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: Geometry
CCSS.Math.Content.4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
CCSS.Math.Content.4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

2. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it?
© Hercules Milas/Alamy
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. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it?
On the road outside of Trikala in central Greece, the Paleokaria bridge joins the banks of the Portaikos River, wedged between two small waterfalls. Though there are numerous stone arch bridges just like this one in the area, the Paleokaria attracts photographers like ants to a picnic. And who can blame them, with this storybook scene?
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. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 1
Image Search/Thinking
Paleokaria is an example of what is called an Arch Bridge. When you search for different examples of arch bridges, what do you notice about the shapes that they create? 2
Web Search/Thinking
Is the space below the arch bridge symmetrical? Even without seeing the bridge, how might symmetry give us a clue into what shape this space forms? 3
Web Search
What angles are found in a semicircle? 4
What is a right angle? What shapes are right angles found in? 5
How would knowing the kind of angles in a shape allow us to solve for other information about it?
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. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 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. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 1
Image Search/Thinking
Paleokaria is an example of what is called an Arch Bridge. When you search for different examples of arch bridges, what do you notice about the shapes that they create? 2
Web Search/Thinking
Is the space below the arch bridge symmetrical? Even without seeing the bridge, how might symmetry give us a clue into what shape this space forms? 3
Web Search
What angles are found in a semicircle? 4
What is a right angle? What shapes are right angles found in? 5
How would knowing the kind of angles in a shape allow us to solve for other information about it?
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. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 1
Image Search/Thinking
Paleokaria is an example of what is called an Arch Bridge. When you search for different examples of arch bridges, what do you notice about the shapes that they create?
(Possible queries: Bing/Images: arch bridge”, Bing/Images: arch bridges”).
Students should examine images such as the ones found here ( and discuss what shapes they notice in the images. Although the bridges may have some variations, they should notice the arch shape that the bridge gets its name from. Students should also examine the space underneath the arches that are created which tends to form a semi-circle. They might notice other shapes, like rectangles and squares, in the shapes that are created by the bridges’ railings as well.

8. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 2
Web Search/Thinking
Is the space below the arch bridge symmetrical? Even without seeing the bridge, how might symmetry give us a clue into what shape this space forms?
(Possible queries: “what is symmetry?”, “how do you know if a shape is symmetrical?”).
Students should use their own understanding of symmetry as well as online resources (for example: to articulate that something is symmetrical when you can fold it in half and have all edges match. They should notice that, based on the image, the space beneath the Paleokaria Bridge does look symmetrical. They should then think about how, even without seeing the bridge, knowing this may narrow down the kind of shape it can be. To answer this, they should think about what shapes are symmetrical (for example, a circle or semi circle, a square, a rhombus, etc…) and what shapes are not (an irregular quadrilateral, some triangles, etc…)

9. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 3
Web Search
What angles are found in a semicircle?
(Possible queries: “what angles are found in a semicircle?”, “what angles are in a semicircle?”).
From
An angle inscribed in a semicircle is always a right angle.
Even if students don’t yet understand the “why” behind the fact that angles inscribed in semicircles are always right angles, this is an opportunity for them to start thinking about (and looking up visual representations of) the idea that certain kinds of angles exist in certain shapes. They should also acknowledge that not ALL the angles in a semicircle are right angles; other angles exist as well. They can think of what other shapes right angles can be found in (leading questions could include: Are right angles found in squares? How about triangles? All triangles?).

10. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 4
Web Search
What is a right angle? What shapes are right angles found in?
(Possible queries: “what is a right angle?”, “definition of a right angle”, “what shapes have right angles?”).
From
A right angle is an angle of 90°, as in a corner of a square or at the intersection of two perpendicular straight lines.
Students should then read a list of shapes with right angles and be able to identify that they are found in squares, rectangles, semicircles and some triangles (among others).

11. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it? 5
Web Search/Thinking
How would knowing the kind of angles in a shape allow us to solve for other information about it?
(Possible queries: “what do the angles in a shape tell us?”, “solving problems based on angles”).
Students should do a quick search to see what kinds of mathematical problems based on angles arise. For example, this website guides students through a lesson: Based on this website, and others, students should think about how knowing specific angle measurements could help them solve problems such as finding the area of a shape. It could also tell them something about perpendicular and parallel lines.

12. What does the shape of the Paleokaria Bridge tell us about the angles that exist in the space below it?
This slide is a chance to summarize the information from the previous slides to build your final answer to the question. Students should ultimately conclude that, based on the image, the space below the Paleokaria Bridge (and other arch bridges) is a semicircle. Based on this, we can conclude that it contains right angles.
It’s okay if at this point students don’t fully understand the proof for why right angles exist in semicircles; it’s more important for them to start thinking conceptually about how certain angles correspond with certain shapes, and what information (for example, area), we can more easily solve for by knowing this.