Understand ratio concepts and use ratio reasoning to solve problems.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1 Understand and describe a ratio relationship between two quantities.
Bus Tour (Ratios)
Donut Box (Ratios)
James is responsible for getting the donuts for the staff meeting this morning. He knows he needs one box with 24 donuts, chocolate and glazed in a 1:3 ratio, and another box with 36 donuts, glazed, cinnamon, and chocolate in a ratio of 2:3:4. When Alberto walks in for the meeting, he realizes some donuts are already gone. Which ones have been taken?
Needed Information: The ratio of cinnamon to chocolate to glazed donuts is now 3:5:6.
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6.RP.2 Understand the concept of a unit rate associated with a ratio.
Penny Tower (Proportional Thinking)
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
a. Make tables of equivalent ratios.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
b. Solve unit rate problems.
Commute (Unit Rate with Speed?
Alberto, Sara, and Andrew take the train from Amsterdam to Paris. Alberto takes the slower train, which travels 120 km/h, and does not stop in Antwerp. Sara and James take the faster train, which travels 150 km/h, but stops in Antwerp. It takes the faster train 40 minutes to get to Antwerp from Amsterdam and will stop there for 30 minutes. Once it continues after the stop in Antwerp, does Sara and Andrew’s train catch Alberto’s train? When?
Cat Food (Unit Rate with Prices)
Dakar Rally (Unit Rate with Speed)
Welcome to the Dakar Rally, the world's most famous and most challenging rally race, racing across undeveloped terrains such as mountain passes and deserts. Driving hundreds of km a day, drivers and their vehicles are pushed to the limit. The rally tests their technique, mental and physical strength, mechanical skill, and experience to cover nearly 9,000 km in two weeks. More than half of the vehicles that begin the race fail to finish it, epitomizing the toughness of the rally. Stage 9 of this year's Dakar Rally covers a distance of 831 kilometers. Let's look at the virtual map to see the location of the teams in the race and their speeds. How long will it take each team to get to the finish?
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Distance Run (Unit Rate with Speed)
Today is marathon day at the local gym, a 12.5-mile run on a treadmill. Sara, Li, and Nia want to get on the leaderboard, so they set the treadmill at a steady pace and go for it. Based on their current pace, where will they rank on the leaderboard?
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Fastest (Unit Rate with Speed)
Li, James, and Alberto are on their way to tour London Stadium, the stadium in London that was used for track during the 2012 Olympics and is now home to West Ham United. Many references to the Olympics remain outside the stadium, including the track world records on a plaque next to one of the entrances. Who ran the fastest?
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Groceries (Unit Rate with Prices)
We all need groceries, but some of us go about it a little differently. Li and James are on a budget and want the cheapest option for the items they need. Which ones are the better deal?
Water Leak (Unit Rate with Measurements)
Andrew and James have a leak under the sink, so they place a 1-gallon bucket under it while they wait for the plumber. They placed the bucket under the leak at 9 a.m. When they returned to check on it, they found 30 fluid ounces of water in the bucket. If they don't empty the bucket now, what time do they need to return to empty it so it doesn't overflow?
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6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
c. Find a percent of a quantity as a rate per 100.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
d. Convert measurement units using rates.
Leaky Faucet (Unit Rates and Unit Conversion)
Sara and James are at their vacation home in the woods when Sara notices the hose bib on the side of the house is leaking water. The calcium buildup prevents the hose bib from completely closing. They could try to clean it or replace it. Sara wants to know how much water leaks out of this hose bib. James gets a stopwatch and measuring spoons and finds out 1 tsp leaks out of the hose bib every 6 minutes. How much water is that in a week, a month, a year?
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