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
Correlation last revised: 9/5/2008