1. Teacher Guide
This lesson is designed to teach kids to ask a critical thinking question that you can’t just put into a search box to solve. To do that, we encourage them with smaller questions that search can help them answer. Make sure that you read the notes for each slide: they not only give you teaching tips but also provide answers and hints so you can help the kids if they are having trouble.
Remember, you can always send feedback to the Bing in the Classroom team at You can learn more about the program at bing.com/classroom and follow the daily lessons on our Partners In Learning site.
Want to extend today’s lesson? Consider using Skype in the Classroom to arrange for your class to chat with another class in today’s location. And if you are using Windows 8, you can also use the Bing apps to learn more about this location and topic; the Travel and News apps in particular make great teaching tools.
Nell Bang-Jensen is a teacher and theater artist living in Philadelphia, PA. Her passion for arts education has led her to a variety of roles including developing curriculum for Philadelphia Young Playwrights and teaching at numerous theaters and schools around the city. She works with playwrights from ages four to ninety on developing new work and is especially interested in alternative literacies and theater for social change. A graduate of Swarthmore College, she currently works in the Artistic Department of the Wilma Theater and, in addition to teaching, is a freelance actor and dramaturg. In 2011, Nell was named a Thomas J. Watson Fellow and spent her fellowship year traveling to seven countries studying how people get their names.
This lesson is designed to teach the Common Core State Standard: Operations & Algebraic Thinking
CCSS.Math.Content.4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1
CCSS.Math.Content.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

2. How much longer is the Aizhai bridge than it is tall?
© Imaginechina/Corbis
Having this up as kids come in is a great settle down activity. You can start class by asking them for thoughts about the picture or about ideas on how they could solve the question of the day.

3. How much longer is the Aizhai bridge than it is tall?
China’s Aizhai Bridge stretches across a valley near Jishou, a city in Hunan province. Connecting two tunnels through the hills of the nearby Wuling Mountains, the Aizhai Bridge holds the distinct record of being the highest and longest tunnel-to-tunnel bridge in the world. The deck of the span is 1,150 above the valley floor. This picture was taken the day the bridge officially opened to traffic, on March 31, 2012.
Depending on time, you can either have students read this silently to themselves, have one of them read out loud, or read it out loud yourself.

4. How much longer is the Aizhai Bridge than it is tall?1
Image Search
Find an image of the Aizhai Bridge. Based on this picture, what would you estimate is the difference between its length and its height? 2
Web Search
What is the definition of a bridge? Could a bridge exist if it was taller than it is long? 3
Thinking
How could you use fractions to compare the Aizhai Bridge’s length and its height? 4
In comparing the length and height of the Aizhai Bridge, what operations might be helpful? What operations would probably not be helpful? 5
How could you write a formula to compare the length of the Aizhai Bridge to its height?
There are a couple of ways to use this slide, depending on how much technology you have in your classroom. You can have students find answers on their own, divide them into teams to have them do all the questions competitively, or have each team find the answer to a different question and then come back together. If you’re doing teams, it is often wise to assign them roles (one person typing, one person who is in charge of sharing back the answer, etc.)

5. How much longer is the Aizhai bridge than it is tall?5
Minutes
You can adjust this based on how much time you want to give kids. If a group isn’t able to answer in 5 minutes, you can give them the opportunity to update at the end of class or extend time.

6. How much longer is the Aizhai bridge than it is tall?1
Image Search
Find an image of the Aizhai Bridge. Based on this picture, what would you estimate is the difference between its length and its height? 2
Web Search
What is the definition of a bridge? Could a bridge exist if it was taller than it is long? 3
Thinking
How could you use fractions to compare the Aizhai Bridge’s length and its height? 4
In comparing the length and height of the Aizhai Bridge, what operations might be helpful? What operations would probably not be helpful? 5
How could you write a formula to compare the length of the Aizhai Bridge to its height?
You can ask the students verbally or let one of them come up and insert the answer or show how they got it. This way, you also have a record that you can keep as a class and share with parents, others.

7. How much longer is the Aizhai bridge than it is tall?1
Image Search
Find an image of the Aizhai Bridge. Based on this picture, what would you estimate is the difference between its length and its height?
(Possible query: “Bing/Images: Aizhai Bridge”).
Students should study an image, such as the one found here: in order to estimate what the difference is between its length and its height. Answers will vary. Students may guess the bridge is anywhere from 2-5 times as long as it is tall.

8. How much longer is the Aizhai bridge than it is tall?2
Web Search
What is the definition of a bridge? Could a bridge exist if it was taller than it is long?
(Possible queries: “what is a bridge?”, “define: bridge”).
From
A bridge is a structure that is built above and across a river, road, or other obstacle to allow people or vehicles to cross it
This is an opportunity for students to visualize what the length and height of bridges actually mean and to think about whether the Aizhai Bridge is unusual in that it’s longer than it is tall. They should note that according to this definition (or similar ones), there are no restrictions as to what makes a bridge in terms of its length and height. A bridge could, in fact, be very high up (for example, a bridge connecting two mountain peaks), but not very long.

9. How much longer is the Aizhai bridge than it is tall?3
Thinking
How could you use fractions to compare the Aizhai Bridge’s length and its height?
Students should think about how fractions might help them compare the Aizhai Bridge’s length and height. They should think about fractions as a way to represent part of a whole. In this case, because we know the bridge is longer than it is tall, the bridge’s height could represent a fraction of its length. For example, if we created a fraction that showed that the bridge was 1/3 as tall as it is long, we could also say that the bridge is 3 times as long as it is tall. Putting these distances into a fraction would be one way to get a sense of them in relationship to each other. Leading questions for students could include: Given what we know, which distance (length or height) would be the denominator of the fraction? Which would be the numerator? How do fractions help us compare two sizes in relationship to each other? If we knew the bridge’s height represented a specific fraction, how could you turn this around to express it as the length being “x” times the height?

10. How much longer is the Aizhai bridge than it is tall?4
Thinking
In comparing the length and height of the Aizhai Bridge, what operations might be helpful? What operations would probably not be helpful?
Students should think about what, mathematically, it means to express a verbal comparison as something being “x times” the size of something else. They should consider whether addition, subtraction, multiplication or division may help them do this and conclude that multiplication and division would be the most useful. It may be helpful for students to answer this question by using actual (smaller) numbers to conceptualize it. For example, if there was a bridge that was 6 feet long, and 2 feet tall, how could you solve to compare its length and height? What operation would help you solve this equation? Students should ultimately conclude that multiplication (figuring out 2 x ? = 6) or division (6 / 2 = ?) would be most useful.

11. How much longer is the Aizhai bridge than it is tall?5
Thinking
How could you write a formula to compare the length of the Aizhai Bridge to its height?
Students should think what it means to translate a verbal comparison into a mathematical formula. Even if they don’t know the actual length and height of the Aizhai Bridge, they can use actual (smaller) numbers to begin to conceptualize this. To use a previous example, if we knew that the length of a bridge was 6 feet and the height was 2 feet, how would we write an equation so that we could say that the length is “x times” the height?
Students should conclude that they could use either of the following formulas:
Height of Bridge x ? = Length of Bridge or
Length of Bridge / Height of Bridge

12. How much longer is the Aizhai bridge than it is tall?
This slide is a chance to summarize the information from the previous slides to build your final answer to the question. At this point students should have thought conceptually about how to solve this. They can then do a search (Possible queries: “height of Aizhai Bridge,” “how tall is the Aizhai Bridge?”, “how long is the Aizhai Bridge?”, “length of the Aizhai Bridge”) in order to find the actual numbers and plug it into the formulas they have developed. For example, from
Height of Bridge: 1,150 ft
Length of Bridge: 3,760 ft
They could then solve to compare the two.
3,760 (length of bridge) / 1,150 (height of bridge) = 3.27
In other words, the Aizhai Bridge is a little over 3 times as long as it is tall.