Acc7.8 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.
  • When I have a square root, I can reason about which two whole numbers it is between.

Lesson 5

  • I can explain what the Pythagorean Theorem says.

Lesson 6

  • 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.

Lesson 7

  • 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 8

  • I can use the Pythagorean Theorem to solve problems.

Lesson 9

  • 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 10

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

Lesson 11

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

Lesson 12

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

Lesson 13

  • 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.