LESSON SUMMARY
PRIOR KNOWLEDGE:
- Understanding of the relationship between square numbers and square roots, including non-perfect squares
- Understanding the connection between squares and square roots to area of a square and side length of a square
- Solving equations of the form x^2=p
- Knowledge of types of triangles
- Students will be able to explain a proof of the Pythagorean Theorem
Detailed implementation guide for teachers
STARTER Students will go to the website padlet.com/patelk/righttriangle and answer the question "What do you know about right triangles?". Students should be given 5 minutes to complete this task. Teachers should facilitate a discussion that results in students understanding key components of a right triangle.
sequencing of student responses:
questions for students:
sequencing of student responses:
- triangle has 3 sides and 3 angles
- right triangle means that one of the angles is 90 degrees
- we represent a 90 degree angle with the square in the corner of the triangle
- the other angles must add to 90 for a total of 180 in the triangle (all triangles)
- If students are struggling to come up with something to post on the padlet, remind them by asking them to draw a picture of a right triangle and asking "How did you know what to draw?"
questions for students:
- What do you notice about the location of the hypotenuse?
- What do you notice about the legs?
- How do the hypotenuse and the legs relate to one another?
- Since we know these are squares formed by the side lengths of the triangle, what does that tell us about the the other sides? the angles?
- How would we find the area of each square?
- What if we had the area, how would we find the side length?
WORK SESSION Students will work in pairs. The pair will be given the two puzzles and accompanying questions for exploration. As students are working, the teacher should circulate, asking questions and listening to student observations.
The work session should conclude with a Think-Pair-Share activity. Students should make a conjecture based on what they noticed while working with their puzzle then share that with their partner. Do both partners' puzzles show that the conjecture is true? After being given 2 minutes to share with their partners, students should share conjectures with the class. The teacher should record the conjectures, allowing time for the class to ask questions/make observations that critique the statements (informal formative assessment).
PUZZLE ONE and PUZZLE TWO and PUZZLE STUDENT GUIDE
sequencing of student responses for Think-Pair-Share
CLOSING Students will watch the video linked here that is a visual representation of the Pythagorean Theorem. As a ticket out the door (formative assessment), students should answer the question "How does the video support the conjectures we made today in class?"
PRIOR TO THE LESSON:
The work session should conclude with a Think-Pair-Share activity. Students should make a conjecture based on what they noticed while working with their puzzle then share that with their partner. Do both partners' puzzles show that the conjecture is true? After being given 2 minutes to share with their partners, students should share conjectures with the class. The teacher should record the conjectures, allowing time for the class to ask questions/make observations that critique the statements (informal formative assessment).
PUZZLE ONE and PUZZLE TWO and PUZZLE STUDENT GUIDE
sequencing of student responses for Think-Pair-Share
- the pieces in the two small squares are the same as the large square
- the two small squares fit exactly in the large square
- the two small squares are on the leg while the biggest square is on the hypotenuse
- the sum of the area of the leg-squares is the area of the hypotenuse-square
- What do you notice?
- How does moving the slider affect each piece of the puzzle?
- How does the end result relate to the starting picture?
CLOSING Students will watch the video linked here that is a visual representation of the Pythagorean Theorem. As a ticket out the door (formative assessment), students should answer the question "How does the video support the conjectures we made today in class?"
PRIOR TO THE LESSON:
- Teachers need to create the padlet in the starter by going to padlet.com (create an account if not a member already).
- Teachers should arrange students in pairs. Within each pair at least one student should have a complete understanding of the relationship between side lengths and area of a square.