### 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

Correlation last revised: 4/4/2018