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Massachusetts Math Standards - Grades 5-6
MathScore aligns to the Massachusetts Math Standards for Grades 5-6. 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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Number Sense and Operations
6.N.1 Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten, e.g., 102, 105. (Exponent Basics )6.N.2 Demonstrate an understanding of place value to billions and thousandths. (Decimal Place Value )
6.N.3 Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. (Place Value , Decimal Place Value , Order Large Numbers , Order Decimals )
6.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. (Fraction Pictures , Ratios )
6.N.5 Identify and determine common equivalent fractions, mixed numbers, decimals, and percents. (Fractions to Decimals , Decimals To Fractions , Percentages )
6.N.6 Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line. (Positive Number Line , Number Line , Compare Integers )
6.N.7 Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents. (Compare Mixed Values 2 , Fraction Comparison , Compare Decimals , Compare Integers , Basic Fraction Comparison )
6.N.8 Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10-to the solution of problems. (Prime Numbers , Prime Factoring , Prime Factoring 2 , Greatest Common Factor , Least Common Multiple , Divisibility Rules )
6.N.9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. (Arithmetic Word Problems , Fraction Word Problems , Fraction Word Problems 2 , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Algebraic Word Problems )
6.N.10 Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers.
6.N.11 Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷). (Using Parentheses , Order Of Operations )
6.N.12 Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. (Missing Term , Inverse Equations 1 , Single Variable Equations )
6.N.13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. (Long Addition , Long Subtraction , Long Multiplication , Long Division , Long Division with Remainders , Small Decimal Division , Mental Addition and Subtraction to 100 , Mental Addition and Subtraction , Multiply By Multiples Of 10 , Money Multiplication , Money Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division )
6.N.14 Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. (Fraction Simplification , Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division )
6.N.15 Add and subtract integers, with the exception of subtracting negative integers. (Integer Addition , Positive Integer Subtraction , Integer Equivalence )
6.N.16 Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates. (Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction , Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
Patterns, Relations, and Algebra
6.P.1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13 …; 3, 9, 27, …. (Patterns: Numbers , Patterns: Shapes )6.P.2 Replace variables with given values and evaluate/simplify, e.g., 2(Ο) + 3 when Ο = 4. (Variable Substitution )
6.P.3 Use the properties of equality to solve problems, e.g., if [] + 7 = 13, then [] = 13 - 7, therefore [] = 6; if 3 x [] = 15, then 1/3 x 3 x [] = 1/3 x 15, therefore [] = 5. (Missing Factor , Missing Term )
6.P.4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables. (Function Tables , Function Tables 2 )
6.P.5 Solve linear equations using concrete models, tables, graphs, and paper-pencil methods. (Linear Equations )
6.P.6 Produce and interpret graphs that represent the relationship between two variables in everyday situations. (Function Tables , Function Tables 2 )
6.P.7 Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.
Geometry
6.G.1 Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles. (Triangle Types , Quadrilateral Types )6.G.2 Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.
6.G.3 Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular. (Parallel and Perpendicular Lines )
6.G.4 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). (Ordered Pairs )
6.G.5 Find the distance between two points on horizontal or vertical number lines. (Line Segments )
6.G.6 Predict, describe, and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.
6.G.7 Identify types of symmetry, including line and rotational.
6.G.8 Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections. (Congruent And Similar Triangles )
6.G.9 Match three-dimensional objects and their two-dimensional representations, e.g., nets, projections, and perspective drawings.
Measurement
6.M.1 Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate. (Perimeter and Area Word Problems )6.M.2 Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals. (Triangle Types , Quadrilateral Types )
6.M.3 Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Distance, Rate, and Time )
6.M.4 Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes. (Triangle Area , Parallelogram Area , Compare Rectangle Area and Perimeter , Perimeter and Area of Composite Figures )
6.M.5 Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d = 2r, π = C/d), and use the concepts to solve problems. (Circle Measurements , Circle Area , Circle Circumference )
6.M.6 Find volumes and surface areas of rectangular prisms. (Rectangular Solids )
6.M.7 Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles. (Triangle Angles , Quadrilateral Angles , Polygon Angles )
Data Analysis, Statistics, and Probability
6.D.1 Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range. (Mean, Median, Mode )6.D.2 Construct and interpret stem-and-leaf plots, line plots, and circle graphs. (Stem And Leaf Plots )
6.D.3 Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes.
6.D.4 Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event. (Probability )
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