Lessons & Units :: What's Your Angle, Pythagoras? 3rd Grade Unit

Read-Aloud Lesson: What's Your Angle, Pythagoras?

Lesson Plan

What's Your Angle, Pythagoras? | AD670L

What's Your Angle, Pythagoras?
Learning Goal
Identify problems faced by the father of Pythagoras and other citizens of Samos, and how Pythagoras solved those problems; and then discuss the theme of problem solving and how math can be used to solve problems people face in their daily lives.
Duration
TBD
Necessary Materials
Provided:
  1. Detailed lesson plan
  2. Graphic organizer for guided practice
  3. Independent student worksheet
  4. Diagram of triangles

Not Provided:
What’s Your Angle, Pythagoras?
 
  1. This lesson is a close reading of the entire text. So it’s important to engage students often, to enhance their learning. Here are two tips:

    •   When you ask the more complex questions from the lesson, ask students to “turn-and-talk” or “buddy-talk” before answering.

    •   Once you are deep into the lesson, instead of asking students every question provided, ask them to share with you what questions they should be asking themselves at that point in the text. This is also a great opportunity to use "turn-and-talk."
       
  2. Suggested teacher language is included in the lesson.

  3. We recommend you read the book once to your students, either the day or morning before teaching the lesson.

  4. This research-based, read-aloud lesson may seem long. Why do students need the lesson to be this way?
 

Part 1: Teacher Modeling and Questioning

 

Write the following student-friendly learning goal on the board, then read the learning goal out loud with the class.

We will look at how the main character is able to solve the problems of the people around him. We will then discuss the topic of problem solving.

 
Prepare Students for the Lesson
 
Draw or show pictures of two triangles to students. One should be a right triangle; the other should not be. (Two appropriate triangles are provided below for your convenience.) Explain that a right triangle is a triangle with a square corner.
 
Transition Students into the Text
 
Teacher says: What if you could solve the problems around you by looking at them closely and thinking hard? We are about to read the story of a boy who does just that.
 
Read page 3 out loud, then stop. Page 3 ends with, “...sometimes it paid off.” Show students the accompanying illustration. If possible, always show students the illustrations on the pages you read throughout the lesson.
1.
Teacher asks: We just read that long ago there lived a certain boy in a place called ancient Greece. What is the name of this boy?
 
Students answer: The name of this boy is Pythagoras.
2.
Teacher asks: What is Pythagoras like?
 
Students answer: Pythagoras is curious.
 
Read the first four paragraphs of page 4. The fourth paragraph on page 4 ends with, “‘...the columns on the porch!’”
3.
Teacher asks: One day Pythagoras sees two workmen building a temple. A temple is a religious building where people go to pray and worship. What do the workmen building the temple begin to do as Pythagoras watches?
 
Students answer: The workmen begin to argue.
4.
Teacher asks: What are the workmen arguing about?
 
Students answer: The workmen are arguing about their ladder.
5.
Teacher asks: What is the problem with the workmen’s ladder?
 
Students answer: Responses may vary in degree of detail. At minimum, students should recognize that the ladder is too short for someone climbing on it to reach the temple roof.
6.
Teacher says (models thinking): I remember that part of our goal for this lesson is to look at how Pythagoras solves the problems of the people around him. Now we have come across our first problem. The workmen’s ladder is too short to reach the roof. I know that Pythagoras is curious, so I am going to predict that he will try to learn more about this problem as the story goes on.
Read more
 
Read the remainder of page 4. Continue reading through page 7. Page 7 ends with, “...home for dinner.”
7.
Teacher asks: What does Pythagoras ask when he hears Pepros say that the ladder is “as bad as the columns on the porch”?
 
Students answer: Pythagoras asks what is wrong with the columns.
8.
Teacher asks: What does Pepros tell Pythagoras after Pythagoras asks what is wrong with the columns?
 
Students answer: Pepros tells Pythagoras to stop bothering him and Saltos.
9.
Teacher asks: What does Pythagoras do after being told to stop bothering Pepros and Saltos?
 
Students answer: Pythagoras goes to look at the columns.
10.
Teacher asks: What is the problem with the columns?
 
Students answer:
  • The columns are crooked. (make sure this response is given before moving on)
  • The columns cannot hold up a roof.
11.
Teacher says (models thinking): Earlier we read that Pythagoras was curious. Now we see an example of Pythagoras’s curiosity. When he hears that something is wrong with the columns, he asks what it is. When Pepros does not tell him, Pythagoras goes to see for himself. As we keep reading, be on the lookout for other examples of his curiosity.
 
Read pages 8 and 9 out loud, then stop. Page 9 ends with, “...much to learn.”
12.
Teacher says: Remember that Pythagoras lives on an island. Rhodes and Crete are two other islands nearby.
13.
Teacher asks: Where does Pythagoras’s father sail first when he goes to Crete?
 
Students answer: Pythagoras’s father sails to Rhodes first.
14.
Teacher asks: What does Pythagoras say would be a faster way to sail to Crete?
 
Students answer: Pythagoras says that sailing straight from here (his home island) to Crete would be faster.
15.
Teacher asks: Why doesn’t Pythagoras’s father sail straight from his own island to Crete?
 
Students answer:
  • It’s too dangerous.
  • He could miss Crete and end up anywhere.
16.
Teacher asks: Pythagoras’s father says that it would only be safe to sail straight to Crete if he knew one thing. What is that one thing?
 
Students answer: That one thing is the exact distance to Crete.
 
Read pages 10-12 out loud, then stop. Page 12 ends with, “...a master builder.”
17.
Teacher asks: What does Pythagoras think of after he sees how straight the base of the lighthouse is?
 
Students answer: Pythagoras thinks of the crooked columns on the temple at home.
 
Read page 13 out loud, then stop. Page 13 ends with, “...for cutting stone.”
18.
Teacher asks: What does Nef call the triangle he makes with his rope?
 
Students answer: He calls it a right triangle.
19.
Teacher asks: What kind of corner does the right triangle have?
 
Students answer: It has a square corner.
 
Read pages 14-17. Page 17 ends with, “...making a square.”
20.
Teacher says: I notice that Pythagoras is very interested in Nef’s right triangle. He takes a piece of old rope and tries to make a right triangle on his own. Here is another example of Pythagoras’s curiosity.
21.
Teacher asks: What are some other things Pythagoras does in Alexandria that show how curious he is?
 
Students answer: Responses may vary.
  • Pythagoras asks Nef questions about the base of the lighthouse and the rope triangle.
  • Pythagoras puts tiles around the statue base to see how they look.
 
Read page 18. Continue reading through the first four paragraphs of page 19. The fourth paragraph ends with, “‘...the big red and blue square!’”
22.
Teacher asks: What kind of triangle does Pythagoras notice the statue base is?
 
Students answer: Pythagoras notices the statue base is a right triangle.
23.
Teacher asks: What does Pythagoras do with the tiles?
 
Students answer (responses may vary but should resemble the following): Pythagoras uses the tiles to make a square along each side of the statue base.
 
Read the remainder of page 19. Continue reading through the next-to-last paragraph on page 24. The next-to-last paragraph is a single sentence: “He fixed the ladder and headed home.”
24.
Teacher asks: Think of the ladder leaning diagonally against the wall of the temple. What shape would it make together with the wall and the ground?
 
Students answer: It would make a triangle.
 
Use the picture of the right triangle from the beginning of the lesson to help students visualize how Pythagoras fixes the ladder. The vertical line in that triangle is like the wall. The horizontal line is like the ground. The diagonal line is like the ladder.
25.
Teacher asks: What kind of corner does this triangle have here?
 
Point to the corner with a 90-degree angle—the “square corner.”
 
Students answer: The triangle has a square corner.
26.
Teacher asks: What is the name for a triangle with a square corner?
 
Students answer: The name for a triangle with a square corner is a right triangle.
27.
Teacher asks: Think back to the statue base in Alexandria that Pythagoras placed tiles around. What kind of triangle was the statue base?
 
Students answer: The statue base was a right triangle.
28.
Teacher says: Now Pythagoras is using what he learned from placing tiles around the statue base. He is using this information to work with another right triangle—the one made by the ladder, the wall, and the ground.
29.
Teacher asks: What does Pythagoras discover about the length of the ladder?
 
Students answer: Responses may vary and include the following:
  • Pythagoras discovers that the ladder needs to be longer. (acceptable answer)
  • Pythagoras discovers that the ladder needs to be 13 feet long. (strong answer)
30.
Teacher asks: What was the problem with the ladder that we read about in the beginning of the story?
 
Students answer: The ladder was too short to reach the roof.
31.
Teacher asks: Has Pythagoras solved the problem of the ladder? Explain why or why not, supporting your answer with evidence from the book.
 
Students answer: Responses may vary, as long as they are supported by the book. For example, students may respond that Pythagoras has solved the problem of the ladder because he has made the ladder longer. Alternatively, students may respond that there is not enough information to determine whether Pythagoras has fixed the problem of the ladder because no one has tried climbing it to the roof since he elongated it.
 
Read the rest of page 24 out loud and continue through page 27, then stop. Page 27 ends with, “...any time you like.”
32.
Teacher asks: What does Saltos say Pythagoras did to the ladder?
 
Students answer: Saltos says Pythagoras made the ladder the perfect length.
 
Read pages 28-29 out loud, then stop. Page 29 ends with, “...185 miles.”
33.
Teacher asks: What shape do the islands of Samos, Rhodes, and Crete make?
 
Students answer: The islands make a right triangle.
 
Use page 29 as a visual aid for students.
34.
Teacher says: The short side of this triangle is the distance from Samos to Rhodes. The medium side of this triangle is the distance from Rhodes to Crete.
35.
Teacher asks: What is the long side of this triangle?
 
Students answer: The long side of this triangle is the distance from Samos to Crete.
36.
Teacher asks: How is figuring out the distance to Crete similar to figuring out the correct length for the ladder?
 
Students answer: Responses may vary but should mention right triangles. For example:
  • Pythagoras uses the same right triangle pattern to figure out the distance to Crete that he used to figure out the correct length for the ladder.
  • Pythagoras uses the two shorter sides of a right triangle to figure out the length of the longest side.
 
Finish reading the story out loud.
37.
Teacher says: There are three main problems that Pythagoras comes across in the story. The first problem is the ladder that does not reach the temple roof.
38.
Teacher asks: What is the second problem that Pythagoras comes across in the story?
 
Students answer: The second problem is the crooked columns.
39.
Teacher asks: What is the third problem that Pythagoras comes across in the story?
 
Students answer: The third problem is how to sail to Crete faster.
40.
Teacher asks: How many of these problems does Pythagoras solve?
 
Students answer: Pythagoras solves all three of these problems.
41.
Teacher says (models thinking): I wonder what makes Pythagoras so good at solving problems. Let’s think about the things he does that help him solve these three problems. I can think of one thing. He asks a lot of questions.
42.
Teacher asks: What are some questions Pythagoras asks?
 
Students answer: Responses may vary and include the following:
  • Pythagoras asks why his father can’t sail straight to Crete.
  • Pythagoras asks Nef how he made the base of the lighthouse so straight.
43.
Teacher asks: How do Pythagoras’s questions help him solve problems? Give an example.
 
Students answer: Responses may vary and include the following:
  • Pythagoras’s questions help him understand what the problems are. For example, asking why his father doesn’t sail straight to Crete makes Pythagoras realize that first the distance from his home island to Crete must be determined.
  • Pythagoras’s questions result in him learning new ways to solve problems. For example, when he asks how Nef made the base of the lighthouse so straight, Nef shows him what a right triangle is.
44.
Teacher asks: What’s another thing Pythagoras does that helps him solve problems? Give an example.
 
Students answer (responses may vary and include the following): Pythagoras thinks creatively about different ways to do things. For example, he thinks of sailing straight to Crete instead of stopping at Rhodes first. He also takes an old piece of rope and ties knots in it so that he can try making a right triangle on his own.
45.
Teacher says: One of the most important things Pythagoras does to solve problems is to use math. He notices patterns and similarities. He sees how the triangle he makes with the tiles is similar to the triangle formed by the ladder, the wall, and the ground.
46.
Teacher asks: How is the triangle that Pythagoras makes with the tiles similar to the triangle formed by the ladder, the wall, and the ground?
 
Students answer: They are both right triangles.
47.
Teacher says: Pythagoras uses that similarity to solve the problem of how to fix the ladder. He also uses the pattern of the right triangle to solve the problem of the crooked columns and the problem of how to sail faster to Crete.
 

Part 2: Guided Practice and Discussion

 
For this oral lesson, it is suggested to have the completed graphic organizer on the board with the answers concealed before this part of the lesson. After students provide a correct answer, reveal the corresponding answer on the graphic organizer. For many of the fields, more than one correct answer is possible. In such instances the answers provided on the completed graphic organizer are meant to serve as examples, not definitive responses.
1.
Teacher says: In the first part of the lesson, we looked at three problems that Pythagoras solved. Now we are going to make a list of the things he did that helped him solve those problems. Let’s start by making sure we remember what the problems were. The first problem was the ladder that did not reach the temple roof.
2.
Teacher asks: What was the second problem?
 
Students answer: The second problem was that the columns of the temple were crooked.
3.
Teacher asks: What was the third problem?
 
Students answer: The third problem was how to sail to Crete faster.
4.
Teacher says: Now let’s work on our list of things Pythagoras did that helped him solve those problems. One thing he did was ask a lot of questions.
5.
Teacher asks: How did asking questions help Pythagoras solve problems?
 
Students answer: Pythagoras’s questions resulted in him learning about the right triangle. He realized that it was the same shape made by the ladder leaning against the wall.
6.
Teacher asks: What are some other things Pythagoras did that helped him solve problems? Explain how each thing helped.
 
Students answer: Answers may vary.
  • Pythagoras saw patterns and similarities between things. He saw how the triangle made by the knotted rope was like the triangle with the tiles, and how the triangle with the tiles was like the triangle with the ladder.
  • Pythagoras experimented, or tried things out on his own. He knotted a piece of rope and pulled it into different triangles to understand how right triangles are made. That discovery helped him see how to make the bases of the columns straight.
 
Continue asking for things Pythagoras did until students run out of answers.
Read more
 
After the answers for the graphic organizer have been completed and discussed with the class, ask the following extension questions.
 
Teacher asks: We talked about how Pythagoras used patterns and similarities to help him solve problems. He also used measurements and counting. What are some ways he used measurements and counting in the story?
 
Students answer: By counting the number of tiles around the right triangle in the courtyard, Pythagoras discovered how the lengths of the different sides were related to each other.
 
Teacher asks: What are some ways people can use patterns and similarities to help solve problems in their daily lives? Give an example.
 
Students answer (responses may vary and include the following): If someone has an allowance, he or she can use patterns to figure out how long it will take to get enough money for something. For example, my allowance is $1 a week. I want to buy a bottle of soda that costs $2. I will have to save my allowance money for two weeks to buy the soda.
 
Teacher asks: What are some ways people can use measurements and counting to help solve problems in their daily lives? Give an example.
 
Students answer (responses may vary and include the following): If someone wants to buy a poster for his or her bedroom door but does not know what size to get, taking measurements could help. The person could measure how wide and how tall the door is. Then he or she would know what size poster to buy.
 

Part 3: Student Independent Practice

 
Both the student question set and teacher answer sheet are provided in the 'Text & Materials' section.

Texts & Materials

Standards Alignment

(To see all of the ReadWorks lessons aligned to your standards, click here.)

User Comments

ReadWorks is very challenging and works so well with students. Thank you for the splendid program

Submitted by SMCbuthod_1541117 on 9/8/15