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Unit 3 Study Guide Standard Learning Target I can apply the properties of operations as 7.EE.1 strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Example: 7.EE.2 Simplify the expression: 5x + 2x + 8 + 9y -3y Factor the expression: 10x + 2 I can use equivalent expressions to understand the relationships between quantities. Example: 8.EE.1 (a) + (0.05a) = (1.05a) means that “increase by 5%“ is the same as “multiply by 1.05.” I can use the properties of integer exponents to simplify expressions. Example: 8.EE.2 32 x 3−5 = 3−3 = 1/ 33 = 1/27 I can recognize taking a square root as the inverse of squaring a number. Example: 2 √16 = 4 and 42 = 16 I can recognize taking a cube root as the inverse of cubing a number. Example: 3 √27 = 3 and 33 = 27 I can evaluate the square root of a perfect square. Example: 2 √25 = 5 and 25 is a “perfect square” I can evaluate the cube root of a perfect cube. Example: 3 √64 = 4 and 64 is a “perfect cube” I can justify that the square root of a non-perfect square will be irrational. Example: The √2 is irrational because it does not terminate and there is no pattern to the decimal equivalent. Vocabulary Notes/Examples 8.EE.3 I can write an estimation of a large quantity by expressing it as the product of a single-digit number and a positive power of ten. Example: 3,000,000 = 3 x 106 I can write an estimation of a very small quantity by expressing it as a product of a single digit number and a negative power of ten. Example: 0.000003 = 3 x 10−6 I can compare quantities written as a product of a single-digit number and a power of ten by stating their multiplicative relationships. Example: 8.EE.4 Estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109 , and determine that the world population is more than 20 times larger. I can add and subtract two numbers written in scientific notation. Example: 7 x 106 + 5.2 x 104 15 x 108 – 2.3 x 106 I can multiply and divide two numbers written in scientific notation. Example: (3 x 104)(2x 105) (6 x 106) ÷ (2 x 103) I can select the appropriate units for measuring derived measurements when comparing quantities written in scientific notation. Example: Use millimeters per year for seafloor spreading.