# High School Math Element Cards

### General Information

Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Keywords: Element Cards, Access Points math concepts
Instructional Component Type(s):
Instructional Design Framework(s): Direct Instruction
Resource Collection: Student Support Resources

## Aligned Standards

This vetted resource aligns to concepts or skills in these benchmarks.

## Aligned Access Points

This vetted resource aligns to concepts or skills in these access points.

MAFS.912.A-APR.1.AP.1a
Understand the definition of a polynomial.

MAFS.912.A-APR.1.AP.1b
Understand the concepts of combining like terms and closure.

MAFS.912.A-APR.1.AP.1c
Add, subtract, and multiply polynomials and understand how closure applies under these operations.

MAFS.912.A-APR.2.AP.3a
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.).

MAFS.912.A-APR.2.AP.3b
Use the zeros of a function to sketch a graph of the function.

MAFS.912.A-CED.1.AP.1a
Create linear, quadratic, rational, and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems.

MAFS.912.A-CED.1.AP.2a
Graph equations in two or more variables on coordinate axes with labels and scales.

MAFS.912.A-CED.1.AP.3a
Identify and interpret the solution of a system of linear equations from a real-world context that has been graphed.

MAFS.912.A-CED.1.AP.4a
Solve multi-variable formulas or literal equations for a specific variable.

MAFS.912.A-REI.1.AP.1a
Solve equations with one or two variables and explain the process.

MAFS.912.A-REI.2.AP.3a
Solve linear equations in one variable, including coefficients represented by letters.

MAFS.912.A-REI.2.AP.3b
Solve linear inequalities in one variable, including coefficients represented by letters.

MAFS.912.A-REI.1.AP.2a
Solve simple rational and radical equations in one variable.

MAFS.912.A-REI.2.AP.4a
Solve quadratic equations by completing the square.

MAFS.912.A-REI.2.AP.4b

MAFS.912.A-REI.2.AP.4c

MAFS.912.A-REI.3.AP.5a
Create a multiple of a linear equation showing that they are equivalent (e.g., x + y = 6 is equivalent to 2x + 2y = 12).

MAFS.912.A-REI.3.AP.5b
Find the sum of two equations.

MAFS.912.A-REI.3.AP.6a
Given a graph, describe or select the solution to a system of linear equations.

MAFS.912.A-REI.4.AP.10a
Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables.

MAFS.912.A-REI.4.AP.11a
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically

MAFS.912.A-REI.4.AP.12a
Graph a linear inequality in two variables using at least two coordinate pairs that are solutions.

MAFS.912.A-REI.4.AP.12b
Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality.

MAFS.912.A-SSE.1.AP.1a
Identify the different parts of the expression and explain their meaning within the context of a problem.

MAFS.912.A-SSE.2.AP.3a
Write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros.

MAFS.912.A-SSE.1.AP.1b
Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts.

MAFS.912.A-SSE.2.AP.3b
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).

MAFS.912.A-SSE.2.AP.3c
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).

MAFS.912.F-BF.1.AP.1a
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.

MAFS.912.F-BF.2.AP.3a
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).

MAFS.912.F-IF.1.AP.1a
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.

MAFS.912.F-IF.1.AP.1b
Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship.

MAFS.912.F-IF.1.AP.2a
Match the correct function notation to a function or a model of a function (e.g., x f(x) y).

MAFS.912.F-IF.1.AP.3a
Recognize that the domain of a sequence is a subset of the integers. .

MAFS.912.F-IF.2.AP.4a
Recognize and interpret the key features of a function.

MAFS.912.F-IF.2.AP.4b
Select the graph that matches the description of the relationship between two quantities in the function.

MAFS.912.F-IF.2.AP.5a
Given the graph of a function, determine the domain.

MAFS.912.F-IF.2.AP.6a
Describe the rate of change of a function using words.

MAFS.912.F-IF.2.AP.6b
Describe the rate of change of a function using numbers.

MAFS.912.F-IF.2.AP.6c
Pair the rate of change with its graph.

MAFS.912.F-IF.3.AP.7a
Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5).

MAFS.912.F-IF.3.AP.7b
Locate the key features of linear and quadratic equations.

MAFS.912.F-IF.3.AP.8a
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].

MAFS.912.F-IF.3.AP.8b
Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).

MAFS.912.F-IF.3.AP.9a
Compare the properties of two functions.

MAFS.912.F-LE.1.AP.1a
Select the appropriate graphical representation of a linear model based on real-world events.

MAFS.912.G-C.1.AP.1a
Compare the ratio of diameter to circumference for several circles to establish all circles are similar.

MAFS.912.G-CO.1.AP.3a
Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure onto itself.

MAFS.912.G-CO.1.AP.5a
Transform a geometric figure given a rotation, reflection, or translation using graph paper, tracing paper, or geometric software.

MAFS.912.G-CO.2.AP.7a
Use definitions to demonstrate congruency and similarity in figures.

MAFS.912.G-CO.1.AP.1a
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.

MAFS.912.G-CO.1.AP.2a
Represent transformations in the plane using, e.g., transparencies and geometry software.

MAFS.912.G-CO.1.AP.2b
Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

MAFS.912.G-CO.1.AP.4a
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.

MAFS.912.G-CO.1.AP.5b
Create sequences of transformations that map a geometric figure on to itself and another geometric figure.

MAFS.912.G-CO.2.AP.6a
Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.

MAFS.912.G-CO.2.AP.6b
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.

MAFS.912.G-CO.2.AP.8a
Use the definition of congruence, based on rigid motion, to develop and explain the triangle congruence criteria; ASA, SSS, and SAS.

MAFS.912.G-CO.3.AP.9a
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.

MAFS.912.G-CO.3.AP.10a
Measure the angles and sides of equilateral, isosceles, and scalene triangles to establish facts about triangles.

MAFS.912.G-CO.3.AP.11a
Measure the angles and sides of parallelograms to establish facts about parallelograms.

MAFS.912.G-CO.4.AP.12a
Copy a segment.

MAFS.912.G-CO.4.AP.12b
Copy an angle.

MAFS.912.G-CO.4.AP.12c
Bisect a segment.

MAFS.912.G-CO.4.AP.12d
Bisect an angle.

MAFS.912.G-CO.4.AP.12e
Construct perpendicular lines, including the perpendicular bisector of a line segment.

MAFS.912.G-CO.4.AP.12f
Construct a line parallel to a given line through a point not on the line.

MAFS.912.G-CO.4.AP.13a
Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.

MAFS.912.G-GMD.2.AP.4a
Identify shapes created by cross sections of two-dimensional and three-dimensional figures.

MAFS.912.G-SRT.1.AP.1a
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.

MAFS.912.G-SRT.1.AP.2a
Determine if two figures are similar.

MAFS.912.G-SRT.1.AP.2b
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.

MAFS.912.G-SRT.1.AP.1b
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.

MAFS.912.G-SRT.1.AP.3a
Apply the angle-angle (AA) criteria for triangle similarity on two triangles.

MAFS.912.G-SRT.2.AP.4a
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.

MAFS.912.G-SRT.2.AP.5a
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.

MAFS.912.G-SRT.3.AP.6a
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.

MAFS.912.G-SRT.3.AP.7a
Explore the sine of an acute angle and the cosine of its complement and determine their relationship.

MAFS.912.N-Q.1.AP.1a
Interpret units in the context of the problem.

MAFS.912.N-Q.1.AP.1b
When solving a multi-step problem, use units to evaluate the appropriateness of the solution.

MAFS.912.N-Q.1.AP.1c
Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context.

MAFS.912.N-Q.1.AP.3a
Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely).

MAFS.912.N-Q.1.AP.1d
Choose and interpret both the scale and the origin in graphs and data displays.

MAFS.912.N-Q.1.AP.2a
Determine and interpret appropriate quantities when using descriptive modeling.

MAFS.912.N-RN.1.AP.2a
Convert from radical representation to using rational exponents and vice versa.

MAFS.912.N-RN.2.AP.3a
Know and justify that when adding or multiplying two rational numbers the result is a rational number.

MAFS.912.N-RN.1.AP.1a
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

MAFS.912.N-RN.1.AP.1b
Extend the properties of exponents to justify that (51/2)2=5

MAFS.912.N-RN.2.AP.3b
Know and justify that when adding a rational number and an irrational number the result is irrational.

MAFS.912.N-RN.2.AP.3c
Know and justify that when multiplying of a nonzero rational number and an irrational number the result is irrational.

MAFS.912.S-ID.1.AP.1a
Complete a graph given the data, using dot plots, histograms or box plots.

MAFS.912.S-ID.1.AP.2a
Describe a distribution using center and spread

MAFS.912.S-ID.1.AP.4a
Use descriptive stats like range, median, mode, mean and outliers/gaps to describe the data set.

MAFS.912.S-ID.2.AP.5a
Recognize associations and trends in data from a two-way table.

MAFS.912.S-ID.2.AP.6a
Create a scatter plot from two quantitative variables.

MAFS.912.S-ID.2.AP.6b
Describe the form, strength, and direction of the relationship.

MAFS.912.S-ID.3.AP.7a
Interpret the meaning of the slope and y-intercept in context.

MAFS.912.S-ID.1.AP.2b
Use the correct measure of center and spread to describe a distribution that is symmetric or skewed.

MAFS.912.S-ID.1.AP.2c
Identify outliers (extreme data points) and their effects on data sets.

MAFS.912.S-ID.1.AP.2d
Compare two or more different data sets using the center and spread of each.

MAFS.912.S-ID.1.AP.3a
Use statistical vocabulary to describe the difference in shape, spread, outliers and the center (mean).

MAFS.912.S-ID.2.AP.6c
Categorize data as linear or not.

MAFS.912.S-ID.2.AP.6d
Use algebraic methods and technology to fit a linear function to the data.

MAFS.912.S-ID.2.AP.6e
Use the function to predict values.

MAFS.912.S-ID.2.AP.6f
Explain the meaning of the constant and coefficients in context.

MAFS.912.S-ID.3.AP.8a
Identify the correlation coefficient (r) of a linear fit.

MAFS.912.S-ID.3.AP.8b
Describe the correlation coefficient (r) of a linear fit (e.g., a strong or weak positive, negative, perfect correlation).

MAFS.912.S-ID.3.AP.9a
Given a correlation in a real-world scenario, determine if there is causation.

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