• # Sequences

In Module 1, students develop an understanding of Arithmetic Sequences and Geometric Sequences by looking at multiple representations (patterns/context, tables, equations, and graphs).

By the end of this module, students should be able to do the following:

• Identify a sequence as being arithmetic (adding), geometric (multiplying), or neither.
• Determine the constant difference (growth) of an arithmetic sequence.
• Determine the common ratio (growth factor) of a geometric sequence.
• Determine the initial value of a sequence (both when n=0 and n=1).
• Write an explicit equation and recursive equation for arithmetic and geometric sequences.
• Solve problems involving arithmetic and geometric sequences.

Module 1 Resources:

• # Linear & Exponential Functions

In Module 2, students will work with continuous linear and exponential functions in various representations (context, table, equation, graph). They will also compare these functions to arithmetic and geometric sequences to understand the difference between continuous and discrete.

By the end of this module, students should be able to do the following:

• Identify whether a situation/context is continuous or discrete.
• Identify whether a problem (context, table, equation, graph) is linear, exponential, or neither.
• Identify a function's rate of change and compare it to another function's rate of change.
• Use the linear Point-Slope Form to graph and solve problems.
• Make tables, write equations, and graph problems of linear functions.
• Make tables, write equations, and graph problems of exponential functions.

Module 2 Resources:

• # Features of Functions

In Module 3, students identify a function's key features (continuous, discrete, increasing, decreasing, domain, range, maximum, minimum, intercepts, rate of change, step-functions, function values, and more).

By the end of this module, students should be able to do the following:

• Determine if a function is continuous or discrete.
• Identify intervals where a function is increasing or decreasing from a table or graph.
• Identify the domain and range of a function.
• Locate local maximum values and local minimum values of a function.
• Identify intercepts of a function.
• Determine the rate of change of a function.
• Determine function values, including using function notation.
• Interpret the key features as they relate to a context.
• Write intervals in interval notation and inequality notation.

Module 3 Resources:

• # Equations & Inequalities

In Module 4, students build on prior knowledge of solving linear equations and inequalities. They work with more complicated equations/inequalities (multi-step) and examine the meaning of the symbols as applied to a context.

By the end of this module, students should be able to do the following:

• Solve multi-step linear equations using equivalent (simplified) equations to isolate the unknown. (i.e. "Keep the equation balanced").
• Solve multi-step linear inequalities using properties of inequalities.
• Solve literal equations ("formulas" or equations with letter coefficients).
• Write and solve an equation or inequality for a context/application.
• Write solutions to inequalities in both interval notation and set notation.
• Graph solutions to one-variable inequalities on a number line.

Module 4 Resources:

• # Transformations & Symmetry

In Module 6, students use rigid geometric transformations (reflection, rotation, translation) to understand important properties of geometric shapes. They will also use geometric transformations to understand ideas of algebra (namely, slopes of parallel or perpendicular lines).

By the end of this module, students should be able to do the following:

• Reflect a shape on a grid (on graph paper) across a line to the precise new location.
• Rotate a shape on a grid (on graph paper) around a point to the precise new location.
• Translate a shape on a grid (on graph paper) to the precise new location.
• Identify a sequence of transformations that will match an original image ("preimage") to a transformed/new image ("image").
• Write an equation of a line that is parallel to a give/know line.
• Write an equation of a line that is perpendicular to a give/known line.
• Identify features of geometric shapes (mainly polygons). These features include lines of symmetry, centers of rotation, congruent angles, congruent sides, properties of diagonals, etc.

Module 6 Resources:

• # Congruence, Construction & Proof

In Module 7, students use compass and straight edge constructions to further understand properties of shapes as well as understand the minimum conditions required to ensure two triangles are congruent (matching in size and shape).

By the end of this module, students should be able to do the following:

• Complete a number of geometric constructions (construct a rhombus, a square, parallelograms, equilateral triangles, inscribed hexagons, parallel lines, perpendicular bisector, perpendicular line through a given point, angle bisector, etc.)
• Identify whether two triangles are congruent using SAS, ASA, AAS, and SSS Triangle Congruence.
• Identify corresponding parts of congruent shapes.

Module 7 Resources:

• # Connecting Algebra & Geometry

In Module 8, students work with geometric shapes on the coordinate plane to connect ideas from geometry to ideas found in algebra. Specifically, students use the geometric Pythagorean Theorem while on the coordinate plane to create the algebraic Distance Formula for coordinates.

By the end of this module, students should be able to do the following:

• Calculate the distance between two points on the coordinate plane.
• Calculate the perimeter and/or area of a geometric shape drawn on the coordinate plane.
• Prove the slope criteria for parallel lines (same slope) and perpendicular lines (opposite reciprocal slope).
• Classify shapes that are drawn on the coordinate plane by connecting algebraic and geometric properties.
• Transform algebraic functions by translating up or down.

Module 8 Resources:

• # Modeling Data

In Module 9, students work with data displayed in various ways - a simple list, histogram, stem-and-leaf, two-way table, scatter plot, and more. Emphasis is placed on interpreting the data display within a context and making informed decisions after analyzing the data.

By the end of this module, students should be able to do the following:

• Describe data set by describing shape, center, and spread.
• Interpret two-way frequency tables.
• Interpret relative frequency tables.
• Estimate the line of best fit and the correlation co-efficient.
• Use technology to calculate the line of best fit (linear regression) and the correlation co-efficient.

Module 9 Resources: