NO: Number Systems and Operations

1.1: Understand that the real number system is composed of rational and irrational numbers.

NO.1: Students will… Define the real number system as composed of rational and irrational numbers.

NO.1.a: Explain that every number has a decimal expansion; for rational numbers, the decimal expansion repeats or terminates.

Circumference and Area of Circles
Percents, Fractions, and Decimals

NO.2: Students will… Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers.

Circumference and Area of Circles
Square Roots

AF: Algebra and Functions

2.1: Apply concepts of integer exponents and radicals.

AF.3: Students will… Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

AF.4: Students will… Use square root and cube root symbols to represent solutions to equations.

AF.4.a: Evaluate square roots of perfect squares (less than or equal to 225) and cube roots of perfect cubes (less than or equal to 1000).

Square Roots

AF.5: Students will… Estimate and compare very large or very small numbers in scientific notation.

Number Systems
Unit Conversions 2 - Scientific Notation and Significant Digits

AF.6: Students will… Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

AF.6.a: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

Unit Conversions 2 - Scientific Notation and Significant Digits

2.2: Analyze the relationship between proportional and non-proportional situations.

AF.7: Students will… Determine whether a relationship between two variables is proportional or non-proportional.

Direct and Inverse Variation

AF.8: Students will… Graph proportional relationships.

AF.8.a: Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope.

Direct and Inverse Variation

AF.9: Students will… Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

AF.9.a: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

Slope-Intercept Form of a Line

AF.9.b: Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

Slope

AF.9.c: Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

Point-Slope Form of a Line
Slope-Intercept Form of a Line

AF.9.d: Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.

Slope-Intercept Form of a Line

AF.10: Students will… Compare proportional and non-proportional linear relationships represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) to solve real-world problems.

Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

2.3: Analyze and solve linear equations and systems of two linear equations.

AF.11: Students will… Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

AF.11.a: Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

Solving Equations by Graphing Each Side

AF.11.b: Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

AF.12: Students will… Solve systems of two linear equations in two variables by graphing and substitution.

AF.12.a: Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

AF.12.b: Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

2.4: Explain, evaluate, and compare functions.

AF.13: Students will… Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.

Introduction to Functions
Linear Functions

AF.14: Students will… Evaluate functions defined by a rule or an equation, given values for the independent variable.

Points, Lines, and Equations

AF.15: Students will… Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

AF.15.a: Distinguish between linear and non-linear functions.

Absolute Value with Linear Functions
Linear Functions

2.5: Use functions to model relationships between quantities.

AF.16: Students will… Construct a function to model a linear relationship between two variables.

AF.16.a: Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship or from two points in a table or graph.

Cat and Mouse (Modeling with Linear Systems)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

AF.17: Students will… Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Absolute Value with Linear Functions
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions

DSP: Data Analysis, Statistics, and Probability

3.1: Investigate patterns of association in bivariate data.

DSP.18: Students will… Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

DSP.19: Students will… Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

DSP.20: Students will… Use a linear model of a real-world situation to solve problems and make predictions.

DSP.20.a: Describe the rate of change and y-intercept in the context of a problem using a linear model of a real-world situation.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

DSP.21: Students will… Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects, using relative frequencies calculated for rows or columns to describe possible associations between the two variables.

Polling: City

GM: Geometry and Measurement

4.1: Understand congruence and similarity using physical models or technology.

GM.22: Students will… Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

GM.22.a: Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

Reflections
Rotations, Reflections, and Translations

GM.23: Students will… Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.

Dilations
Rotations, Reflections, and Translations

GM.24: Students will… Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Dilations
Similar Figures

4.2: Analyze parallel lines cut by a transversal.

GM.25: Students will… Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

GM.25.a: Use informal arguments to establish that the sum of the interior angles of a triangle is 180 degrees.

Triangle Angle Sum

4.3: Understand and apply the Pythagorean Theorem.

GM.26: Students will… Informally justify the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

GM.27: Students will… Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

Distance Formula

GM.28: Students will… Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

4.4: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

GM.29: Students will… Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions.

Pyramids and Cones

GM.30: Students will… Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

Prisms and Cylinders
Pyramids and Cones