M7:2: Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent rational numbers across number formats, numbers with whole-number bases and whole-number exponents (e.g., 3 cubed, 4 cubed), integers, absolute values, or numbers represented in scientific notation using number lines or equality and inequality symbols.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values
Unit Conversions 2 - Scientific Notation and Significant Digits

M7:3: Demonstrates conceptual understanding of operations with integers, exponents, and square roots of perfect square numbers and nonperfect square numbers using models, diagrams, or explanations.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Square Roots

M7:4: Accurately solves problems involving proportional reasoning; percents involving discounts, tax, or tips; and rates. And accurately solves problems involving integers, raising numbers to whole-number powers, and determining square roots of perfect square numbers and nonperfect square numbers.

Adding on the Number Line
Addition of Polynomials
Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Geometric Probability
Operations with Radical Expressions
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Simplifying Radical Expressions
Square Roots
Time Estimation

M7:7: Estimates and evaluates the reasonableness of solutions appropriate to grade level.

Estimating Sums and Differences

M7:8: Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], composition/decomposition, divisibility, prime factorization, inverses, and identities), and commutative, distributive, and associative properties of operations, and exponents using powers of ten and scientifi c notation to solve problems and to simplify computations.

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

M7:9: Uses properties of angle relationships resulting from two or three intersecting lines (adjacent angles, vertical angles, straight angles, or angle relationships formed by two nonparallel lines cut by a transversal), or two parallel lines cut by a transversal to solve problems.

Triangle Angle Sum

M7:10: Applies theorems or relationships (triangle inequality or sum of the measures of interior angles of regular polygons) to solve problems.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum
Triangle Inequalities

M7:11: Applies the properties of number of vertices, number of edges, faces, and types of angles, symmetry, to identify and distinguish among three-dimensional shapes (rectangular prisms, triangular prisms, pyramids, cubes) and uses properties to solve problems involving three-dimensional shapes.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M7:13: Applies concepts of similarity by solving problems involving scaling up or down and their impact on angle measures, linear dimensions and areas of polygons, and circles when the linear dimensions are multiplied by a constant factor. Describes effects using models orsc explanations.

Similar Figures

M7:14: Demonstrates conceptual understanding of the area of circles or the area or perimeter of composite fi gures (quadrilaterals, triangles, or parts of circles), and the surface area of rectangular prisms, or volume of rectangular prisms, triangular prisms, or cylinders using models, formulas, or by solving related problems. Expresses all measures using appropriate units.

Area of Triangles
Fido's Flower Bed (Perimeter and Area)
Surface and Lateral Areas of Prisms and Cylinders

M7:15: Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within systems.

Unit Conversions

M7:17: Sketches three-dimensional solids and the nets of prisms, cylinders, and pyramids.

Surface and Lateral Areas of Prisms and Cylinders

M7:19: 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 using words and symbols; generalizes a linear relationship to find a specific case; or writes an expression or equation using words or symbols to express the generalization of a nonlinear relationship.

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

M7:20: 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, by describing the meaning of slope in concrete situations, or informally determining the slope of a line from a table or graph; and distinguishes between constant and varying rates of change in concrete situations represented in tables or graphs; 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 rates of change.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Slope-Intercept Form of a Line

M7:21: Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write algebraic expressions (including those with whole-number exponents or more than one variable); or by evaluating algebraic expressions (including those with whole-number exponents or more than one variable); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 5 x cubed– 2).

Order of Operations
Simplifying Algebraic Expressions I

M7:22: Demonstrates conceptual understanding of equality by showing equivalence between two expressions (expressions consistent with the parameters of the left- and right-hand sides of the equations being solved at this grade level) using models or different representations of the expressions, solving multistep linear equations of the form ax ± b = c with a not equal to 0, ax ± b = cx ± d with a, c not equal to 0, and (x/a) ± b = c with a not equal to 0, where a, b, c and d are whole numbers; or by translating a problem-solving situation into an equation consistent with the parameters of the type of equations being solved for this grade level.

Circles
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Using Algebraic Expressions

M7:23: Interprets a given representation (circle graphs, scatter plots that represent discrete linear relationships, or histograms) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. And (Frequency charts, tables, bar graphs, pictographs, Venn diagrams, line plots).

Correlation
Forest Ecosystem
Graphing Skills
Histograms
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Solving Using Trend Lines
Trends in Scatter Plots

M7:24: Analyzes patterns, trends, or distributions in data in a variety of contexts by solving problems using measures of central tendency (mean, median, or mode), dispersion (range or variation), or outliers to analyze situations to determine their effect on mean, median, or mode; and evaluates the sample from which the statistics were developed (bias).

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

M7:25: Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M7:23. Organizes and displays data using line graphs or histograms, bar graphs, tables, frequency tables, line plots, and stem-and-leaf plots to answer question related to the data, to analyze the data to formulate or justify conclusions, or to make predictions.

Describing Data Using Statistics
Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Mean, Median, and Mode
Polling: City
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

M7:26: Uses counting techniques to solve problems in context involving combinations using a variety of strategies (e.g., organized lists, tables, tree diagrams, area models, Fundamental Counting Principle, or others); or determines the possible outcomes for a sample space that may or may not contain equally likely outcomes.

Independent and Dependent Events
Permutations and Combinations
Spin the Big Wheel! (Probability)

M7:27: For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of a simple event or an event in a problem-solving situation.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

M7:28: 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 makes predictions, asks new questions, or makes connection to real-world situations.

Correlation
Graphing Skills

M7:29: Compares and contrasts theoretical and experimental probabilities of events; and uses theoretical or experimental probabilities to determine the fairness of a game. Represents probabilities using fractions, decimals, or percents.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability