CRM.NR: Numerical & Quantitative Reasoning – Real Number System

CRM.NR.2: Utilize exact and approximate calculations to quantify real-world phenomena and solve problems.

CRM.NR.2.1: Through multi-step/multi-operational problems, perform mathematical operations on real numbers demonstrating fluency using the order of operations.

Order of Operations

CRM.NR.2.2: Represent and solve problems using proportional reasoning with ratios, rates, proportions, and scaling.

Beam to Moon (Ratios and Proportions)
Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions

CRM.NR.2.3: Apply the rules of exponents to simplify numerical expressions, extending the properties of exponents to rational exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

CRM.NR.2.4: Perform mathematical operations on real numbers to include numerical radical expressions and complex fractions.

Operations with Radical Expressions

CRM.PAR: Patterning & Algebraic Reasoning – Expressions, Equations, & Inequalities

CRM.PAR.3: Construct expressions, equations, and inequalities, and use them to represent and solve problems by choosing appropriate procedures and interpreting solutions in context.

CRM.PAR.3.1: Create equations in one variable and use them to solve problems.

Compound Interest
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side

CRM.PAR.3.2: Create inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

CRM.PAR.3.3: Using multiple representations, solve equations and inequalities and use the solutions to draw reasonable conclusions about a situation being modeled, including possible constraints.

Compound Interest
Direct and Inverse Variation
Linear Programming
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

CRM.PAR.3.4: Solve quadratic equations using a variety of methods.

Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

CRM.PAR.3.5: Rearrange literal equations to highlight a specified variable using the same reasoning as in solving equations.

Solving Formulas for any Variable

CRM.PAR.3.6: Solve inequalities in one variable graphically and algebraically.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

CRM.PAR.3.7: Using multiple methods, create and solve systems of linear equations and inequalities.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

CRM.FGR: Functional & Graphical Reasoning – Building & Interpreting Functions

CRM.FGR.4: Define, build and interpret functions that arise in various contexts by applying knowledge of the characteristics of the different families of functions, and analyze the effects of parameters.

CRM.FGR.4.1: Define a function through maps, sets, equations and graphs using function notation.

Introduction to Functions
Linear Functions
Points, Lines, and Equations

CRM.FGR.4.2: Identify and sketch by hand the parent graph of functions expressed algebraically and show key characteristics of the graph using technology.

Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Translating and Scaling Functions

CRM.FGR.4.3: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function.

Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Translating and Scaling Functions

CRM.FGR.4.4: Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph.

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

CRM.FGR.4.6: Construct linear and exponential functions, given a graph, a description of a relationship, or two input-output pairs.

Exponential Functions
Introduction to Exponential Functions
Slope-Intercept Form of a Line

CRM.FGR.4.7: Construct arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect linear functions to arithmetic sequences and exponential functions to geometric sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

CRM.FGR.4.8: Identify the effect on the parent graph of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Translating and Scaling Functions

CRM.GSR: Geometric & Spatial Reasoning – Measurement, Surface Area, Volume, & Right Triangle Trigonometry

CRM.GSR.5: Reason deductively and inductively about figures and their properties and make sense of geometric situations using measurements in real-world contexts.

CRM.GSR.5.1: Use the distance formula, midpoint formula or slope to verify simple geometric properties.

Distance Formula
Slope

CRM.GSR.5.2: Use coordinates to compute perimeters of polygons, circumference of circles and areas of triangles, rectangles and circles.

Distance Formula

CRM.GSR.5.3: Informally derive the formulas for the volume and surface area of a cylinder, sphere, prism, pyramid, and cone.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

CRM.GSR.5.4: Use formulas for finding the volume and surface area of spheres, right and oblique prisms, cylinders, pyramids, and cone.

Measuring Volume
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

CRM.GSR.5.5: Apply the Pythagorean Theorem and trigonometric ratios to solve problems involving right triangles.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios

CRM.DSR: Data & Statistical Reasoning – Interpreting Data & Calculating Probabilities of Compound Events

CRM.DSR.6: Make sense of and reason about variation in data using graphs, tables and probability models to solve problems and draw appropriate conclusions from solutions.

CRM.DSR.6.1: Represent univariate data on the real number line

Box-and-Whisker Plots
Histograms

CRM.DSR.6.2: Calculate, compare, and interpret shape, center, and spread of two or more univariate data sets, accounting for possible effects of extreme data points.

Describing Data Using Statistics
Mean, Median, and Mode
Real-Time Histogram

CRM.DSR.6.4: Represent bivariate data on a scatter plot and describe how the variables are related in terms of strength and direction.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

CRM.DSR.6.5: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

CRM.DSR.6.6: Compute using technology and interpret the correlation coefficient “r” of a linear fit

Correlation

CRM.DSR.6.7: Distinguish between correlation and causation, and interpolation and extrapolation.

Correlation

CRM.DSR.6.10: Calculate the conditional probability of A given B.

Independent and Dependent Events