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Colorado Academic Standards (CAS)

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CO.HS.1.Number Sense, Properties, and Operations

Number Sense, Properties, and Operations

HS.1.1. The complex number system includes real numbers and imaginary numbers. Students can:

HS.1.1.a. Extend the properties of exponents to rational exponents. (CCSS: NRN)

HS.1.1.a.ii. Rewrite expressions involving radicals and rational exponents using the properties of exponents. (CCSS: N-RN.2)

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

HS.1.1.b. Use properties of rational and irrational numbers. (CCSS: N-RN)

HS.1.1.b.ii. Explain why the sum of a rational number and an irrational number is irrational. (CCSS: N-RN.3)

Flip Charts Math Grade 8

Flip Charts The Real Numbers

HS.1.1.b.iii. Explain why the product of a nonzero rational number and an irrational number is irrational. (CCSS: N-RN.3)

Flip Charts Math Grade 8

Flip Charts The Real Numbers

HS.1.2. Quantitative reasoning is used to make sense of quantities and their relationships in problem situations. Students can:

HS.1.2.a. Reason quantitatively and use units to solve problems (CCSS: N-Q)

HS.1.2.a.i. Use units as a way to understand problems and to guide the solution of multi-step problems. (CCSS: N-Q.1)

HS.1.2.a.i.2. Choose and interpret the scale and the origin in graphs and data displays. (CCSS: N-Q.1)

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

HS.1.2.a.iv. Describe factors affecting take-home pay and calculate the impact (PFL).

Flip Charts Applying Percents

Flip Charts Math Grade 8

CO.HS.2.Patterns, Functions, and Algebraic Structures

Patterns, Functions, and Algebraic Structures

HS.2.1. Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables. Students can:

HS.2.1.a. Formulate the concept of a function and use function notation. (CCSS: F-IF)

HS.2.1.a.i. Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. (CCSS: F-IF.1)

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

HS.2.1.a.iii. Demonstrate that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (CCSS: F-IF.3)

Flip Charts Arithmetic & Sequences

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

HS.2.1.b. Interpret functions that arise in applications in terms of the context. (CCSS: F-IF)

HS.2.1.b.i. For 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. (CCSS: F-IF.4)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

HS.2.1.b.iii. Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. (CCSS: F-IF.6)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

HS.2.1.c. Analyze functions using different representations. (CCSS: F-IF)

HS.2.1.c.i. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (CCSS: F-IF.7)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

HS.2.1.c.ii. Graph linear and quadratic functions and show intercepts, maxima, and minima. (CCSS: F-IF.7a)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

HS.2.1.c.vi. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS: F-IF.8)

HS.2.1.c.vi.2. Use the properties of exponents to interpret expressions for exponential functions. (CCSS: F-IF.8b)

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

HS.2.1.d. Build a function that models a relationship between two quantities. (CCSS: F-BF)

HS.2.1.d.i. Write a function that describes a relationship between two quantities. (CCSS: F-BF.1)

HS.2.1.d.i.1. Determine an explicit expression, a recursive process, or steps for calculation from a context. (CCSS: F-BF.1a)

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

HS.2.2. Quantitative relationships in the real world can be modeled and solved using functions. Students can:

HS.2.2.a. Construct and compare linear, quadratic, and exponential models and solve problems. (CCSS: F-LE)

HS.2.2.a.i. Distinguish between situations that can be modeled with linear functions and with exponential functions. (CCSS: F-LE.1)

HS.2.2.a.i.1. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (CCSS: F-LE.1a)

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

HS.2.2.d. Model personal financial situations.

HS.2.2.d.i. Analyze the impact of interest rates on a personal financial plan (PFL).

Flip Charts Applying Percents

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent

HS.2.3. Expressions can be represented in multiple, equivalent forms. Students can:

HS.2.3.b. Write expressions in equivalent forms to solve problems. (CCSS: A-SSE)

HS.2.3.b.i. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (CCSS: A-SSE.3)

HS.2.3.b.i.3. Use the properties of exponents to transform expressions for exponential functions. (CCSS: A-SSE.3c)

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

HS.2.3.c. Perform arithmetic operations on polynomials. (CCSS: A-APR)

HS.2.3.c.i. Explain 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. (CCSS: A-APR.1)

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

HS.2.4. Solutions to equations, inequalities and systems of equations are found using a variety of tools. Students can:

HS.2.4.a. Create equations that describe numbers or relationships. (CCSS: A-CED)

HS.2.4.a.i. Create equations and inequalities in one variable and use them to solve problems. (CCSS: A-CED.1)

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

HS.2.4.a.ii. Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales. (CCSS: A-CED.2)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

HS.2.4.a.iii. Represent 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. (CCSS: A-CED.3)

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

HS.2.4.a.iv. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (CCSS: A-CED.4)

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

HS.2.4.b. Understand solving equations as a process of reasoning and explain the reasoning. (CCSS: A-REI)

HS.2.4.b.i. Explain 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. (CCSS: A-REI.1)

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

HS.2.4.c. Solve equations and inequalities in one variable. (CCSS: A-REI)

HS.2.4.c.i. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (CCSS: A-REI.3)

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

HS.2.4.d. Solve systems of equations. (CCSS: A-REI)

HS.2.4.d.i. Prove 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. (CCSS: A-REI.5)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

HS.2.4.d.ii. Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. (CCSS: A-REI.6)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

HS.2.4.e. Represent and solve equations and inequalities graphically. (CCSS: A-REI)

HS.2.4.e.ii. Explain 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); find the solutions approximately. (CCSS: A-REI.11)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

HS.2.4.e.iii. Graph 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 correspondin

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

CO.HS.3.Data Analysis, Statistics, and Probability

Data Analysis, Statistics, and Probability

HS.3.1. Visual displays and summary statistics condense the information in data sets into usable knowledge. Students can:

HS.3.1.b. Summarize, represent, and interpret data on two categorical and quantitative variables. (CCSS: S-ID)

HS.3.1.b.i. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

HS.3.1.b.ii. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS: S-ID.6)

HS.3.1.b.ii.2. Informally assess the fit of a function by plotting and analyzing residuals. (CCSS: S-ID.6b)

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

HS.3.1.b.ii.3. Fit a linear function for a scatter plot that suggests a linear association. (CCSS: S-ID.6c)

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

HS.3.3. Probability models outcomes for situations in which there is inherent randomness. Students can:

HS.3.3.a. Understand independence and conditional probability and use them to interpret data. (CCSS: S-CP)

HS.3.3.a.ii. Explain that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (CCSS: S-CP.2)

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

CO.HS.4.Shape, Dimension, and Geometric Relationships

Shape, Dimension, and Geometric Relationships

HS.4.1. Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically. Students can:

HS.4.1.a. Experiment with transformations in the plane. (CCSS: G-CO)

HS.4.1.a.i. State 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. (CCSS: G-CO.1)

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

Flip Charts Plane Geometry

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

HS.4.1.a.iii. Describe transformations as functions that take points in the plane as inputs and give other points as outputs. (CCSS: G-CO.2)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

HS.4.1.a.v. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. (CCSS: G-CO.3)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.a.vi. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. (CCSS: G-CO.4)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.a.vii. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using appropriate tools. (CCSS: G-CO.5)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.a.viii. Specify a sequence of transformations that will carry a given figure onto another. (CCSS: G-CO.5)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.b. Understand congruence in terms of rigid motions. (CCSS: G-CO)

HS.4.1.b.i. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. (CCSS: G-CO.6)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.b.ii. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. (CCSS: G-CO.6)

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

HS.4.1.c. Prove geometric theorems. (CCSS: G-CO)

HS.4.1.c.i. Prove theorems about lines and angles. (CCSS: G-CO.9)

Flip Charts Math Grade 8

Flip Charts Plane Geometry

HS.4.2. Concepts of similarity are foundational to geometry and its applications. Students can:

HS.4.2.a. Understand similarity in terms of similarity transformations. (CCSS: G-SRT)

HS.4.2.a.i. Verify experimentally the properties of dilations given by a center and a scale factor. (CCSS: G-SRT.1)

HS.4.2.a.i.1. Show that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. (CCSS: G-SRT.1a)

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

HS.4.2.a.i.2. Show that the dilation of a line segment is longer or shorter in the ratio given by the scale factor. (CCSS: G-SRT.1b)

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

HS.4.2.a.ii. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. (CCSS: G-SRT.2)

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

HS.4.2.b. Prove theorems involving similarity. (CCSS: G-SRT)

HS.4.2.b.iii. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS: G-SRT.5)

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

HS.4.3. Objects in the plane can be described and analyzed algebraically. Students can:

HS.4.3.a. Express Geometric Properties with Equations. (CCSS: G-GPE)

HS.4.3.a.ii. Use coordinates to prove simple geometric theorems algebraically. (CCSS: G-GPE)

HS.4.3.a.ii.2. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. (CCSS: G-GPE.5)

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

HS.4.3.a.ii.4. Use coordinates and the distance formula to compute perimeters of polygons and areas of triangles and rectangles. (CCSS: G-GPE.7)

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

HS.4.4. Attributes of two- and three-dimensional objects are measurable and can be quantified. Students can:

HS.4.4.a. Explain volume formulas and use them to solve problems. (CCSS: G-GMD)

HS.4.4.a.i. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (CCSS: G-GMD.1)

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

HS.4.4.a.ii. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (CCSS: G-GMD.3)

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement