Unit 2 Exponents

OVERVIEW of Unit 2 Exponents and Equations

In this unit student will:

• distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system;
• recognize that every rational number has a decimal representation that either terminates or repeats;
• recognize that irrational numbers must have decimal representations that neither terminate nor repeat;
• understand that the value of a square root can be approximated between integers and that non–perfect square roots are irrational;
• locate rational and irrational numbers on a number line diagram;
• use the properties of exponents to extend the meaning beyond counting-number exponents;
• recognize perfect squares and cubes, understanding that non-perfect squares and nonperfect cubes are irrational;
• recognize that squaring a number and taking the square root of a number are inverse operations; likewise, cubing a number and taking the cube root are inverse operations;
• express numbers in scientific notation;
• compare numbers, where one is given in scientific notation and the other is given in standard notation;
• compare and interpret scientific notation quantities in the context of the situation;
• use laws of exponents to add, subtract, multiply and divide numbers written in scientific notation;
• solve one-variable equations with the variables being on both sides of the equals sign, including equations with rational numbers, the distributive property, and combining like terms; and
• analyze and represent contextual situations with equations, identify whether there is one, none, or many solutions, and then solve to prove conjectures about the solutions.