RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
warm-up
1) My brother is 72 inches tall. Write his height in feet. Write his height in yards.
2) My little sister is 36 inches tall. Write her height in feet. Write her height in yards.
3) My teenage sister is 54 inches tall. How many yards is that?
4) I am 48 inches tall. How many feet tall am I?
2) My little sister is 36 inches tall. Write her height in feet. Write her height in yards.
3) My teenage sister is 54 inches tall. How many yards is that?
4) I am 48 inches tall. How many feet tall am I?
mini lesson - independent work/share out/discussion
1. A ladder is leaning against the side of a building. Each time I step from one rung to the next, my foot moves 6 inches closer to the building and 8 inches further from the ground. The base of the ladder is 9 ft from the wall. How far up the wall does the ladder reach?
2. To buy a ticket for a weekly state lottery, a person selects 6 integers from 1 to 36, the order not being important. There are 1,947,792 such combinations of six digits. Alex and nine friends want to win the lottery by buying every possible ticket (all 1,947,792 combinations), and plan to spend 16 hours a day doing it. Assume that each person buys one ticket every five seconds. What do you think of this plan? Can the project be completed within a week?
3. The Millers must make a 70-mile Thanksgiving trip to visit their grandparents. Pat Miller believes in driving at a steady rate of 50 miles per hour.
a) With Pat in the driver’s seat, how much time will the trip take?
b) How many miles will the Millers travel in 18 minutes?
c) Write an expression for the number of miles they will cover in minutes of driving.
d) After minutes of driving, how many miles remain to be covered?
2. To buy a ticket for a weekly state lottery, a person selects 6 integers from 1 to 36, the order not being important. There are 1,947,792 such combinations of six digits. Alex and nine friends want to win the lottery by buying every possible ticket (all 1,947,792 combinations), and plan to spend 16 hours a day doing it. Assume that each person buys one ticket every five seconds. What do you think of this plan? Can the project be completed within a week?
3. The Millers must make a 70-mile Thanksgiving trip to visit their grandparents. Pat Miller believes in driving at a steady rate of 50 miles per hour.
a) With Pat in the driver’s seat, how much time will the trip take?
b) How many miles will the Millers travel in 18 minutes?
c) Write an expression for the number of miles they will cover in minutes of driving.
d) After minutes of driving, how many miles remain to be covered?
team challenge
Currency Exchange
Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars (at a rate of $1.02 CDN per $1 US). On the way home from the bank, Joe’s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos (at a rate of 10.8 pesos per $1 CDN). How many Mexican pesos did Joe get?
Converting Square Units
Jada has a rectangular board that is 60 inches long and 48 inches wide.
The board has an area of 48 in × 60 in = 2,880 square inches .
If I divide the area by 12, I can find out the area in square feet.
So the area of the board is 2,880 ÷ 12 = 240 square feet .
What went wrong with Jada's reasoning? Explain.
Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars (at a rate of $1.02 CDN per $1 US). On the way home from the bank, Joe’s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos (at a rate of 10.8 pesos per $1 CDN). How many Mexican pesos did Joe get?
Converting Square Units
Jada has a rectangular board that is 60 inches long and 48 inches wide.
- How long is the board measured in feet? How wide is the board measured in feet?
- Find the area of the board in square feet.
- Jada said,
The board has an area of 48 in × 60 in = 2,880 square inches .
If I divide the area by 12, I can find out the area in square feet.
So the area of the board is 2,880 ÷ 12 = 240 square feet .
What went wrong with Jada's reasoning? Explain.