## Mathematics Vision Project - Math 1 Overview

__Module 1: Getting Ready__**(N.Q.1, N.Q.2, A.SSE.1, A.CED.1, A.CED.4, A.REI.1, A.REI.3)**

Combine like terms; use the distributive property; write expressions to represent a context and/or given a visual; solve linear equations; solve linear inequalities & graph solutions on a number line; solve literal equations; convert between slope-intercept and standard form of linear functions; graph lines in slope-intercept and standard form; find slope between two coordinate pairs; write linear equations and inequalities to represent a context.

__Module 2: Systems__**(**

**A.CED.2, A.CED.3, A.CED.4, A.REI.5, A.REI.6, A.REI. 10, A.REI.12, A.SSE.1, N.Q.1, N.Q.2, F.LE.1b, F.LE.5)**

Write linear equations and inequalities to represent a set of constraints; use graphs to solve systems of equations and inequalities; use technology to graph linear functions and determine the most appropriate window to use; solve systems of equations algebraically; identify types of solutions to a system of linear equations including one solution, no solution, or infinitely many solutions; interpret solutions of systems in the context of a situation; determine if a given point is a solution to an equation, inequality, or system of equations; write an objective function to determine the optimal solution for a situation; identify corner points of a feasible region of the graph of a system of inequalities algebraically and graphically; understand that the optimal solution for linear programming problems is always on the boundary of the feasible region.

__Module 3: Arithmetic and Geometric Sequences__**(F.BF.1, F.LE.1, F.LE.2, F.LE.5, A.REI.3)**

Determine if a sequence is arithmetic or geometric; identify the common difference or common ratio in a sequence; find the next terms in arithmetic and geometric sequences; write recursive and explicit rules/formulas for arithmetic and geometric sequences; use function notation to evaluate functions; model sequences with a table of values and graph the sequences; find the arithmetic and geometric means of a given sequence.

__Module 4: Linear and Exponential Functions__**(F.IF.3, F.IF.6, F.IF.7, F.LE.1, F.LE.2, F.LE.3, F.LE.5, F.BF.1, F.BF.2, A.SSE.1, A.SSE.3, A.CED.2, A.REI.3)**

Transition from arithmetic and geometric sequences to linear and exponential models; distinguish between continuous v discrete; compare linear and exponential models; apply linear and exponential function to model situations (population); solve linear and exponential equations; develop and use simple and compound interest formulas; analyze rate of change for a given context; represent linear equations using slope-intercept, standard, and point-slope forms and identify the benefits and ideal uses of each form.

__Module 5: Features of Functions__**(F.IF.1, F.IF.2, F.IF.3, F.IF.4, F.IF.5, F.IF.7, F.BF.1B , A.REI.11, A.CED.3, A.CED.4)**

Use a context to graph and describe key features of functions; use tables and graphs to interpret key features of functions; describe the key features using interval notation; combine functions and analyze contexts using functions; use graphs to solve problems given in function notation; identify whether or not a relation is a function given various representations.

__Module 6: Congruence, Construction, and Proof__**(G.CO.1, G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, G.CO.8, G.CO.12, G.CO.13, G.GPE.5)**

Develop definitions of rigid motion transformations: translations, rotations, and reflections; examine slope of perpendicular and parallel lines; examine which rigid motion transformation carries one image onto another congruent image; write and apply formal definitions of the rigid motion transformations; find rotational symmetry and lines of symmetry in quadrilaterals; examine characteristics of regular polygons that emerge from rotational symmetry and lines of symmetry; make and justify properties of quadrilaterals using symmetry transformations; describe a sequence of transformations that will carry congruent images onto each other; establish the ASA, SAS, and SSS criteria for congruent triangles; explore compass and straightedge constructions; write procedures for compass and straightedge constructions and why it creates the desired object(s).

__Module 7: Connecting Algebra and Geometry__**(G.GPE.4, G.GPE.5, G.GPE.7, F.BF.3, F.BF.1, F.IF.9)**

Use coordinates to find distances and determine the perimeter of geometric shapes; prove the slope criteria for parallel and perpendicular lines; use coordinates to algebraically prove geometric theorems; write the equation f(t) = m(t) + k by comparing parallel lines and finding

*k; d*etermine the transformations needed to map one function onto another; translate linear and exponential functions using multiple representations.

__Module 8: Modeling Data__**(S.ID.1, S.ID.3, S.ID.5, S.ID.6, S.ID.7, S.ID.8)**

Describe and compare data distributions/sets in a context, table, and/or graph; interpret and create two-way frequency tables; interpret and write conditional statements using relative frequency tables; describe the relationship between a scatterplot and its correlation coefficient; determine lines of best fit and compare these lines to linear regression equations; use residual plots to analyze the strength of a linear model.