IXL - Massachusetts eighth-grade math standards

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Skills available for Massachusetts eighth-grade math standards

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Standards document:

2011 Massachusetts Curriculum Framework (Common Core) 2011 Massachusetts Curriculum Framework (Common Core)
2000 Massachusetts Curriculum Frameworks 2000 Massachusetts Curriculum Frameworks

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7-8.8.N Number Sense and Operations

7-8.8.N.1 Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents.
7-8.8.N.2 Define, compare, order, and apply frequently used irrational numbers, such as square root of 2 and pi.
7-8.8.N.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
7-8.8.N.4 Represent numbers in scientific notation, and use them in calculations and problem situations.
7-8.8.N.5 Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.
7-8.8.N.6 Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3.
- Integers: Absolute value and opposite integers (Eighth grade - B.2)
- Rational numbers: Absolute value of rational numbers (Eighth grade - D.5)
7-8.8.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.
7-8.8.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).
7-8.8.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.
7-8.8.N.10 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).
7-8.8.N.11 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
- Ratios and proportions: Estimate population size using proportions (Eighth grade - H.10)
- Problem solving: Guess-and-check word problems (Eighth grade - M.2)
7-8.8.N.12 Select and use appropriate operations-addition, subtraction, multiplication, division, and positive integer exponents-to solve problems with rational numbers (including negatives).

7-8.8.P Patterns, Relations, and Algebra

7-8.8.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.
7-8.8.P.2 Evaluate simple algebraic expressions for given variable values, e.g., 3a? - b for a = 3 and b = 7.
7-8.8.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.
7-8.8.P.4 Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.
7-8.8.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.
7-8.8.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.
- Linear functions: Find slope from an equation (Eighth grade - V.11)
- Linear functions: Graph a line using slope (Eighth grade - V.12)
7-8.8.P.7 Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.
7-8.8.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 = pi d, A = pi r? (A as a function of r), A rectangle = lw (A rectangle as a function of l and w).
7-8.8.P.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.
7-8.8.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.
- Linear functions: Slopes of parallel and perpendicular lines (Eighth grade - V.13)

7-8.8.G Geometry

7-8.8.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.
- Geometry: Find missing angles in triangles and quadrilaterals (Eighth grade - Q.6)
- Geometry: Interior angles of polygons (Eighth grade - Q.8)
7-8.8.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.
7-8.8.G.3 Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.
7-8.8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.
7-8.8.G.5 Use a straight-edge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.
7-8.8.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.
7-8.8.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.
- Geometry: Names and parts of 3-dimensional figures (Eighth grade - Q.23)
7-8.8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects, e.g., nets, projections, and perspective drawings.

7-8.8.M Measurement

7-8.8.M.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.
7-8.8.M.2 Given the formulas, convert from one system of measurement to another. Use technology as appropriate.
- Measurement: Convert between customary and metric systems (Eighth grade - L.4)
- Measurement: Convert between Celsius and Fahrenheit (Eighth grade - L.6)
7-8.8.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.
7-8.8.M.4 Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.
7-8.8.M.5 Use models, graphs, and formulas to solve simple problems involving rates, e.g., velocity and density.
- Ratios and proportions: Rate of change (Eighth grade - H.11)
- Ratios and proportions: Constant rate of change (Eighth grade - H.12)

7-8.8.D Data Analysis, Statistics, and Probability

7-8.8.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.
- Statistics: Identify representative, random, and biased samples (Eighth grade - BB.6)
7-8.8.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.
7-8.8.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.
7-8.8.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.