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7.RP.1 Anticipation and Goals for Unit Rate Learning Cycle Goals: 1. 2. 3. 4. Identify unit rate Compute unit rate. Compare and contrast unit rate Apply implications of density as a unit rate Development anticipation: Calculation mistakes Students will get the units confused Missed labeling Put as a ratio but denominator not a one Attempt to describe a unit rate where there is no proportion. Solidify anticipation: Measurement issuers Redirection/connection between one problem and the next. Making the jump in reasoning in order to solve Archimedes problem Practice anticipation: Candy bars- 2 for 50 cents or 3 for dollar ounces or bar as unit discussion. Movie ticket discount when 12th ticket purchased Pesos exchanged reversed variables. Remembering unit rate is one. Which is better? 1. There are three stages of a 100 meter race: a start, middle, and finish. When reviewing the video it was revealed that at 10 meters 1 second had elapsed. At 50 meters 5 seconds had elapsed, and at 100 meters 10 seconds had elapsed. What would you anticipate the elapsed time would be at 150 meters? Use a chart to justify your answer. 2. Sally is a runner trying to qualify for the summer Olympics in London. She completes her 100 meter dash in 10 seconds. a. What is her speed? b. Lorraine is attempting the 100 meter dash as well. She covers each meter in .3 seconds. Who is faster, Sally or Lorraine? 3. Peter is at the store and decides that he wants something sweet. When he goes to the candy aisle, he decides he either wants an almond joy or a Milkyway candy bar. The Almond joys are on sale for 50 cents each. The Milkways are on sale 3 for a dollar Which is the better buy? Justify your answer using a visual model. Would your decision change if Milkyways cost 65 cents each unless three were purchased together? 4. When we purchase gas to fill our cars, we typically are concerned with how many miles we can travel per gallon. However, airlines are concerned with how many gallons are used per mile. What would explain this difference in thinking? 5. A 767 jumbo jet was filled with 2000 gallons of fuel in anticipation of its 800 mile flight. Johnny claims the jet would have a unit rate of 2.5 miles per gallon. Is he right or wrong? Explain. Unit Rates in Density Part 1: For each substance, identify the unit rate of mass per volume. TYPE of CUBE CUBE MASS (g) CUBE VOLUME (cm3) 1.Acrylic 19.2 16.25 2. Aluminum 43.8 16.25 3. Brass 136.5 16.25 4.Pine (lighter wood-dark rings) 5.68 16.25 5.Poplar (lighter wood-light rings) 8.1 16.25 CUBE DENSITY (g/cm3) Part 2: Which object do you think is the most dense? Make a prediction, then describe a method you could use to find out. Object MASS (g) VOLUME (cm3) Substance 1 Substance 2 Substance 3 Substance 4 Substance 5 1. What do you notice about Substance 3 and 5? DENSITY (g/cm3) 2. What do you think this means? Archimedes was a famous early scientist in Greece who was approached by a King that suspected he had been cheated. He had given a gold smith a block of gold and asked him to make a crown from the gold. When the crown was delivered, the king suspected the goldsmith had kept some of the gold and used a junk metal to make up the missing mass. How could you tell if the crown was pure gold or not? Design a method and justify your answer. Unit Rate Practice 1. Granola comes in a 14 ounce box for $2.00 or a 72 ounce box for $9.00? Justify the better buy using a visual model. 2. Determine the missing number of grams of trail mix and explain how you know your answer is correct. Grams of Trail Mix Calories 50 150 150 450 300 900 500 1500 1350 3. Find the unit rate (per bead) if it costs 12 cents for 20 beads. Find the unit rate (per cent) if it costs 30 cents for 50 beads. (Be careful!) Are these rates the same? Convince me with a written explanation. 4. Gerardo is traveling to Mexico. The exchange rate is 3 Pesos per dollar. When he was returning home he exchanged his Pesos back into dollars. He exchanged 42.75 Pesos and got $125. Should he complain to a manager? What would be his justification, if he does? 5. Use the following table to determine the cost of 18 gallons of gas. Are you sure that your answer is correct? What makes you sure? Gallons of Gas 3 5 8 13 Cost 8.55 14.25 22.80 37.05 6. Use the table below to find the cost of one movie ticket. How did you obtain that cost? Movie Tickets Total Cost 2 4 5 10 8 16 12 20 If you were responsible for purchasing tickets for a group of 24, how much would you charge each member of the group, including yourself? 7. The current 100-meter dash world record is 9.58 seconds. A local sprinter ran 55 meters in 5.1 seconds at a recent competition. Will he threaten to break the 100-meter dash world record? Explain your reasoning. Learning Cycle on Unit Rates: Goal: Students will be able to compute unit rates Goal: Students will be able to apply implications of density as a unit rate Develop: Which is better? Solidify: Unit Rates in Density Practice: Unit Rate problems