Math 2 - Fourth period
Module A: Congruence and Transformations 
Outcome 1: I can use and apply geometric theorems to prove properties of lines and angles. 
a. I can prove and use angle relationships involving two intersecting lines. G.CO.9 
b. I can use theorems about angle measures in triangles to solve problems. G.CO.10 
c. I can identify relationships between angles created by parallel lines.G.CO.9 
d. I can prove two lines are parallel.G.CO.9 
e. I can use relationships between angles created by parallel lines to solve problems. G.CO.9 

Outcome 2: I can use the properties of rigid motions to reason with congruent figures. 
a. I can verify that a transformation satisfies its definition in terms of angles and lines. G.CO.4 
b. I can describe a sequence of transformations that will carry a figure onto another or onto itself. G.CO.3,5 
c. I can represent transformations with a graph given a rule. G.CO.2, G.SRT.1 
d. I can write a function using function notation to express a transformation of a geometric figure. F.IF.1,2 
e. I can determine if two figures are congruent using rigid transformations. G.CO.6,7 

Outcome 3: I can prove theorems about triangles and use them to solve problems. 
a. I can determine and justify if two triangles are congruent.G.CO.8 
b. I can create a simple deductive argument to prove triangles are congruent. G.CO.8 
c. I can create a simple deductive argument to show corresponding angles or corresponding sides of congruent triangles are congruent. G.CO.8 
d. I can use the properties of perpendicular bisectors of a line segment to solve problems. G.CO.9 
e. I can use the properties of angle bisectors to solve problems. G.CO.9 

Module B: Quadratic Functions 
Outcome 4: I can use the structure of a quadratic to analyze quadratic functions. 
a. I can show and interpret key features of a quadratic function using multiple representations. F.IF.4,7 
b. I can write a quadratic function using key features given a graph or ordered pairs. A.CED.2, F.BF.1 
c. I can rewrite a quadratic expression to identify the key features (y-intercept, zeros, axis of symmetry, and minimum/maximum) of a quadratic function. F.IF.4, F.IF.8, F.BF.3 
d. I can rewrite a quadratic expression in vertex form by completing the square. A.SSE.3, F.IF.8 
e. I can compare the key features of two quadratic functions represented in different ways.F.IF.9 

Outcome 5: I can solve quadratic equations. 
a. I can solve quadratic equations by tables or graphs. A.REI.4, A.CED.1,2 
b. I can use the quadratic formula or completing the square to solve quadratic equations. A.REI.4a,b 
c. I can determine and justify if a quadratic equation has no real solutions. A.REI.4b 
d. I can solve quadratic equations with non-real solutions expressed as complex numbers.N.CN.1,A.REI.4b 
e. I can justify a chosen solution method for solving quadratics and explain each step of the process. A.REI.1 

Outcome 6: I can build new functions from existing functions. 
a. I can build a quadratic function given a relationship between two quantities. A.CED.2, F.BF.1 
b. I can interpret parts of a quadratic function in context. A.SSE.1a,b 
c. I can add, subtract and multiply polynomials. A.APR.1 
d. I can identify the effect of k・f(x) given k is a real number. F.BF.3 
e. I can identify the effect of f(x)+ k given k is a real number. F.BF.3 
f. I can identify the effect of f(x + k) given k is a real number. F.BF.3 

Module C: Rational and Radical Functions 
Outcome 7: I can interpret and solve problems involving inverse variation functions. 
a. I can create another representation of an inverse variation function given any one of function rule, table, graph, and/or contextual situation.A.CED.1,2 F.IF.7, F.BF.1 
b. I can determine and interpret the constant of proportionality of an inverse variation function. A.SSE.1a 
c. I can show and interpret key features of an inverse variation function using multiple representations. F.IF.4,7 
d. I can solve inverse variation equations using graphs, tables, or algebraic reasoning. A.REI.2, A.CED.1 
e. I can compare and contrast two variation functions represented in different ways. F.IF.9 
f. I can classify the sum or product of two real numbers as irrational or rational.N.RN.3 

Outcome 8: I can interpret and solve problems involving square root functions. 
a. I can show and interpret key features of a square root function using multiple representations. F.IF.4,7 
b. I can compare and contrast two square root functions represented in different ways.F.IF.9 
c. I can create square root equations and use them to solve problems.A.CED.1, A.REI.1,2 
d. I can solve square root equations using graphs, tables, or algebraic reasoning (identifying any extraneous solutions).A.REI.2, A.CED.2 
e. I can use properties of exponents to rewrite expressions involving radical and rational exponents. N.RN.1,2 

Module D: Similarity and Trigonometry 
Outcome 9: I can reason and solve problems involving similar figures. 
a. I can verify the properties of dilations with given center and scale factor.G.SRT.1 
b. I can specify a sequence of transformations that will transform one figure onto the other. G.SRT.2a,b 
c. I can determine the scale factor and center of dilation of two similar figures. G.SRT.2 
d. I can use the AA Similarity Theorem to prove two triangles are similar. G.SRT.3 
e. I can use the triangle proportionality theorem to solve problems. G.CO.10, G.SRT.4 

Outcome 10: I can reason and solve problems involving right triangles. 
a. I can explain the trigonometric ratios using similar triangles.G.SRT.6 
b. I can use trigonometric ratios to find missing angles and side lengths. G.SRT.8, A.CED.1 
c. I can use right triangles to model and solve a problem in context. G.SRT.8, A.SSE.1a 
d. I can use special right triangles to solve problems. G.SRT.12 

Module E: Inequalities and Systems 
Outcome 11: I can solve problems that involve inequalities in one variable. 
a. I can create and solve an inequality for a given function in one variable. A.CED.1 
b. I can write a question to match a given inequality. A.CED.1 
c. I can use graphic representations of inequalities to solve problems. A.CED.1, A.REI.11 
d. I can represent the solution to an inequality in multiple ways (interval notation, symbolically, and graphically). SMP 6 

Outcome 12: I can solve systems of nonlinear equations and justify the solution. 
a. I can create systems of nonlinear equations to model situations in context. A.CED.2, A.CED.3 
b. I can solve systems of nonlinear equations by tables and graphs. A.REI.7, A.REI.11 
c. I can solve a system of a linear and quadratic equation using algebraic methods. A.REI.1, 7 

Module F: Probability 
Outcome 13: I can determine the probability of events. 
a. I can determine the probability of events including unions, intersections and complements from a two-way frequency table. S.CP.1, 3a 
b. I can construct and interpret a two-way frequency table. S.CP.4
c. I can analyze results from simulations and compare to the theoretical probability. S.IC.2 
d. I can compute probabilities using the appropriate rule. S.CP.7,8 
e. I can determine the conditional probability of an event. S.CP.3,4, S.CP.5, S.CP.6 
f. I can use conditional probability to justify if two events are independent. S.CP.3b,5
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