Geometry

Completion: 0%

Transformations

8.G.18.G.28.G.3HSG-CO.2HSG-CO.5
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Translate a Shape on the Coordinate Plane--
Plot Reflections of a Point Across the x-axis--
Plot Reflections of a Point Across the y-axis--
Plot Reflections of a Point (Mixed Axes)--
Rotate a Point 90° Counterclockwise about the Origin--
Rotate a Point 180° Counterclockwise about the Origin--
Rotate a Point 270° Counterclockwise about the Origin--
Rotate a Point -90° (90° Clockwise) about the Origin--
Rotate a Point -180° (180° Clockwise) about the Origin--
Rotate a Point -270° (270° Clockwise) about the Origin--
Rotate a Point (Mixed Positive and Negative Multiples of 90°)--

Angles

7.G.58.G.5
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Classify Angle Types--
Find Complementary Angles--
Find Supplementary Angles--
Find Vertical Angles--

Polygons and Angle Sums

8.G.5HSG-CO.1
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Identify Number of Sides by Polygon Name--
Find Interior Angle Sums of Polygons--
Find Interior Angles of Regular Polygons--

Area & Perimeter

6.G.17.G.47.G.6
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Rectangle Area--
Rectangle Perimeter--
Triangle Area--
Parallelogram Area--
Circle Area--
Circle Circumference--
Trapezoid Area--
Identify Area Formulas--

Pythagorean Theorem

8.G.68.G.78.G.8HSG-SRT.8
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Find the Hypotenuse--
Find the Missing Leg--
Identify Right Triangles--
Pythagorean Theorem Mixed Practice--

Trigonometric Ratios

HSG-SRT.6HSG-SRT.7HSG-SRT.8
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Identify the Sine Ratio--
Identify the Cosine Ratio--
Identify the Tangent Ratio--
Trigonometric Ratios Mixed Practice--

Circles

HSG-C.A.2
0%
Identify Chords, Secants, and Tangents--
Intersecting Chords Theorem--
Two Secants Theorem--
Secant-Tangent Theorem--

Common Core Standards

Grade 8

NS — The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.
  • 8.NS.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
  • 8.NS.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

EE — Expressions & Equations

Work with radicals and integer exponents.
  • 8.EE.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.
  • 8.EE.2Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
  • 8.EE.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
  • 8.EE.4Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
Understand the connections between proportional relationships, lines, and linear equations.
  • 8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
  • 8.EE.6Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Analyze and solve linear equations and pairs of simultaneous linear equations.
  • 8.EE.7Solve linear equations in one variable.
  • 8.EE.8Analyze and solve pairs of simultaneous linear equations.

F — Functions

Define, evaluate, and compare functions.
  • 8.F.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  • 8.F.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • 8.F.3Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
Use functions to model relationships between quantities.
  • 8.F.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
  • 8.F.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

G — Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software.
  • 8.G.1Verify experimentally the properties of rotations, reflections, and translations.
  • 8.G.2Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  • 8.G.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • 8.G.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
  • 8.G.5Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Understand and apply the Pythagorean Theorem.
  • 8.G.6Explain a proof of the Pythagorean Theorem and its converse.
  • 8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • 8.G.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
  • 8.G.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

SP — Statistics & Probability

Investigate patterns of association in bivariate data.
  • 8.SP.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • 8.SP.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
  • 8.SP.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
  • 8.SP.4Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

High School

N-RN — The Real Number System

Extend the properties of exponents to rational exponents.
  • HSN-RN.1Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
  • HSN-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Use properties of rational and irrational numbers.
  • HSN-RN.3Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

N-Q — Quantities

Reason quantitatively and use units to solve problems.
  • HSN-Q.1Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • HSN-Q.2Define appropriate quantities for the purpose of descriptive modeling.
  • HSN-Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A-SSE — Seeing Structure in Expressions

Interpret the structure of expressions.
  • HSA-SSE.1Interpret expressions that represent a quantity in terms of its context.
  • HSA-SSE.2Use the structure of an expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems.
  • HSA-SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • HSA-SSE.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

A-APR — Arithmetic with Polynomials & Rational Expressions

Perform arithmetic operations on polynomials.
  • HSA-APR.1Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Understand the relationship between zeros and factors of polynomials.
  • HSA-APR.2Know and apply the Remainder Theorem.
  • HSA-APR.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

A-CED — Creating Equations

Create equations that describe numbers or relationships.
  • HSA-CED.1Create equations and inequalities in one variable and use them to solve problems.
  • HSA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • HSA-CED.3Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
  • HSA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI — Reasoning with Equations & Inequalities

Understand solving equations as a process of reasoning and explain the reasoning.
  • HSA-REI.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
  • HSA-REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable.
  • HSA-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • HSA-REI.4Solve quadratic equations in one variable.
Solve systems of equations.
  • HSA-REI.5Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
  • HSA-REI.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • HSA-REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Represent and solve equations and inequalities graphically.
  • HSA-REI.10Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
  • HSA-REI.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).
  • HSA-REI.12Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F-IF — Interpreting Functions

Understand the concept of a function and use function notation.
  • HSF-IF.1Understand that 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.
  • HSF-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • HSF-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Interpret functions that arise in applications in terms of the context.
  • HSF-IF.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • HSF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • HSF-IF.6Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations.
  • HSF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • HSF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • HSF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F-BF — Building Functions

Build a function that models a relationship between two quantities.
  • HSF-BF.1Write a function that describes a relationship between two quantities.
  • HSF-BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Build new functions from existing functions.
  • HSF-BF.3Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
  • HSF-BF.4Find inverse functions.

F-LE — Linear, Quadratic, & Exponential Models

Construct and compare linear, quadratic, and exponential models and solve problems.
  • HSF-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • HSF-LE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.
  • HSF-LE.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Interpret expressions for functions in terms of the situation they model.
  • HSF-LE.5Interpret the parameters in a linear or exponential function in terms of a context.

G-CO — Congruence

Experiment with transformations in the plane.
  • HSG-CO.1Know 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.
  • HSG-CO.2Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.
  • HSG-CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • HSG-CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • HSG-CO.5Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Understand congruence in terms of rigid motions.
  • HSG-CO.6Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.
  • HSG-CO.7Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
  • HSG-CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

G-SRT — Similarity, Right Triangles, & Trigonometry

Understand similarity in terms of similarity transformations.
  • HSG-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor.
  • HSG-SRT.2Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles.
  • HSG-SRT.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity.
  • HSG-SRT.4Prove theorems about triangles.
  • HSG-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles.
  • HSG-SRT.6Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
  • HSG-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.
  • HSG-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

S-ID — Interpreting Categorical & Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable.
  • HSS-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • HSS-ID.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • HSS-ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables.
  • HSS-ID.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data.
  • HSS-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Interpret linear models.
  • HSS-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
  • HSS-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • HSS-ID.9Distinguish between correlation and causation.