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Vermont Math Standards - 5th Grade
MathScore aligns to the Vermont Math Standards for 5th 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
M5: 1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 9,999,999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; positive fractional numbers (proper, mixed number, and improper) (halves, fourths, eighths, thirds, sixths, twelfths, fifths, or powers of ten [10, 100, 1000]), decimals (to thousandths), or benchmark percents (10%, 25%, 50%, 75% or 100%) as a part to whole relationship in area, set, or linear models using models, explanations, or other representations.* M(N&O)-5-1*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. (Decimal Place Value , Positive Number Line , Fraction Pictures , Percentage Pictures )
M5: 2 Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent positive fractional numbers, decimals, or benchmark percents within number formats (fractions to fractions, decimals to decimals, or percents to percents); or integers in context using models or number lines. M(N&O)-5-2 (Order Numbers , Order Large Numbers , Order Decimals , Compare Mixed Values , Fraction Comparison , Compare Decimals , Compare Integers , Basic Fraction Comparison , Basic Fraction Simplification , Fraction Simplification )
M5: 3 Demonstrates conceptual understanding of mathematical operations by describing or illustrating the meaning of a remainder with respect to division of whole numbers using models, explanations, or solving problems. M(N&O)-5-3 (Division with Remainders , Long Division with Remainders , Small Decimal Division , Word Problems With Remainders )
M5: 4 Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors, multiples, prime, or composite numbers; and addition or subtraction of fractions (proper) and decimals to the hundredths place. (Division of whole numbers by up to a two-digit divisor.) (IMPORTANT: Applies the conventions of order of operations with and without parentheses.) M(N&O)-5-4 (Using Parentheses , Order Of Operations , Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 , Long Addition , Long Subtraction , Long Multiplication , Long Division By One Digit , Long Division , Division with Remainders , Long Division with Remainders , Small Decimal Division , Word Problems With Remainders , Money Addition , Money Subtraction , Making Change , Unit Cost , Prime Numbers , Prime Factoring , Greatest Common Factor , Factoring , Least Common Multiple , Fraction Addition , Fraction Subtraction , Fraction Word Problems , Decimal Addition , Decimal Subtraction )
M5: 5 No M5: 5 at this grade level
M5: 6 Mentally multiplies and divides whole numbers through twelve with accuracy. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
M5: 7 Estimates and evaluates the reasonableness of solutions appropriate to grade level. (Rounding Large Numbers , Decimal Rounding to .01 , Decimal Rounding , Money Addition , Money Subtraction , Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
M5: 8 Applies properties of numbers (odd, even, factor, multiple, prime, composite, divisibility, remainders, composition/decomposition) to solve problems and to simplify computations. (Odd or Even Theory , Division with Remainders , Long Division with Remainders , Small Decimal Division , Word Problems With Remainders , Prime Numbers , Prime Factoring , Greatest Common Factor , Factoring , Least Common Multiple , Divisibility Rules )
Geometry and Measurement Concepts
M5: 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, or equilateral) or quadrilaterals (rectangles, squares, rhombi, trapezoids, or parallelograms). M(G&M)-5-1 (Triangle Types , Quadrilateral Types , Parallel and Perpendicular Lines )
M5: 10 No M5: 10 at this grade level
M5: 11 Uses properties or attributes (shape of bases, number of lateral faces, or number of bases) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, spheres, pyramids, or cones). M(G&M)-5-3
M5: 12 Demonstrates conceptual understanding of congruency by matching congruent figures using reflections, translations, or rotations (flips, slides, or turns), or as the result of composing or decomposing shapes using models or explanations. (Congruent And Similar Triangles )
M5: 13 Demonstrates conceptual understanding of similarity by describing the proportional effect on the linear dimensions of polygons 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.
M5: 14 Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles or right triangles through models, manipulatives, or formulas, the area of polygons or irregular figures on grids, and volume of rectangular prisms (cubes) using a variety of models, manipulatives, or formulas. Expresses a measures using appropriate units. M(G&M)-5-6 (Perimeter , Rectangular Solids , Compare Rectangle Area and Perimeter , Perimeter and Area of Composite Figures , Perimeter and Area Word Problems )
M5: 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)-5-7 (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion )
M5: 16 Determines elapsed and accrued time to the nearest minute. (Time Intervals )
M5: 17 No M5: 17 at this grade level
M5: 18 Solves problems using the Cartesian coordinate system (all quadrants) to locate coordinates and to represent data from tables. (Ordered Pairs )
Functions and Algebra Concepts
M5: 19 Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, or in problem situations; and writes a rule in words or symbols for finding specific cases of a linear relationship. M(F&A)-5-1 (Patterns: Numbers , Function Tables , Function Tables 2 )
M5: 20 Demonstrates a conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing situations that represent constant rates of change.
M5: 21 Demonstrates conceptual understanding of algebraic expressions by using letters to represent unknown quantities to write linear algebraic expressions involving any two of the four operations; or by evaluating linear algebraic expressions using whole numbers. M(F&A)-5-3 (Phrases to Algebraic Expressions , Algebraic Word Problems , Variable Substitution , Algebraic Sentences )
M5: 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)-5-3), by solving one-step linear equations of the form ax = c, x ± b = c, or x/a = c, where a, b, and c are whole numbers with a ≠0; or by determining which values of a replacement set make the equation (multistep of the form ax ± b = c where a, b, and c are whole numbers with a ≠0) a true statement (e.g., 2 x + 3 = 11, { x: x = 2, 3, 4, 5}). M(F&A)-5-4 (Missing Factor , Missing Term , Missing Operator , Compare Expressions , Single Variable Equations )
Data, Statistics, and Probability Concepts
M5: 23 Interprets a given representation (tables, bar graphs, circle graphs, or line graphs) 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 M5: 24.) M(DSP)-5-1 And (tally charts, frequency charts, line graphs, Venn diagrams, pictographs, line plots, histograms). (Tally and Pictographs , Bar Graphs , Line Graphs )
M5: 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 range to analyze situations, or to solve problems. M(DSP)-5-2 (Mean, Median, Mode )
M5: 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 M5: 23. M(DSP)-5-3 Organizes and displays data using line plots, bar graphs, tally charts and frequency charts, or tables to answer question 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 M5: 24.)
M5: 26 Uses counting techniques to solve problems in context involving combinations using a variety of strategies (e.g., organized lists, tables, tree diagrams, or others); or determines the possible outcomes for a sample space that contains equally likely outcomes.
M5: 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 and expresses the result as a fraction. M(DSP)-5-5 (Probability )
M5: 28 In response to a teacher - or student-generated question or 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 connections to real-world situations. (IMPORTANT: Analyzes data consistent with concepts and skills in M5: 24.) (Requires outside materials )
M5: 29 Uses experimental probability, evaluates the possible outcomes, and describes the likelihood or chance of an event as a ratio of actual times the event occurred to the number of trials written as either a ratio or as part to whole. (Probability )
Mathematical Problem Solving and Reasoning
M5: 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. (Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 , Word Problems With Remainders , Making Change , Unit Cost , Fraction Word Problems , Algebraic Terms , Algebraic Word Problems )
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