Learners will develop a foundational understanding of the number system, operations, and computational fluency to create connections and solve problems within and across concepts.

MAT-12.NO.18 Multiply a vector by a scalar.

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction. Use the components to perform scalar multiplication (e.g., as c(vx, vy) = (cvx , cvy)).

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v.

Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

MAT-03.GM.G.01 In two-dimensional shapes, identify lines, angles (right, acute, obtuse), and perpendicular and parallel lines.

MAT-05.GM.G.02 Identify the x-coordinate and y-coordinate to graph and name points in the first quadrant of the coordinate plane.

MAT-05.GM.G.03 Form ordered pairs and graph points in the first quadrant of the coordinate plane to solve authentic word problems.

MAT-06.GM.GF.01 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.

MAT-06.GM.GF.02 Draw polygons in the coordinate plane given coordinates for vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.

MAT-10.GM.27 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.

MAT-10.GM.28 Verify simple geometric theorems algebraically using coordinates. Verify algebraically, using coordinates, that a given set of points produces a particular type of triangle or quadrilateral.

MAT-10.GM.29 Determine the midpoint or endpoint of a line segment using coordinates. (+) Find the point on a directed line segment between two given points that partitions the segments in a given ratio.

MAT-12.NO.10 Represent complex numbers on the complex plane in rectangular, trigonometric, and polar forms. Find the modulus (absolute value) of a complex number. Explain why the rectangular, trigonometric, and polar forms of a given
complex number represent the same number.

MAT-12.NO.11 Represent addition, subtraction, multiplication, conjugation, powers, and roots of complex numbers geometrically on the complex and/or polar plane; use properties of this representation for computation.

MAT-12.NO.14 Recognize vector quantities as having both magnitude and direction, writing them in polar form.

MAT-12.NO.15 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

MAT-12.NO.16 Solve problems involving magnitude and direction that can be represented by vectors.

MAT-12.NO.17 Add and subtract vectors.

MAT-12.NO.18 Multiply a vector by a scalar.

MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

MAT-12.AR.F.19 Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

Transformations

MAT-08.GM.GF.01 Perform single transformations to a figure on or off the coordinate plane and determine whether the figures are congruent or similar.

MAT-08.GM.GF.02 Describe the characteristics of transformations on the coordinate plane using transformation language.

MAT-08.GM.GF.03 Name the type of transformation(s) needed to map a pre-image to its image.

MAT-09.AR.F.09 Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with f(x) + k, f(x - h) and af(x), for specific values of a, h, and k (both positive and negative).
Find the values of a, h, and k given the graph of the function.

MAT-10.GM.02 Represent transformations in the plane. Describe transformations as functions that take points as outputs. Compare transformations that preserve distance and angle to those that do not (i.e., rigid versus non-rigid motion).

MAT-10.GM.03 Describe the rotations and reflections of a triangle, rectangle, parallelogram, trapezoid, or regular polygon that map each figure onto itself or another figure.

MAT-10.GM.04 Develop or verify the characteristics of rotations, reflections, and translations in angles, circles, perpendicular lines, parallel lines, and line segments.

MAT-10.GM.05 Draw the image of a figure that has undergone a series of transformations [rotation(s),

reflection(s), or translation(s)] of a geometric figure using a variety of methods (e.g., graph paper, tracing paper, or geometry software).

MAT-10.GM.06 Predict the effect of a specified rigid motion on a given figure using geometric descriptions of rigid motions. Determine whether two figures are congruent using the definition of congruence in terms of rigid motions.

MAT-10.GM.14 Verify experimentally and justify the properties of dilations given by a center and a scale factor.

MAT-10.GM.15 Use transformations to decide if two given figures are similar. Apply the meaning of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MAT-10.GM.16 Prove similarity theorems about triangles.

MAT-10.GM.17 Apply knowledge of congruence and similarity criteria for triangles to solve problems and prove relationships in various geometric figures.

MAT-12.AR.F.4 Identify the effect of transformations on the graph of a function by replacing f(x) with af(x), f(bx), f(x-h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the values of a, b, h, and
k given the graph of the function. Recognize even and odd functions from their graphs and equations.