Aligned Access Points
This vetted resource aligns to concepts or skills in these access points.
Add, subtract, and multiply polynomials and understand how closure applies under these operations.
Find the zeros of a polynomial when the polynomial is factored (e.g., If given the polynomial equation y = x2 + 5x + 6, factor the polynomial as y = (x + 3)(x + 2). Then find the zeros of y by setting each factor equal to zero and solving. x = -2 and x = -3 are the two zeroes of y.).
Create linear, quadratic, rational, and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems.
Identify and interpret the solution of a system of linear equations from a real-world context that has been graphed.
Solve linear inequalities in one variable, including coefficients represented by letters.
Create a multiple of a linear equation showing that they are equivalent (e.g., x + y = 6 is equivalent to 2x + 2y = 12).
Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically
Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.
Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality.
Identify the different parts of the expression and explain their meaning within the context of a problem.
Write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros.
Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts.
Given a quadratic function, explain the meaning of the zeros of the function (e.g., if f(x) = (x - c) (x - a) then f(a) = 0 and f(c) = 0).
Given a quadratic expression, explain the meaning of the zeros graphically (e.g., for an expression (x - a) (x - c), a and c correspond to the x-intercepts (if a and c are real).
Select a function that describes a relationship between two quantities (e.g., relationship between inches and centimeters, Celsius Fahrenheit, distance = rate x time, recipe for peanut butter and jelly- relationship of peanut butter to jelly f(x)=2x, where x is the quantity of jelly, and f(x) is peanut butter.
Write or select the graph that represents a defined change in the function (e.g., recognize the effect of changing k on the corresponding graph).
Demonstrate that to be a function, from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship.
Match the correct function notation to a function or a model of a function (e.g., x f(x) y).
Select the graph that matches the description of the relationship between two quantities in the function.
Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5).
Write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).
Select the appropriate graphical representation of a linear model based on real-world events.
Compare the ratio of diameter to circumference for several circles to establish all circles are similar.
Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure onto itself.
Transform a geometric figure given a rotation, reflection, or translation using graph paper, tracing paper, or geometric software.
Identify precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Represent transformations in the plane using, e.g., transparencies and geometry software.
Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Using previous comparisons and descriptions of transformations, develop and understand the meaning of rotations, reflections, and translations based on angles, circles, perpendicular lines, parallel lines, and line segments.
Create sequences of transformations that map a geometric figure on to itself and another geometric figure.
Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.
Knowing that rigid transformations preserve size and shape or distance and angle, use this fact to connect the idea of congruency and develop the definition of congruent.
Use the definition of congruence, based on rigid motion, to develop and explain the triangle congruence criteria; ASA, SSS, and SAS.
Measure lengths of line segments and angles to establish the facts about the angles created when parallel lines are cut by a transversal and the points on a perpendicular bisector.
Measure the angles and sides of equilateral, isosceles, and scalene triangles to establish facts about triangles.
Measure the angles and sides of parallelograms to establish facts about parallelograms.
Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
Identify shapes created by cross sections of two-dimensional and three-dimensional figures.
Given a center and a scale factor, verify experimentally that when dilating a figure in a coordinate plane, a segment of the pre-image that does not pass through the center of the dilation, is parallel to its image when the dilation is performed. However, a segment that passes through the center remains unchanged.
Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides.
Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor.
Establish facts about the lengths of segments of sides of a triangle when a line parallel to one side of the triangles divides the other two sides proportionally.
Apply the criteria for triangle congruence and/or similarity (angle-side-angle [ASA], side-angle-side [SAS], side-side-side [SSS], angle-angle [AA] to determine if geometric shapes that divide into triangles are or are not congruent and/or can be similar.
Using a corresponding angle of similar right triangles, show that the relationships of the side ratios are the same, which leads to the definition of trigonometric ratios for acute angles.
Explore the sine of an acute angle and the cosine of its complement and determine their relationship.
When solving a multi-step problem, use units to evaluate the appropriateness of the solution.
Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context.
Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely).
Choose and interpret both the scale and the origin in graphs and data displays.
Determine and interpret appropriate quantities when using descriptive modeling.
Know and justify that when adding or multiplying two rational numbers the result is a rational number.
Understand that the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand (e.g., 51/2 = √5). Extend the properties of exponents to justify that (51/2)2=5
Know and justify that when adding a rational number and an irrational number the result is irrational.
Know and justify that when multiplying of a nonzero rational number and an irrational number the result is irrational.
Use descriptive stats like range, median, mode, mean and outliers/gaps to describe the data set.
Use the correct measure of center and spread to describe a distribution that is symmetric or skewed.
Use statistical vocabulary to describe the difference in shape, spread, outliers and the center (mean).
Describe the correlation coefficient (r) of a linear fit (e.g., a strong or weak positive, negative, perfect correlation).