8th grade Math Guide

5

8.15

8.4

6.NS.6c

6

8.1

8.14, 8.15

7.NS.2d

8.13

7

8.14

5.NBT.3

LEARNING INTENTIONS

● Know that real numbers that are not rational are irrational. ● Understand that fnite decimal expansions of irrational numbers are approximations. ● Show that rational numbers have decimal expansions that repeat eventually. ● Convert a decimal expansion, which repeats eventually, into a rational number. ● Compare and order irrational numbers. ● Place irrational numbers on a number line. ● Use approximations of irrational numbers to estimate the value of expressions. ● Simplify radicals such as: 1 3 2 , 8, 16, 3 27 ● Perform operations and collect like terms such as: 6( 15+ 6), 27−12, 26+66 ● Evaluate the square roots of small perfect squares and cube roots of small perfect cubes. ● Represent the solutions to equations using square root and cube root symbols. ● Know that in a right triangle a² + b² = c² (the Pythagorean Theorem). ● Explore proofs of the Pythagorean Theorem (for example, by decomposing a square in different ways) and be able to explain a proof of the Pythagorean Theorem. ● Understand and explain a proof of the converse of the Pythagorean Theorem. ● Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other two sides. ● Use the Pythagorean Theorem to solve and model problems in real-world and mathematical problems. ● Use the Pythagorean Theorem to solve and model problems involving three-dimensional contexts (cones, diagonals of rectangular prisms, etc.). ● Recognize that applying the Pythagorean Theorem can result in rational and irrational numbers (this could be the frst time students encounter irrational numbers). ● Calculate the distance between two points in a coordinate system using the Pythagorean Theorem.

KEY VOCABULARY

● Square Root ● Irrational Number ● Rational Number

● Pythagorean Theorem ● Hypotenuse

● CubeRoot ● Legs