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Acc7.8 Pythagorean Theorem and Irrational Numbers

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.

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 $\sqrt{3}$.

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

I can find a decimal approximation for square roots.
I can plot square roots on the number line.
When I have a square root, I can reason about which two whole numbers it is between.

I can explain what the Pythagorean Theorem says.

I can explain why the Pythagorean Theorem is true.
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.

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.

I can use the Pythagorean Theorem to solve problems.

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.

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

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

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

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.