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Vermont Math Standards - 6th Grade
MathScore aligns to the Vermont Math Standards for 6th 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
M6: 1 Demonstrates conceptual understanding of rational numbers with respect to ratios (comparison of two whole numbers by division a/b, a : b, and a ÷ b , where b ≠ 0); and rates (e.g., a out of b, 25%) using models, explanations, or other representations.* Demonstrates conceptual understanding of proportional reasoning, and fluently moves between equivalent representations of commonly used fractions and decimals. M(N&O)-6-1 *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. (Unit Cost , Fractions to Decimals , Decimals To Fractions , Percentages , Percentage Pictures , Percent of Quantity , Proportions 1 , Distance, Rate, and Time , Ratios )M6: 2 Demonstrates understanding of the relative magnitude of numbers by ordering or comparing numbers with whole-number bases and whole-number exponents (e.g., 33, 43), integers, or rational numbers within and across number formats (fractions, decimals, or whole-number percents from 1 to 100) using number lines or equality and inequality symbols. M(N&O)-6-2 (Compare Mixed Values , Compare Mixed Values 2 , Positive Number Line , Number Line , Compare Integers )
M6: 3 Demonstrates understanding of mathematical operations by describing or illustrating the meaning of a power by representing the relationship between the base (whole number) and the exponent (whole number) (e.g., 33 , 43); and the effect on the magnitude of a whole number when multiplying or dividing it by a whole number, decimal, or fraction. M(N&O)-6-3 (Exponent Basics )
M6: 4 Accurately solves problems involving single or multiple operations on fractions (proper, improper, and mixed), or decimals; and addition or subtraction of integers; percent of a whole; or problems involving greatest common factor or least common multiple. (IMPORTANT: Applies the conventions of order of operations with and without parentheses.) M(N&O)-6-4 (Using Parentheses , Order Of Operations , Making Change , Money Multiplication , Money Division , Unit Cost , Greatest Common Factor , Least Common Multiple , Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division , Fraction Word Problems , Fraction Word Problems 2 , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division , Percent of Quantity , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Equivalence )
M6: 5 No M6: 5 at this grade level
M6: 6 Mentally multiplies and divides whole numbers through twelve with accuracy. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
M6: 7 Estimates and evaluates the reasonableness of solutions appropriate to grade level. (Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
M6: 8 Applies properties of numbers (factor, multiple, prime, composite, greatest common factor [GCF], least common multiple [LCM], composition/decomposition), divisibility, remainders), and commutative and associative properties of operations to solve problems and to simplify computations. (Long Division with Remainders , Small Decimal Division , Word Problems With Remainders , Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Prime Numbers , Prime Factoring , Prime Factoring 2 , Greatest Common Factor , Factoring , Least Common Multiple , Divisibility Rules )
Geometry and Measurement Concepts
M6: 9 Uses properties or attributes of angles (right, acute, or obtuse) or sides (number of congruent sides, parallelism, or perpendicularity) to identify, describe, classify, or distinguish among different types of triangles (right, acute, obtuse, equiangular, scalene, isosceles, or equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or parallelograms). M(G&M)-6-1 (Triangle Types , Quadrilateral Types , Parallel and Perpendicular Lines )
M6: 10 No M6: 10 at this grade level
M6: 11 Uses properties or attributes (shape of bases, number of lateral faces, number of bases, number of edges, or number of vertices) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or cones). M(G&M)-6-3
M6: 12 Demonstrates congruency using the results of combining and subdividing shapes (e.g., rectangle into two triangles), by using transformations (flips, slides, and turns), and by using the properties of angles, and length of segments.
M6: 13 Demonstrates conceptual understanding of similarity by describing the proportional effect on the linear dimensions of polygons or circles when scaling up or down while preserving the angles of polygons, or by solving related problems (including applying scales on maps). Describes effects using models or explanations. M(G&M)-6-5 And applies concepts of similarity using constant of proportionality/scale factor to make larger and smaller scale drawings. (Area And Volume Proportions , Proportions 2 )
M6: 14 Demonstrates conceptual understanding of perimeter of polygons, the area of quadrilaterals or triangles, and the volume of rectangular prisms by using models, formulas, or by solving problems; and demonstrates understanding of the relationships of circle measures (radius to diameter and diameter to circumference) by solving related problems. Expresses all measures using appropriate units. M(G&M)-6-6 (Circle Measurements , Triangle Area , Parallelogram Area , Perimeter , Rectangular Solids , Compare Rectangle Area and Perimeter , Circle Circumference , Trapezoids )
M6: 15 Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands. M(G&M)-6-7 (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
M6: 16 No M6: 16 at this grade level
M6: 17 No M6: 17 at this grade level
M6: 18 Solves problems using the Cartesian coordinate system (all quadrants) to locate coordinates and to represent data from tables. (Ordered Pairs , Translations and Reflections )
Functions and Algebra Concepts
M6: 19 Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; or writes a rule in words or symbols for finding specific cases of a linear relationship; or writes a rule in words or symbols for finding specific cases of a nonlinear relationship; and writes an expression or equation using words or symbols to express the generalization of a linear relationship (e.g., twice the term number plus 1 or 2 n + 1). M(F&A)-6-1 (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Function Tables , Function Tables 2 )
M6: 20 Demonstrates conceptual understanding of linear relationships (y = kx; y = mx + b) as a constant rate of change by constructing or interpreting graphs of real occurrences and describing the slope of linear relationships (faster, slower, greater, or smaller) in a variety of problem situations; and 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)-6-2 (Determining Slope , Graphs to Linear Equations , Independent and Dependent Variables )
M6: 21 Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write linear algebraic expressions involving two or more of the four operations and consistent with order of operations expected at this grade level; or by evaluating linear algebraic expressions (including those with more than one variable); or by evaluating an expression within an equation (e.g., determine the value of y when x = 4 given y = 3 x - 2). M(F&A)-6-3 (Order Of Operations , Linear Equations , Algebraic Word Problems , Variable Substitution , Algebraic Sentences 2 , Algebraic Sentences , Variable Substitution 2 )
M6: 22 Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions (expressions consistent with the parameters of M(F&A)- 6-3), solving multistep linear equations of the form ax ± b = c, where a, b, and c are whole numbers with a ≠ 0. M(F&A)-6-4 (Single Variable Equations , Single Variable Equations 2 )
Data, Statistics, and Probability Concepts
M6: 23 Interprets a given representation (circle graphs, line graphs, or stem-and-leaf plots) to answer questions related to the data, 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 M6: 24.) M(DSP)-6-1 And (frequency charts, line graphs, Venn diagrams, pictographs, line plots, histograms). (Stem And Leaf Plots , Tally and Pictographs , Line Graphs )
M6: 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) or dispersion (range) to analyze situations, or to solve problems. M(DSP)-6-2 (Mean, Median, Mode )
M6: 25 Organizes and displays data using bar graphs, tables, frequency tables, line plots, circle graphs, 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 M6: 24.)
M6: 26 Uses counting techniques to solve problems in context involving combinations or simple permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, or others). M(DSP)-6-4
M6: 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 an event in a problem solving situation. M(DSP)-6-5 (Probability )
M6: 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 M6: 24.) (Requires outside materials )
M6: 29 Uses experimental probability to make and test conjectures or design fair games. Represent probabilities using fractions, decimals, or percents.
Mathematical Problem Solving and Reasoning
M6: 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. (Making Change , Unit Cost , Fraction Word Problems , Fraction Word Problems 2 , Algebraic Terms , Algebraic Word Problems , Distance, Rate, and Time )
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