M1. Number and Operation Concepts

M1a. Use addition, subtraction, multiplication, division, exponentiation, and root-extraction.

Fractions with Unlike Denominators

Multiplying Fractions

Dividing Fractions

Multiplying Mixed Numbers

Dividing Mixed Numbers

Exponents and Power Rules

Multiplying Exponential Expressions

Dividing Exponential Expressions

M1b. Understand and use opposite, reciprocal, raising to a power, taking a root, and taking a logarithm.

Real Number Line - Activity A

Dividing Mixed Numbers

Exponents and Power Rules

Square Roots

Logarithmic Functions - Activity A

M1c. Have facility with the mechanics of operations as well as understanding of their typical meaning and uses in applications.

Order of Operations

Using Algebraic Equations

M1d. Understand and use number systems.

Comparing and Ordering Integers

Comparing and Ordering Decimals

Comparing and Ordering Rational Numbers

M1e. Represent numbers in various forms and graph them.

Real Number Line - Activity A

Points in the Coordinate Plane - Activity B

M1f. Compare numbers using order relations, differences, ratios, proportions, percents, and proportional change.

Percents, Fractions and Decimals

Ordering Percents, Fractions and Decimals

Ordering Percents, Fractions and Decimals Greater Than 1

M1g. Carry out proportional reasoning.

Percents and Proportions

Part:Part and Part:Whole Ratios

Proportions and Common Multipliers

Percent of Change

Beam to Moon (Ratios and Proportions)

Estimating Population Size

M1h. Understand dimensionless numbers as well as numbers with specific units of measure.

Elapsed Time

Percents and Proportions

Triple Beam Balance

Multiplying with Decimals

M1i. Carry out counting procedures such as those involving sets and arrangements.

Permutations

Permutations and Combinations

M1j. Use concepts in solving problems involving integers.

Finding Factors with Area Models

M1l. Recognize and represent basic number patterns.

Finding Patterns

Arithmetic and Geometric Series

Exponential Functions - Activity A

M2. Geometry and Measurement Concepts

M2b. Work with two- and three- dimensional figures and their properties.

Polygon Angle Sum - Activity B

Parallelogram Conditions

Chords and Arcs

Inscribing Angles

Prisms and Cylinders - Activity B

Pyramids and Cones - Activity B

M2c. Use congruence and similarity in describing relationships between figures.

Similar Polygons

Similarity in Right Triangles

Perimeters and Areas of Similar Figures

Investigating Angle Theorems - Activity B

Constructing Congruent Segments and Angles

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

M2d. Visualize objects, paths, and regions in space and describe these using geometric language.

3D and Orthographic Views - Activity B

M2e. Know, use, and derive formulas for perimeter, circumference, area, surface area, and volume.

Area of Parallelograms - Activity B

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity B

Pyramids and Cones - Activity B

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

M2f. Use the Pythagorean Theorem in many types of situations.

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity B

Distance Formula - Activity A

M2g. Work with similar triangles and use the three basic trigonometric functions.

Similarity in Right Triangles

Sine and Cosine Ratios - Activity B

M2h. Analyze figures in terms of their symmetries.

Reflections

M2i. Compare slope and angle of elevation as measures of steepness.

Slope - Activity B

M2j. Investigate geometric patterns.

Finding Patterns

M2k. Work with geometric and non-geometric measures.

Elapsed Time

Triple Beam Balance

Perimeter, Circumference, and Area - Activity B

M2l. Use quotient measures and product measures.

Density Laboratory

Potential Energy on Shelves

Distance-Time and Speed-Time Graphs

M2o. Represent geometric curves and graphs of functions in standard coordinate systems.

Quadratics in Polynomial Form - Activity A

Absolute Value with Linear Functions - Activity B

Exponential Functions - Activity A

Logarithmic Functions - Activity A

M2p. Analyze geometric figures and prove simple things about them using deductive methods.

Investigating Angle Theorems - Activity B

Polygon Angle Sum - Activity B

M3. Function and Algebra Concepts

M3b. Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.

Standard Form of a Line

Quadratics in Polynomial Form - Activity A

Radical Functions

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Rational Functions

General Form of a Rational Function

Fourth-Degree Polynomials - Activity A

M3c. Utilizes the concepts of slope, evaluation, and inverse in working with functions.

Slope-Intercept Form of a Line - Activity B

Point-Slope Form of a Line - Activity A

Logarithmic Functions - Activity A

M3d. Works with rates of many kinds, expressed numerically, symbolically, and graphically.

Freefall Laboratory

Simple and Compound Interest

Density Laboratory

Half-life Laboratory

Distance-Time and Speed-Time Graphs

M3e. Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).

Distance-Time and Speed-Time Graphs

Solving Using Trend Lines

M3f. Understands and uses linear functions as a mathematical representation of proportional relationships.

Direct Variation

Simple and Compound Interest

M3g. Uses arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively.

Arithmetic Sequences

Geometric Sequences

Slope-Intercept Form of a Line - Activity B

Exponential Functions - Activity A

M3h. Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.

Solving Formulas for any Variable

M3i. Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.

Using Tables, Rules and Graphs

Introduction to Functions

M3j. Solves equations symbolically, graphically, and numerically, especially linear, quadratic, and exponential equations; and knows how to use the quadratic formula for solving quadratic equations.

Modeling One-Step Equations - Activity B

Modeling and Solving Two-Step Equations

Standard Form of a Line

Exponential Growth and Decay - Activity A

Solving Equations By Graphing Each Side

Roots of a Quadratic

M3k. Makes predictions by interpolating or extrapolating from given data or a given graph.

Solving Using Trend Lines

Lines of Best Fit Using Least Squares - Activity A

Estimating Population Size

M3l. Understands the basic algebraic structure of number systems.

Number Systems

M3m. Uses equations to represent curves such as lines, circles, and parabolas.

Standard Form of a Line

Circles

Parabolas - Activity B

M3o. Uses functions to analyze patterns and represent their structure.

Arithmetic Sequences

Geometric Sequences

M4. Statistics and Probability Concepts

M4a. Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distribution, circle graphs, line plots, histograms, and summary statistics.

Line Plots

Constructing Box-and-Whisker Plots

Histograms

Stem-and-Leaf Plots

M4b. Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.

Correlation

Solving Using Trend Lines

Lines of Best Fit Using Least Squares - Activity A

M4c. Uses sampling techniques to draw inferences about large populations.

Estimating Population Size

M4d. Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.

Estimating Population Size

M4e. Formulates hypotheses to answer a question and uses data to test hypotheses.

Solving Using Trend Lines

M4f. Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.

Box-and-Whisker Plots

M4h. Creates and uses models of probabilistic situations and understands the role of assumptions in this process.

Probability Simulations

Theoretical and Experimental Probability

Compound Independent and Dependent Events

Binomial Probabilities

M4i. Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.

Probability Simulations

M4j. Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.

Theoretical and Experimental Probability

Compound Independent and Dependent Events

Binomial Probabilities

M4k. Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.

Binomial Probabilities

M4l. Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.

Theoretical and Experimental Probability

Binomial Probabilities

M4m. Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.

Theoretical and Experimental Probability

M4n. Designs simulations including Monte Carlo simulations to estimate probabilities.

Compound Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

Geometric Probability - Activity A

Binomial Probabilities

M4o. Works with the normal distribution in some of its basic applications.

Binomial Probabilities

M6. Mathematical Skills and Tools

M6b. Use a variety of methods to estimate the values, in appropriate units, to an appropriate degree of accuracy.

Estimating Sums and Differences

Triple Beam Balance

M6f. Use the number line and Cartesian coordinates in the plane and in space.

Points in the Coordinate Plane - Activity B

Real Number Line - Activity A

M6h. Set up and solve equations symbolically and graphically.

Solving Equations By Graphing Each Side

Solving Linear Systems by Graphing

M6l. Use tools in solving problems.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles