Kidbridges

ESTIMATION
Print a worksheet for class

Group: Tisha, April, Damian, Jose, Kamika
Class: 7-2A
Date: October 12

Define Your Problem
Ms. T: What is your problem? Make sure the problem is quantitative. That is, the answer should be a number.

Group: Our problem is to find out how many cars can fit on the Brooklyn Bridge.

Ms. T: OK

Think About Your Problem
Ms. T: Can you get an exact answer? Or do you have to estimate? Explain your group's reason for your response. Remember , when we estimate, for now, we form an opinion about the answer to a problem based on incomplete or inexact information. This opinion will be an approximation, which we try to make as close to the correct answer as possible.

Group: We'll have to estimate. We don't have enough information yet to determine the exact answer. Damian says, "We're not even sure if there is an exact answer!"

Ms. T: Good thinking Damian, you've raised a complicated issue and we'll come back to that soon. What information would you need to come up with the correct answer?

Group: We'd need to know how big the bridge is, and we'd need to know how big the cars are.

Ms. T: Right! To be more precise, you need to know the length (L) and width (W), or number of lanes, of the bridge's roadway and the length of the vehicles. Are all vehicles the same size? What else would you need to know? Why don't you need to know how wide a car is?

Making an Estimate
Ms. T: What are your first guesses about the information you need?

Group: We think that the bridge is 5 miles long and it's as wide as a football field. A car is about 10 feet long.

Ms. T: How wide is a football field? Why 10 feet for the length of a car? I guess your car isn't a stretch limo! What I mean is, are your guesses within a reasonable range? Remember, a reasonable range means that your numbers are not so big or so small that they don't make sense. If your first guesses aren't reasonable, that's okay. The first step in making a guess into a good estimate is to define what a reasonable range is!

Relevant Fact: The longest bridge in the world is the Akashi-Kaikyo Bridge in Tokyo, it is 2.5 miles long.

Group: Uh oh!

Ms. T: What do you need to do next to improve your estimate? Remember, you want your estimate to be close to the correct answer.

Group: We had to really put our heads together on this one. Before we went to the real bridge we decided to imagine the bridge and the roadway in our minds. Isis said, "Let's draw it," so we did. Right away we saw that cars have to have space between them, and we have to count that space in our estimate. That means there's not going to be as many cars. Roland drew trucks and buses, but we're not even sure if they're allowed on the bridge. Help!! If some cars are buses, then how big is a car?

Ms. T: You really did a lot of good thinking. First, you'll need to get an average car length. That means you'll need to know what proportion of each type of vehicle is on the bridge. So you can compute a weighted average. You'll also need to know the average distance between vehicles. How can you find out what kinds of vehicles are allowed on the bridge before we actually go there? Can your group come up with a formula to express your estimate?

Group Response: That's not the hardest part! Here it is.
N = number of cars
n = number of lanes
L = length of roadway
C = average car length
S = average space between cars
So N=L/(C+S) x n

Ms. T: Now, calculate your final estimate? How will you check to see if it's a good one?

Group Response: It's only as good as the numbers in our formula. We have to get L, C and S right by looking at the real bridge and measuring things. We could also try to count the cars to see if we're right but we'd have to be up in a helicopter to see them all.

Ms. T: Right. L, C and S are your variables, and your result will only be as good as they are, even when your formula is correct. I don't think the Board of Education will pay for a helicopter ride! How else would you determine how many cars are actually on the bridge tomorrow? If you found out there were 1000 cars on the bridge and your formula gave you N = 1200 does that mean your calculation has an error in it? What if N = 800? Can your answer ever be completely exact? Or in some sense is it just if a certain set of conditions are true, then the answer is this one?

But now we're being philosophical as well as mathematical!!

BRIDGE STATISTICS: based on the opening of the bridge, 1893

Length of the bridge: 5,989 Feet
Length of the river span: 1,595.5 Feet
Length of each land span: 930 Feet
Length of the Brooklyn approach: 971 Feet
Length of the NY approach: 1562.5 Feet
Width of the bridge floor: 85 Feet




	ESTIMATION Print a worksheet for class Group: Tisha, April, Damian, Jose, Kamika Class: 7-2A Date: October 12 Define Your Problem Ms. T: What is your problem? Make sure the problem is quantitative. That is, the answer should be a number. Group: Our problem is to find out how many cars can fit on the Brooklyn Bridge. Ms. T: OK Think About Your Problem Ms. T: Can you get an exact answer? Or do you have to estimate? Explain your group's reason for your response. Remember , when we estimate, for now, we form an opinion about the answer to a problem based on incomplete or inexact information. This opinion will be an approximation, which we try to make as close to the correct answer as possible. Group: We'll have to estimate. We don't have enough information yet to determine the exact answer. Damian says, "We're not even sure if there is an exact answer!" Ms. T: Good thinking Damian, you've raised a complicated issue and we'll come back to that soon. What information would you need to come up with the correct answer? Group: We'd need to know how big the bridge is, and we'd need to know how big the cars are. Ms. T: Right! To be more precise, you need to know the length (L) and width (W), or number of lanes, of the bridge's roadway and the length of the vehicles. Are all vehicles the same size? What else would you need to know? Why don't you need to know how wide a car is? Making an Estimate Ms. T: What are your first guesses about the information you need? Group: We think that the bridge is 5 miles long and it's as wide as a football field. A car is about 10 feet long. Ms. T: How wide is a football field? Why 10 feet for the length of a car? I guess your car isn't a stretch limo! What I mean is, are your guesses within a reasonable range? Remember, a reasonable range means that your numbers are not so big or so small that they don't make sense. If your first guesses aren't reasonable, that's okay. The first step in making a guess into a good estimate is to define what a reasonable range is! Relevant Fact: The longest bridge in the world is the Akashi-Kaikyo Bridge in Tokyo, it is 2.5 miles long. Group: Uh oh! Ms. T: What do you need to do next to improve your estimate? Remember, you want your estimate to be close to the correct answer. Group: We had to really put our heads together on this one. Before we went to the real bridge we decided to imagine the bridge and the roadway in our minds. Isis said, "Let's draw it," so we did. Right away we saw that cars have to have space between them, and we have to count that space in our estimate. That means there's not going to be as many cars. Roland drew trucks and buses, but we're not even sure if they're allowed on the bridge. Help!! If some cars are buses, then how big is a car? Ms. T: You really did a lot of good thinking. First, you'll need to get an average car length. That means you'll need to know what proportion of each type of vehicle is on the bridge. So you can compute a weighted average. You'll also need to know the average distance between vehicles. How can you find out what kinds of vehicles are allowed on the bridge before we actually go there? Can your group come up with a formula to express your estimate? Group Response: That's not the hardest part! Here it is. N = number of cars n = number of lanes L = length of roadway C = average car length S = average space between cars So N=L/(C+S) x n Ms. T: Now, calculate your final estimate? How will you check to see if it's a good one? Group Response: It's only as good as the numbers in our formula. We have to get L, C and S right by looking at the real bridge and measuring things. We could also try to count the cars to see if we're right but we'd have to be up in a helicopter to see them all. Ms. T: Right. L, C and S are your variables, and your result will only be as good as they are, even when your formula is correct. I don't think the Board of Education will pay for a helicopter ride! How else would you determine how many cars are actually on the bridge tomorrow? If you found out there were 1000 cars on the bridge and your formula gave you N = 1200 does that mean your calculation has an error in it? What if N = 800? Can your answer ever be completely exact? Or in some sense is it just if a certain set of conditions are true, then the answer is this one? But now we're being philosophical as well as mathematical!! BRIDGE STATISTICS: based on the opening of the bridge, 1893 Length of the bridge: 5,989 Feet Length of the river span: 1,595.5 Feet Length of each land span: 930 Feet Length of the Brooklyn approach: 971 Feet Length of the NY approach: 1562.5 Feet Width of the bridge floor: 85 Feet