Slide 1 / 82 Slide 2 / 82 Algebra I Relationships Between Quantities 2015-11-02 www.njctl.org Slide 3 / 82 Table of Contents Click on the topic to go to that section Relationships Between Different Units of Measurement. · Picking the Appropriate Unit of Measurement · Choosing the Appropriate Level of Accuracy · Glossary ·
Slide 3 (Answer) / 82 Table of Contents Click on the topic to go to that section Relationships Between Different Units of Measurement. · Vocabulary Words are bolded Teacher Notes Picking the Appropriate Unit of Measurement · in the presentation. The text box the word is in is then Choosing the Appropriate Level of Accuracy · linked to the page at the end of the presentation with the Glossary · word defined on it. [This object is a pull tab] Slide 4 / 82 Relationships Between Different Units of Measurement Return to Table of Contents Slide 5 / 82 Units You have probably seen a word problem like the following: While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal.
Slide 6 / 82 Word Problems As with all word problems, we will follow the 4 step process: Step 1 - Read the problem thoroughly, UNDERSTAND what it is they want you to find out. Step 2 - PLAN how you will solve the problem. Step 3 - SOLVE it! Step 4 - CHECK your answer. Is it reasonable, does it make sense? UPS Slide 7 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. Sonia wants to find out how the price of gas compares from England to the U.S. In order to find this out we will need to convert units. England uses metric measurement. The US uses a system called the Customary System. (Outside of the US it is referred to as the US Measurement System). Slide 8 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. We will also need to convert the currency since England uses pounds and the U.S. uses dollars so we can use the $1.56 ratio of £1
Slide 9 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. Use a proportion to solve this problem. First we have to create a ratio out of our initial value. £1.4 1L Slide 10 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. Remember, we want to change to dollars per gallon but that means we have to change both the top and the bottom. That also means we need two more ratios. 1L $1.56 and £1 .26gal Slide 11 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. Next multiply all three ratios together. 1L £1.4 $1.56 x x = ? .26gal £1 1L Notice that they are set up so that the labels that are not needed are diagonal from each other.
Slide 12 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. £1.4 1L $1.56 x x = ? .26gal £1 1L 1.4 x 1 x 1.56 2.184 = = $8.40 per gallon .26 1 x .26 x 1 Notice that all of the unwanted labels have been cancelled out. Slide 13 / 82 Units While traveling in England, Sonia noticed that the price of gas was 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 rate was £1 = $1.56. Set up and evaluate a conversion expression to find the equivalent price in dollars per gallon. Use the conversion factor 1 L = 0.26 gal. $8.40 per gallon Does your answer make sense? Liters are a much smaller quantity than gallons, .26 to be exact. The exchange rate of the 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 14 / 82 Proportion Try this! A cupcake shop sells an average of 14 dozen cupcakes a day to about 50 customers What is their average sales rate, in cupcakes per customer? **HINT: There are 12 units in a dozen. 12 x 14 168 12 14 doz. x = = = 3.36 1 doz. 50 customers 1 x 50 50 = 3.36 cupcakes per customer Click to reveal proportion and answer
Slide 15 / 82 1 Is this the correct conversion to convert 13 pints to gallons? (There are 8 pints in a gallon.) 8 pts. 13 pts. x 1 gal. x True False Slide 15 (Answer) / 82 1 Is this the correct conversion to convert 13 pints to gallons? (There are 8 pints in a gallon.) 8 pts. 13 pts. Answer x False 1 gal. x True False [This object is a pull tab] Slide 16 / 82 2 Which expression correctly shows how to convert 50 liters per minute into milliliters per second? 1 min 1 min 1000 ml Remember that A x x Hint unwanted units 50 liters 60 sec 1 liter should cancel 50 liters 1 min 1000 ml B x x 1 min 60 sec 1 liter 50 liters 60 sec 1000 ml C x x 1 min 1 min 1 liter
Slide 16 (Answer) / 82 2 Which expression correctly shows how to convert 50 liters per minute into milliliters per second? 1 min 1 min 1000 ml Remember that A x x Hint unwanted units 50 liters 60 sec 1 liter should cancel 50 liters 1 min 1000 ml B x x 1 min 60 sec Answer 1 liter B 50 liters 60 sec 1000 ml C x x 1 min 1 min 1 liter [This object is a pull tab] Slide 17 / 82 3 A car burns .85 gallons of gas per hour while idling. Express this rate in quarts per minute. Round your answer to the hundredths place. Remember to check to see if your answer is reasonable. Slide 17 (Answer) / 82 3 A car burns .85 gallons of gas per hour while idling. Express this rate in quarts per minute. Round your answer to the hundredths place. Remember to check to see if your answer is reasonable. Answer 0.06 quarts per minute [This object is a pull tab]
Slide 18 / 82 4 A police officer saw a car traveling at 1800 feet in 30 seconds. The speed limit is 55 mph. Was the person speeding? Yes No Slide 18 (Answer) / 82 4 A police officer saw a car traveling at 1800 feet in 30 seconds. The speed limit is 55 mph. Was the person speeding? Yes No Answer No [This object is a pull tab] Slide 19 / 82 Graphs Another important skill with units is being able to graph a 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.
Slide 20 / 82 Graphs Let's try one! Click on the house below Stop the video after 1:08 Slide 21 / 82 Graphs Now watch the video again but this time ask yourself the following questions: "How high do you think he was at the top of the stairs? How did you estimate that elevation?" "Were there intervals of time when his elevation wasn't changing? Was he still moving?" Click on the house below Stop the video after 1:08 Slide 22 / 82 Graphs Now we are ready to graph. Why do we need to know his height at the beginning? We need to come up with a scale and we need to know where to start our graph. Click to reveal. Let's use a scale of 0 to 40 feet with intervals of 10 feet for the y 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.
Slide 23 / 82 Graphs Good, now what's next? Slide 24 / 82 Graphs Now we need to label the axes. feet time (in seconds) Slide 25 / 82 Graphs Now it's time to plot our data. 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)
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