Warm Up Write down objective and homework in agenda Lay out homework (Kuta rational exponents wkst) Homework (Multi-Step Equations wkst)

Unit 1 Common Core Standards 8.EE.7 Solve linear equations in one variable. a. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Note: At this level, focus on linear and exponential functions. A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. Note: At this level, limit to formulas that are linear in the variable of interest, or to formulas involving squared or cubed variables.

Unit 1 Common Core Standards A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: At this level, focus on linear and exponential functions. A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Note: At this level, limit to linear expressions, exponential expressions with integer exponents and quadratic expressions. G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. Note: Informal limit arguments are not the intent at this level. G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* Note: At this level, formulas for pyramids, cones and spheres will be given. G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Unit 1 Common Core Standards N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Note: At this level, focus on fractional exponents with a numerator of 1. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Warm Up http://www.youtube.com/watch?v=-T1punCdxas

Warm Up

Multi-Step Equations using the Distributive Property Solving Equations: Equations are not fixed - they can be rearranged as long as the equality of the two sides is maintained. (Think: whatever I do to one side…I have to do to the other) We rewrite equations in order to make them simpler, or to solve them. The goal is to isolate the variable. Ex: 2x = 4 x = 2 Does the answer change if you add two on both sides? 2x + 2 = 4 + 2 No, x will still be equal to 2.

Properties that help rearrange an equation but MAINTAIN equality on both sides: Commutative property: The order in which numbers are added or multiplied does not change the sum or product. a + b = b + a and a • b = b • a Associative Property: The way in which numbers are grouped when added or multiplied does not change the sum or product. (a + b) + c = a + (b + c) and (a • b) • c = a • (b • c)  Additive and Multiplicative Inverses: For every a, there is an inverse (opposite operation) a + (-a) = (-a + a) = 0 and a • 1/a = 1/a • a = 1 Distributive Property: For any numbers a, b, and c: a (b + c) = ab + ac and (b+c)a = ba + ca a(b - c) = ab – ac and (b-c)a = ba – ca

Steps to Solving Multi-Step Equations: 1. Distribute to clear the parenthesis 2. Combine like terms 3. Use addition/ subtraction to get the variables on one side 4. Add or subtract to isolate the variable 5. Multiply or divide to isolate the variable

Combining Like Terms 2c + c + 12 = 78 3c + 12 = 78 -12 -12 3c = 66 3 3 -12 -12 3c = 66 3 3 c = 22 4b + 16 + 2b = 46 6b + 16 = 46 -16 -16 6b = 30 6 6 b = 5

Using Distributive Property -8 -8 -2b = 4 -2 -2 b = -2 3 (k + 8) + 7 = 4 3k + 24 + 7 = 4 3k + 31 = 4 -31 -31 3k = -27 3 3 k = -9

Examples

Examples

Square Puzzle!

Extra Resources http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/PSolvEq.htm