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Massachusetts Math Standards - Grades 9-10
MathScore aligns to the Massachusetts Math Standards for Grades 9-10. 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 Massachusetts Math Standards at other levels.
Number Sense and Operations
10.N.1 Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number. (Distributive Property , Distributive Property 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )10.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems. (Absolute Value 2 , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
10.N.3 Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., √32 - 1 ≈ 2.8 . (Estimating Square Roots )
10.N.4 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
Patterns, Relations, and Algebra
10.P.1 Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonnacci Numbers), linear, quadratic, and exponential functional relationships.10.P.2 Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Applied Linear Equations 1 , Applied Linear Equations 2 )
10.P.3 Add, subtract, and multiply polynomials. Divide polynomials by monomials. (Foil Method , Simplifying Algebraic Expressions )
10.P.4 Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., a2 - b2 = (a + b)(a - b), x2 + 10x + 21 = (x + 3)(x + 7), 5x4 + 10x3 - 5x2 = 5x2 (x2 + 2x - 1)); identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents. (Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification )
10.P.5 Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods. (Quadratic Zero Equations , Quadratic Formula )
10.P.6 Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x - 2| > 5) and apply to the solution of problems. (Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Absolute Value Equations )
10.P.7 Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (Simple Interest , Compound Interest , Continuous Compound Interest )
10.P.8 Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. (System of Equations Substitution , System of Equations Addition , Age Problems , Train Problems , Mixture Word Problems , Work Word Problems )
Geometry
10.G.1 Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry.10.G.2 Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.
10.G.3 Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. (Identifying Angles , Angle Measurements 2 )
10.G.4 Apply congruence and similarity correspondences (e.g., ΔABC ≅ ΔXYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification. (Proportions 2 )
10.G.5 Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. (Triangle Angles , Triangle Angles 2 , Pythagorean Theorem , Solving For Angles )
10.G.6 Use the properties of special triangles (e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.
10.G.7 Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems. (Line Segments , Determining Slope )
10.G.8 Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the "point-slope" form of the equation. (Applied Linear Equations 2 )
10.G.9 Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems.
10.G.10 Demonstrate the ability to visualize solid objects and recognize their projections and cross sections.
10.G.11 Use vertex-edge graphs to model and solve problems.
Measurement
10.M.1 Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. (Triangle Area , Parallelogram Area , Circle Area , Circle Circumference , Trapezoids )10.M.2 Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. (Rectangular Solids , Triangular Prisms , Cylinders )
10.M.3 Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume. (Area And Volume Proportions )
10.M.4 Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.
Data Analysis, Statistics, and Probability
10.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. (Line Graphs , Stem And Leaf Plots )10.D.2 Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
10.D.3 Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
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