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
- Understanding the Pythagorean Theorem as a relationship between the side lengths of a right triangle
- Students will understand, and be able to demonstrate, that the Pythagorean Theorem only applies to right triangles
- Students will be able to decide if a triangle is a right triangle given its three side lengths
Detailed implementation guide for teachers
STARTER Error analysis of one of the challenging problems from lesson 3 ticket out the door.
MINI-LESSON Review what we have learned about the Pythagorean Theorem. This should be student-led and lead to the students: creating a diagram with labeled legs and hypotenuse (knowing the location of these in relation to the right angle) and showing the relationship between the 3 side lengths using the Pythagorean Theorem.
questions for students
questions for students
sequencing of student responses
MINI-LESSON Review what we have learned about the Pythagorean Theorem. This should be student-led and lead to the students: creating a diagram with labeled legs and hypotenuse (knowing the location of these in relation to the right angle) and showing the relationship between the 3 side lengths using the Pythagorean Theorem.
questions for students
- How do we refer to the sides of a right triangle?
- What is the relationship between the lengths of the legs and the length of the hypotenuse?
- What visual can help us show this relationship?
questions for students
- What changed in problem 1? What stayed the same?
- What changed in problem 2? What stayed the same?
- What is different in problem 1 and problem 2?
sequencing of student responses
- the angle didn't change in problem 1
- when the angle is 90 degrees, a^2+b^2 is equal to c^2
- we changed the angle in problem 2
- when the angle gets bigger, the length across from the angle gets bigger (same with when the angle gets smaller)
- when the angle is larger than 90 degrees, a^2+b^2 is not equal to c^2
- when the angle is smaller than 90 degrees, a^2+b^2 is not equal to c^2
- when the angle is anything other than 90 degrees, a^2+b^2 is not equal to c^2
- a^2+b^2 is equal to c^2 only for right triangles
- 3 sides will only satisfy a^2+b^2 = c^2 when it is a right triangle