### 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

Parallelogram Conditions

#### 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

Reflections

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

Slope - Activity B

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

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

#### 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

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

Correlation last revised: 9/5/2008

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.