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# Colorado Common Core Standards Ninth Grade Mathematics resources

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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

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 Circle Around

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 corresponding half-planes. (CCSS: A-REI.12)

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

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. (CCSS: S-ID.5)

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

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 Dot to Dot

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.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