1. Reason abstractly and quantitatively. 2. Construct viable arguments and critique the reasoning of others. 3. Look for and make use of structure. 4. Look for and express regularity in repeated reasoning. 5. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 6. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.