Relationships Between Quantities 2014-10-09 www.njctl.org Slide 3 - PDF document

Slide 1 / 64 Slide 2 / 64 Algebra I Relationships Between Quantities 2014-10-09 www.njctl.org Slide 3 / 64 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 4 / 64 Vocabulary words are identified with a dotted underline. Sometimes when you subtract the fractions, you find that you can't because the first numerator is smaller than the second! When this happens, you need to regroup from the whole number. (Click on the dotted underline.) How many thirds are in 1 whole? How many fifths are in 1 whole? How many ninths are in 1 whole? The underline is linked to the glossary at the end of the Notebook. It can also be printed for a word wall. Slide 5 / 64 The charts have 4 parts. 1 Factor Vocab Word 2 Its meaning (As it is used A whole number A whole number that can divide into that multiplies with in the another number another number to lesson.) with no remainder. make a third number. 5 .1 R 15 3 5 3 16 3 is a factor of 15 3 is not a 3 x 5 = 15 factor of 16 3 Back to 3 and 5 are 4 Instruction factors of 15 Examples/ Link to return to the Counterexamples instructional page. Slide 6 / 64 Relationships Between Different Units of Measurement Return to Table of Contents

Slide 7 / 64 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 8 / 64 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 9 / 64 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 10 / 64 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 ratio of . Slide 11 / 64 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 12 / 64 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 13 / 64 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. £1.4 1L $1.56 x x = ? £1 .26gal 1L Notice that they are set up so that the labels that are not needed are diagonal from each other. Slide 14 / 64 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 = ? £1 .26gal 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 15 / 64 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 16 / 64 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 x14 168 x = = 3.36 50 1 X 50 = 3.36 cupcakes per customer Click to reveal proportion and answer Slide 17 / 64 1 Is this the correct conversion to convert 13 pints to gallons? (There are 8 pints in a gallon.) x Answer True False Slide 18 / 64 2 Which expression correctly shows how to convert 50 liters per minute into milliliters per second? A Remember that unwanted Hint units should cancel B Answer C

Slide 19 / 64 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 Slide 20 / 64 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 Slide 21 / 64 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 22 / 64 Graphs Let's try one! Click on the house below Stop the video after 1:08 Slide 23 / 64 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 24 / 64 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 25 / 64 Graphs Good, now what's next? Slide 26 / 64 Graphs Now we need to label the axes. feet time (in seconds) Slide 27 / 64 Graphs Now it's time to plot our data. He then went What did you down until he estimate his reached a landing starting height at second 5, then another landing at to be? feet second 8 and 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 28 / 64 Graphs So, let's compare our graph to the one in the video. Go back to the clip and watch until the end this time. Slide 29 / 64 5 A man climbs a ladder, stops at the top and works for awhile, descends the ladder and then puts it away in his basement. Which graph correctly depicts this situation? B A feet feet minutes minutes Answer C D minutes minutes feet feet Slide 30 / 64 6 Which of the following situations could match the graph? A A tomato plant grows at a steady rate, inches slows down and then dies. Answer B A tomato plant grows at a steady rate, slows down and then grows again. weeks C A tomato plant grows at a steady pace, then grows very quickly, then slows. D A tomato plant never sprouts.