M8:1: Demonstrates conceptual understanding of rational numbers with respect to percents as a way of describing change (percent increase and decrease) using explanations, models, or other representations.

Percent of Change

M8:2: Demonstrates understanding of the relative magnitude of numbers by ordering or comparing rational numbers, common irrational numbers (the square root of 2 and pi), numbers with whole-number or fractional bases and whole-number exponents, square roots, absolute values, integers, or numbers represented in scientifi c notation using number lines or equality and inequality symbols.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

M8:7: Estimates and evaluates the reasonableness of solutions appropriate to grade level.

Estimating Sums and Differences

M8:8: Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], prime factorization, divisibility, inverses, and identities), and commutative, distributive, and associative properties of operations to solve problems and to simplify computations.

Adding and Subtracting Integers
Chocomatic (Multiplication, Arrays, and Area)
Finding Factors with Area Models
Square Roots
Using Algebraic Equations

M8:9: Models situations geometrically. Uses properties and attributes of lines, angles, and two- and three-dimensional shapes) to formulate and solve problems.

Classifying Quadrilaterals

M8:10: Applies the Pythagorean Theorem to fi nd a missing side of a right triangle, or in problem-solving situations and solves problems by applying the Triangle Inequality Theorem to determine if three line segments with given lengths form a triangle, and the sum of the angles in a convex polygon of any number of sides.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Angle Sum
Triangle Inequalities

M8:13: Applies concepts of similarity to determine the impact of scaling on the volume or surface area of three-dimensional fi gures when linear dimensions are multiplied by a constant factor; to determine the length of sides of similar triangles, or to solve problems involving growth and rate and makes scale drawings.

Beam to Moon (Ratios and Proportions)
Dilations
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

M8:14: Demonstrates conceptual understanding of surface area or volume by solving problems involving surface area and volume of rectangular prisms, cylinders, or pyramids. Expresses all measures using appropriate units.

Surface and Lateral Areas of Prisms and Cylinders

M8:15: Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within or across systems. (See Appendix B for benchmark units and equivalences for each grade.)

Unit Conversions

M8:17: Sketches a variety of three-dimensional objects using orthogonal views (projections and isometric views), or constructs1 or accurately represents angle bisector, perpendicular bisector, congruent segments and regular polygons. Draws nets of three-dimensional shapes.

Concurrent Lines, Medians, and Altitudes
Segment and Angle Bisectors
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M8:19: Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; and generalizes a linear relationship (nonrecursive explicit equation); generalizes a linear relationship to find a specific case; generalizes a nonlinear relationship using words or symbols; or generalizes a common nonlinear relationship to find a specific case.

Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)

M8:20: Demonstrates conceptual understanding of linear relationships (y = kx; y = mx + b) as a constant rate of change by solving problems involving the relationship between slope and rate of change; informally and formally determining slopes and intercepts represented in graphs, tables, or problem situations; or describing the meaning of slope and intercept in context; and distinguishes between linear relationships (constant rates of change) and nonlinear relationships (varying rates of change) represented in tables, graphs, equations, or problem situations; or describes how change in the value of one variable relates to change in the value of a second variable in problem situations with constant and varying rates of change.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Function Machines 1 (Functions and Tables)
Points, Lines, and Equations
Slope-Intercept Form of a Line

M8:21: Demonstrates conceptual understanding of algebraic expressions by evaluating and simplifying (including those with square roots, whole-number exponents, or rational numbers); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 7(square root of x + 2x).

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions

M8:23: Interprets a given representation (line graphs, scatter plots, histograms, or box-and-whisker plots) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.

Box-and-Whisker Plots
Correlation
Histograms
Least-Squares Best Fit Lines
Real-Time Histogram
Solving Using Trend Lines
Trends in Scatter Plots

M8:24: Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, or estimated line of best fi t to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or nonrandom).

Describing Data Using Statistics
Least-Squares Best Fit Lines
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples

M8:25: Organizes and displays data using scatter plots to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems; or identifi es representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M8: 23.

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

M8:26: Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others).

Permutations and Combinations

M8:27: For a probability event in which the sample space may or may not contain equally likely outcomes, determines the possible outcomes by either sample space (organized list, table, tree model, area model) or Fundamental Counting Principle and determines the theoretical probability of that event as a ratio of favorable outcomes to possible outcomes. Expresses the ratio as a fraction, decimal, or percent.

Independent and Dependent Events
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability

M8:28: In response to a teacher- or student-generated question, makes a hypothesis, collects appropriate data, organizes the data, appropriately displays/represents numerical and/or categorical data, analyzes the data to draw conclusions about the questions or hypothesis being tested, and when appropriate to make predictions, asks new questions, or makes connection to real-world situations. (See also GLEs M24, M25 and M29.)

Correlation

M8:29: Compares and contrasts theoretical and experimental probabilities of compound events using fractions, decimals, or percents; and uses theoretical or experimental probabilities to determine the fairness of a game.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability