Factor Vocab Word 2 Its meaning Relationships Between (As it is - PDF document

Slide 1 / 64 Slide 2 / 64 Algebra I Relationships Between Quantities 2014-10-09 www.njctl.org Slide 3 / 64 Slide 4 / 64 Vocabulary words are identified with a Table of Contents dotted underline. click on the topic to go to that section Sometimes when you subtract the fractions, you find that you can't because the first Relationships Between Different Units of Measurement. · numerator is smaller than the second! When this happens, you need to regroup from the Picking the Appropriate Unit of Measurement · whole number. (Click on the dotted underline.) Choosing the Appropriate Level of Accuracy · How many thirds are in 1 whole? How many fifths are in 1 whole? Glossary · 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 Slide 6 / 64 The charts have 4 parts. 1 Factor Vocab Word 2 Its meaning Relationships Between (As it is used A whole number A whole number that can divide into that multiplies with in the Different Units of another number another number to lesson.) with no remainder. make a third number. Measurement 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 Return to Table factors of 15 Examples/ of Contents Link to return to the Counterexamples instructional page.

Slide 7 / 64 Slide 8 / 64 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 what it is they want you to find out. While traveling in England, Sonia noticed that the price of gas was 1. 4 pounds (£) per liter. She wondered how that compared Step 2 - Plan how you will solve the problem. 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 Step 3 - Solve it! gallon. Use the conversion factor 1 L = 0. 26 gal. Step 4 - Check your answer. Is it reasonable, does it make sense? UPS Slide 9 / 64 Slide 10 / 64 Units Units While traveling in England, Sonia noticed that the price of gas was 1. 4 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 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. 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 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. 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 We will also need to convert the currency since England uses to the U.S. pounds and the U.S. uses dollars so we can use the In order to find this out we will need to convert units. ratio of . 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 11 / 64 Slide 12 / 64 Units Units While traveling in England, Sonia noticed that the price of gas was 1. 4 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 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. 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 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. dollars per gallon. Use the conversion factor 1 L = 0. 26 gal. Remember, we want to change to dollars per gallon but that Use a proportion to solve this problem. means we have to change both the top and the bottom. First we have to create a ratio out of our initial value. That also means we need two more ratios. 1L $1.56 and £1.4 £1 .26gal 1L

Slide 13 / 64 Slide 14 / 64 Units Units While traveling in England, Sonia noticed that the price of gas was 1. 4 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 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. 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 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. dollars per gallon. Use the conversion factor 1 L = 0. 26 gal. £1.4 1L $1.56 Next multiply all three ratios together. x x = ? £1 .26gal 1L 1L £1.4 $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 they are set up so that the labels that are not needed are diagonal from each other. Notice that all of the unwanted labels have been cancelled out. Slide 15 / 64 Slide 16 / 64 Units Proportion Try this! 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 A cupcake shop sells an average of 14 dozen cupcakes a day to in Atlanta, where she lives. On that day, the exchange rate was £1 = $1. 56. about 50 customers What is their average sales rate, in cupcakes Set up and evaluate a conversion expression to find the equivalent price in per customer? dollars per gallon. Use the conversion factor 1 L = 0. 26 gal. **HINT: There are 12 units in a dozen. $8.40 per gallon = 12 x14 168 x = = 3.36 50 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 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. Click to reveal proportion and answer Slide 17 / 64 Slide 18 / 64 1 Is this the correct conversion to convert 13 pints to 2 Which expression correctly shows how to convert 50 liters per gallons? minute into milliliters per second? (There are 8 pints in a gallon.) A x Remember that unwanted Answer Hint units should cancel B True False Answer C

Slide 19 / 64 Slide 20 / 64 3 A car burns .85 gallons of gas per hour while idling. Express 4 A police officer saw a car traveling at 1800 feet in 30 seconds. this rate in quarts per minute. Round your answer to the The speed limit is 55 mph. Was the person speeding? hundredths place. Remember to check to see if your answer is reasonable. Yes No Answer Answer Slide 21 / 64 Slide 22 / 64 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 23 / 64 Slide 24 / 64 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 25 / 64 Slide 26 / 64 Graphs Graphs Good, now what's next? Now we need to label the axes. feet time (in seconds) Slide 27 / 64 Slide 28 / 64 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 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 29 / 64 Slide 30 / 64 5 A man climbs a ladder, stops at the top and works for awhile, 6 Which of the following situations could match the graph? descends the ladder and then puts it away in his basement. Which graph correctly depicts this situation? A A tomato plant grows at a steady rate, B A inches slows down and then dies. feet feet Answer minutes B A tomato plant grows at a minutes steady rate, slows down and Answer then grows again. weeks C D C A tomato plant grows at a minutes minutes steady pace, then grows very quickly, then slows. feet feet D A tomato plant never sprouts.