# 8.8 Pythagorean Theorem and Irrational Numbers

### Lesson 1

- I can find the area of a tilted square on a grid by using methods like “decompose and rearrange” and “surround and subtract.”
- I can find the area of a triangle.

### Lesson 2

- I can explain what a square root is.
- If I know the area of a square, I can express its side length using square root notation.
- I understand the meaning of expressions like $\sqrt{25}$ and $\sqrt{3}$.

### Lesson 3

- I know what an irrational number is and can give an example.
- I know what a rational number is and can give an example.

### Lesson 4

- I can find a decimal approximation for square roots.
- I can plot square roots on the number line.

### Lesson 5

- When I have a square root, I can reason about which two whole numbers it is between.

### Lesson 6

- I can explain what the Pythagorean Theorem says.

### Lesson 7

- I can explain why the Pythagorean Theorem is true.

### Lesson 8

- If I know the lengths of two sides, I can find the length of the third side in a right triangle.
- When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.

### Lesson 9

- I can explain why it is true that if the side lengths of a triangle satisfy the equation $a^2+b^2=c^2$ then it must be a right triangle.
- If I know the side lengths of a triangle, I can determine if it is a right triangle or not.

### Lesson 10

- I can use the Pythagorean Theorem to solve problems.

### Lesson 11

- I can find the distance between two points in the coordinate plane.
- I can find the length of a diagonal line segment in the coordinate plane.

### Lesson 12

- I can approximate cube roots.
- I know what a cube root is.
- I understand the meaning of expressions like $\sqrt[3]{5}$.

### Lesson 13

- When I have a cube root, I can reason about which two whole numbers it is between.

### Lesson 14

- I can write a fraction as a repeating decimal.
- I understand that every number has a decimal expansion.

### Lesson 15

- I can write a repeating decimal as a fraction.
- I understand that every number has a decimal expansion.

### Lesson 16

- I can apply what I have learned about the Pythagorean Theorem to solve a more complicated problem.
- I can decide what information I need to know to be able to solve a real-world problem using the Pythagorean Theorem.