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