Massachusetts Math Standards - Grades 7-8

MathScore aligns to the Massachusetts Math Standards for Grades 7-8. 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.

View the Massachusetts Math Standards at other levels.

Number Sense and Operations

8.N.1 Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents. (Compare Mixed Values 2 , Number Line , Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Percentages )
8.N.2 Define, compare, order, and apply frequently used irrational numbers, such as √2 and π.
8.N.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change. (Unit Cost , Area And Volume Proportions , Proportions 2 , Distance, Rate, and Time )
8.N.4 Represent numbers in scientific notation, and use them in calculations and problem situations. (Scientific Notation 2 , Scientific Notation )
8.N.5 Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems. (Prime Factoring , Prime Factoring 2 )
8.N.6 Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3. (Absolute Value 1 )
8.N.7 Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots. (Order Of Operations )
8.N.8 Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 = 1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition). (Distributive Property , Distributive Property 2 )
8.N.9 Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2. (Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Estimating Square Roots , Perfect Squares )
8.N.10 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). (Fraction Simplification , Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division , Percentage Change , Percent of Quantity , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence )
8.N.11 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
8.N.12 Select and use appropriate operations-addition, subtraction, multiplication, division, and positive integer exponents-to solve problems with rational numbers (including negatives). (Fraction Word Problems , Fraction Word Problems 2 , Integers In Word Problems , Exponent Rules For Fractions )

Patterns, Relations, and Algebra

8.P.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. (Patterns: Numbers , Function Tables , Function Tables 2 )
8.P.2 Evaluate simple algebraic expressions for given variable values, e.g., 3a2 - b for a = 3 and b = 7. (Variable Substitution , Variable Substitution 2 )
8.P.3 Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4. (Integer Multiplication , Simplifying Algebraic Expressions 2 )
8.P.4 Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. (Phrases to Algebraic Expressions , Algebraic Sentences 2 , Algebraic Sentences )
8.P.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. (Determining Slope )
8.P.6 Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b. (Graphs to Linear Equations )
8.P.7 Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. (Linear Equations , Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities )
8.P.8 Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = πd, A = πr2 (A as a function of r), Arectangle = lw (Arectangle as a function of l and w). (Function Tables , Function Tables 2 )
8.P.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. (Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems )
8.P.10 Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.

Geometry

8.G.1 Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.
8.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems. (Congruent And Similar Triangles , Proportions 2 )
8.G.3 Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. (Identifying Angles , Angle Measurements 2 )
8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems. (Pythagorean Theorem )
8.G.5 Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures. (Requires outside materials )
8.G.6 Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure, e.g., predict how tessellations transform under translations, reflections, and rotations.
8.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.
8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

Measurement

8.M.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Area and Volume Conversions )
8.M.2 Given the formulas, convert from one system of measurement to another. Use technology as appropriate. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
8.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate. (Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Rectangular Solids , Rectangular Solids 2 , Circle Area , Circle Circumference , Cylinders , Trapezoids )
8.M.4 Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement. (Proportions 2 )
8.M.5 Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density. (Distance, Rate, and Time , Train Problems )

Data Analysis, Statistics, and Probability

8.D.1 Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample, e.g., convenience sampling, responses to a survey, random sampling.
8.D.2 Select, create, interpret, and utilize various tabular and graphical representations of data, e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts. Differentiate between continuous and discrete data and ways to represent them. (Stem And Leaf Plots )
8.D.3 Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. (Mean, Median, Mode )
8.D.4 Use tree diagrams, tables, organized lists, basic combinatorics ("fundamental counting principle"), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice. (Probability 2 )