Vermont Math Standards

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Vermont Math Standards - 7th Grade

MathScore aligns to the Vermont Math Standards for 7th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

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View the Vermont Math Standards at other levels.

Arithmetic, Number and Operation Concepts

M7: 1 Demonstrates conceptual understanding of rational numbers with respect to percents as a means of comparing the same or different parts of the whole when the wholes vary in magnitude (e.g., 8 girls in a classroom of 16 students compared to 8 girls in a classroom of 20 students, or 20% of 400 compared to 50% of 100); and percents as a way of expressing multiples of a number (e.g., 200% of 50) using models, explanations, or other representations.* M(N&O)-7-1
*Specifications for area, set, and linear models for grades 5-8: Fractions: The number of parts in the whole is equal to the denominator, a multiple of the denominator, or a factor of the denominator. Percents: The number of parts in the whole is equal to 100, a multiple of 100, or a factor of 100 (for grade 5); the number of parts in the whole is a multiple or a factor of the numeric value representing the whole (for grades 6-8). Decimals (including powers of ten): The number of parts in the whole is equal to the denominator of the fractional equivalent of the decimal, a multiple of the denominator of the fractional equivalent of the decimal, or a factor of the denominator of the fractional equivalent of the decimal. (Percentages , Percent of Quantity )

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., 3³, 4³), integers, absolute values, or numbers represented in scientific notation using number lines or equality and inequality symbols. M(N&O)-7-2 (Compare Mixed Values 2 , Number Line , Compare Integers , Fractions to Decimals , Decimals To Fractions , Percentages , Absolute Value 1 , Exponent Basics , Scientific Notation )

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. (Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence , Integers In Word Problems , Exponent Basics , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions , Estimating Square Roots , Perfect Squares , Simplifying Radical Expressions )

M7: 4 Accurately solves problems involving proportional reasoning; percents involving discounts, tax, or tips; and rates. (IMPORTANT: Applies the conventions of order of operations including parentheses, brackets, or exponents.) M(N&O)-7-4 And accurately solves problems involving integers, raising numbers to whole-number powers, and determining square roots of perfect square numbers and nonperfect square numbers. (Order Of Operations , Unit Cost , Purchases At Stores , Restaurant Bills , Commissions , Integers In Word Problems , Proportions 2 , Simple Interest , Distance, Rate, and Time , Train Problems , Estimating Square Roots , Perfect Squares )

M7: 5 No M7: 5 at this grade level

M7: 6 No M7: 6 at this grade level

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

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 scientific notation to solve problems and to simplify computations. (Associative Property 2 , Commutative Property 2 , Inverse Equations 1 , Inverse Equations 2 , Distributive Property , Distributive Property 2 , Basic Distributive Property , Prime Factoring 2 , Greatest Common Factor , Least Common Multiple , Divisibility Rules , Estimating Square Roots )

Geometry and Measurement Concepts

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. M(G&M)-7-1 (Identifying Angles , Angle Measurements , Angle Measurements 2 )

M7: 10 Applies theorems or relationships (triangle inequality or sum of the measures of interior angles of regular polygons) to solve problems. M(G&M)-7-2 (Triangle Angles , Quadrilateral Angles , Triangle Angles 2 , Solving For Angles , Polygon Angles )

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.

M7: 12 Applies the concepts of congruency by solving problems on a coordinate plane involving reflections, translations, or rotations. M(G&M)-7-4

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 or explanations. M(G&M)-7-5 (Area And Volume Proportions , Proportions 2 )

M7: 14 Demonstrates conceptual understanding of the area of circles or the area or perimeter of composite figures (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. M(G&M)-7-6 (Rectangular Solids , Rectangular Solids 2 , Circle Area , Triangular Prisms , Cylinders , Irregular Shape Areas , Perimeter and Area of Composite Figures )

M7: 15 Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within systems. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion , Area and Volume Conversions )

M7: 16 No M7: 16 at this grade level

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

M7: 18 No M7: 18 at this grade level

Functions and Algebra Concepts

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. M(F&A)-7-1 (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions , Function Tables , Function Tables 2 )

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. M(F&A)-7-2 (Determining Slope , Graphs to Linear Equations , Independent and Dependent Variables )

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 x3- 2). M(F&A)-7-3 (Linear Equations , Variable Substitution , Variable Substitution 2 )

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 ≠, 0, ax ± b = cx ± d with a, c ≠, 0, and (x/a) ± b = c with a ≠ 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. M(F&A)-7-4 (Single Variable Equations 2 , Single Variable Equations 3 , Algebraic Word Problems , Algebraic Sentences 2 , Algebraic Sentences )

Data, Statistics, and Probability Concepts

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. (IMPORTANT: Analyzes data consistent with concepts and skills in M7: 24.) M(DSP)-7-1 And (Frequency charts, tables, bar graphs, pictographs, Venn diagrams, line plots). (Tally and Pictographs , Bar Graphs , Line Graphs )

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). M(DSP)-7-2 (Mean, Median, Mode )

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. M(DSP)-7-3 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. (IMPORTANT: Analyzes data consistent with concepts and skills in M7: 24.)

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.

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. M(DSP)-7-5 (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. (IMPORTANT: Analyzes data consistent with concepts and skills in M7: 24.) (Requires outside materials )

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.

Mathematical Problem Solving and Reasoning

M7: 30 Demonstrate understanding of mathematical problem solving and communication through:
• Approach & Reasoning-The reasoning, strategies, and skills used to solve the problem;
• Connections-Demonstration of observations, applications, extensions, and generalizations;
• Solution-All of the work that was done to solve the problem, including the answer;
• Mathematical Language-The use of mathematical language in communicating the solution;
• Mathematical Representation-The use of mathematical representation to communicate the solution; and
• Documentation-Presentation of the solution. (Unit Cost , Integers In Word Problems , Algebraic Terms , Algebraic Word Problems , Distance, Rate, and Time , Train Problems )

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