video. Go back to the clip and watch until the end this time. He then went down until he What did you reached a landing estimate his at second 5, then starting height another landing at to be? second 8 and feet We will use 30 finally the bottom feet for this at second 12. example We will assume that each landing was 10 feet. time (in seconds) Slide 27 / 82 Slide 28 / 82 5 A man climbs a ladder, stops at the top and works for 6 Which of the following situations could match the graph? awhile, descends the ladder and then puts it away in his basement. Which graph correctly depicts this situation? A A tomato plant grows at inches a steady rate, slows down and then dies. B A feet feet B A tomato plant grows at a steady rate, slows weeks minutes minutes down and then grows again. C D C A tomato plant grows at a steady pace, then grows minutes minutes very quickly, then slows. feet feet D A tomato plant never sprouts. Slide 29 / 82 Slide 30 / 82 7 At which interval did the plant grow the most quickly? A weeks 0-4 B weeks 4-6 C weeks 6-8 Picking the Appropriate inches Unit of Measurement weeks Return to Table of Contents
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