8.NS Number and Number Sense

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1 Skills available for Virginia eighth-grade math standards Standards are in bold, followed by a list of the IXL math skills that are aligned to that standards. Students can practice these skills online at Standards: Virginia Standards of Learning 8.NS Number and Number Sense 8.1 The student will 8.1.a simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; and Absolute value and opposite integers (8-B.3) Integer addition and subtraction rules (8-C.1) Add and subtract integers using counters (8-C.2) Add and subtract integers (8-C.3) Add and subtract three or more integers (8-C.4) Integer multiplication and division rules (8-C.6) Multiply and divide integers (8-C.7) Evaluate numerical expressions involving integers (8-C.8) Absolute value of rational numbers (8-D.6) Add and subtract rational numbers (8-E.2) Apply addition and subtraction rules (8-E.4) Multiply and divide rational numbers (8-E.5) Apply multiplication and division rules (8-E.7) Apply addition, subtraction, multiplication, and division rules (8-E.8) Evaluate numerical expressions involving rational numbers (8-E.9) Understanding exponents (8-F.1) Evaluate exponents (8-F.2) Solve equations with variable exponents (8-F.3) Exponents with negative bases (8-F.4) Exponents with decimal and fractional bases (8-F.5) Understanding negative exponents (8-F.6) Evaluate negative exponents (8-F.7) Multiplication with exponents (8-F.8) Division with exponents (8-F.9) Multiplication and division with exponents (8-F.10) Power rule (8-F.11) Evaluate expressions involving exponents (8-F.12) Identify equivalent expressions involving exponents (8-F.13) Relationship between squares and square roots (8-F.17) Cube roots of perfect cubes (8-F.19) Multiply numbers written in scientific notation (8-G.3) Divide numbers written in scientific notation (8-G.4) 8.1.b compare and order decimals, fractions, percents, and numbers written in scientific notation. Integers on number lines (8-B.1)

2 Compare and order integers (8-B.4) Integer inequalities with absolute values (8-B.5) Write fractions in lowest terms (8-D.1) Convert between decimals and fractions or mixed numbers (8-D.4) Compare rational numbers (8-D.7) Put rational numbers in order (8-D.8) Convert between standard and scientific notation (8-G.1) Compare numbers written in scientific notation (8-G.2) Identify equivalent ratios (8-H.2) Convert between percents, fractions, and decimals (8-J.1) Compare percents to fractions and decimals (8-J.2) Compare percents of numbers (8-J.8) 8.2 The student will describe orally and in writing the relationships between the subsets of the real number system. Classify numbers (8-A.8) Identify rational and irrational numbers (8-D.5) 8.CE Computation and Estimation 8.3 The student will 8.3.a solve practical problems involving rational numbers, percents, ratios, and proportions; and Add and subtract integers: word problems (8-C.5) Add and subtract rational numbers: word problems (8-E.3) Multiply and divide rational numbers: word problems (8-E.6) Equivalent ratios: word problems (8-H.4) Unit rates (8-H.5) Compare ratios: word problems (8-H.6) Solve proportions: word problems (8-H.7) Do the ratios form a proportion: word problems (8-H.9) Estimate population size using proportions (8-H.11) Scale drawings: word problems (8-H.12) Find the constant of proportionality from a table (8-I.1) Find the constant of proportionality: word problems (8-I.7) Solve problems involving proportional relationships (8-I.8) Find what percent one number is of another: word problems (8-J.4) Estimate percents of numbers (8-J.5) Percents of numbers and money amounts (8-J.6) Percents of numbers: word problems (8-J.7) Percent of change (8-J.10) Percent of change: word problems (8-J.11) Price lists (8-K.1) Unit prices (8-K.2) Unit prices with unit conversions (8-K.3) Unit prices: find the total price (8-K.4) Percent of a number: tax, discount, and more (8-K.5) Find the percent: tax, discount, and more (8-K.6) Sale prices: find the original price (8-K.7)

3 Multi-step problems with percents (8-K.8) Estimate tips (8-K.9) Simple interest (8-K.10) Compound interest (8-K.11) Convert rates and measurements: customary units (8-L.1) Convert rates and measurements: metric units (8-L.2) Mixed customary units (8-L.3) Convert between customary and metric systems (8-L.4) Convert between Celsius and Fahrenheit (8-L.6) 8.3.b determine the percent increase or decrease for a given situation. Percent of change (8-J.10) Percent of change: word problems (8-J.11) Percent of a number: tax, discount, and more (8-K.5) Find the percent: tax, discount, and more (8-K.6) Sale prices: find the original price (8-K.7) Simple interest (8-K.10) 8.4 The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Evaluate one-variable expressions (8-V.4) Evaluate multi-variable expressions (8-V.5) Evaluate absolute value expressions (8-V.6) Evaluate radical expressions (8-V.7) Evaluate rational expressions (8-V.8) Which x satisfies an equation? (8-W.1) Does (x, y) satisfy the linear function? (8-Z.2) Evaluate a linear function (8-Z.6) Complete a table for a linear function (8-Z.7) Does (x, y) satisfy the nonlinear function? (8-Z.15) Evaluate a nonlinear function (8-Z.16) 8.5 The student will 8.5.a determine whether a given number is a perfect square; and Square roots of perfect squares (8-F.14) Positive and negative square roots (8-F.15) 8.5.b find the two consecutive whole numbers between which a square root lies. Estimate positive and negative square roots (8-F.16) Estimate cube roots (8-F.21) 8.MEA Measurement 8.6 The student will 8.6.a verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles; and Identify complementary, supplementary, vertical, adjacent, and congruent angles (8-O.8) Find measures of complementary, supplementary, vertical, and adjacent angles (8-O.9)

4 8.6.b measure angles of less than 360. Measure angles with a protractor (5-AA.7) 8.7 The student will 8.7.a investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and Volume of cubes, prisms, and pyramids (8-T.7) Surface area of cubes, prisms, and pyramids (8-T.8) Volume of cylinders and cones (8-T.9) Surface area of cylinders and cones (8-T.10) 8.7.b describe how changing one measured attribute of a figure affects the volume and surface area. Perimeter, area, and volume: changes in scale (8-T.14) 8.GEO Geometry 8.8 The student will 8.8.a apply transformations to plane figures; and Translations: graph the image (8-P.3) Translations: find the coordinates (8-P.4) Reflections: graph the image (8-P.5) Reflections: find the coordinates (8-P.6) Rotations: graph the image (8-P.7) Rotations: find the coordinates (8-P.8) Dilations: graph the image (8-Q.2) Dilations: find the coordinates (8-Q.3) 8.8.b identify applications of transformations. Identify reflections, rotations, and translations (8-P.2) Dilations: scale factor and classification (8-Q.4) 8.9 The student will construct a three-dimensional model, given the top or bottom, side, and front views. Nets of three-dimensional figures (8-S.2) Front, side, and top view (8-S.3) Base plans (8-S.4) 8.10 The student will 8.10.a verify the Pythagorean Theorem; and 8.10.b apply the Pythagorean Theorem. Pythagorean theorem: find the length of the hypotenuse (8-R.1) Pythagorean theorem: find the missing leg length (8-R.2) Pythagorean theorem: find the perimeter (8-R.3) Pythagorean theorem: word problems (8-R.4) Converse of the Pythagorean theorem: is it a right triangle? (8-R.5) 8.11 The student will solve practical area and perimeter problems involving composite plane figures.

5 Area of compound figures (5-EE.5) Perimeter (8-T.1) Area (8-T.2) Area and perimeter: word problems (8-T.3) Circles, semicircles, and quarter circles (8-T.5) Circles: word problems (8-T.6) Add polynomials to find perimeter (8-BB.5) 8.PS Probability and Statistics 8.12 The student will determine the probability of independent and dependent events with and without replacement. Probability of opposite, mutually exclusive, and overlapping events (8-EE.2) Experimental probability (8-EE.3) Make predictions (8-EE.4) Compound events: find the number of outcomes (8-EE.5) Identify independent and dependent events (8-EE.6) Probability of independent and dependent events (8-EE.7) Combination and permutation notation (8-EE.11) 8.13 The student will 8.13.a make comparisons, predictions, and inferences, using information displayed in graphs; and Interpret tables (8-CC.1) Interpret bar graphs (8-CC.2) Create bar graphs (8-CC.3) Interpret line graphs (8-CC.4) Create line graphs (8-CC.5) Interpret line plots (8-CC.6) Create line plots (8-CC.7) Create and interpret line plots with fractions (8-CC.8) Interpret stem-and-leaf plots (8-CC.9) Interpret histograms (8-CC.10) Create histograms (8-CC.11) Create frequency charts (8-CC.12) Interpret box-and-whisker plots (8-CC.13) Interpret circle graphs (8-CC.15) Circle graphs and central angles (8-CC.16) Choose the best type of graph (8-CC.17) Identify an outlier (8-DD.6) Identify an outlier and describe the effect of removing it (8-DD.7) Outliers in scatter plots (8-DD.8) 8.13.b construct and analyze scatterplots. Scatter plots (8-CC.14) 8.PFA Patterns, Functions, and Algebra 8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of a given

6 relationship. Identify graphs of proportional relationships (8-I.2) Write variable expressions from diagrams (8-V.2) Write variable expressions: word problems (8-V.3) Write an equation from words (8-W.2) Write and solve equations that represent diagrams (8-W.4) Find the slope of a graph (8-Y.1) Find the slope from two points (8-Y.2) Find a missing coordinate using slope (8-Y.3) Find the slope of an equation (8-Y.4) Graph a line using slope (8-Y.5) Graph a line from an equation (8-Y.6) Write a linear equation from a slope and y-intercept (8-Y.7) Write a linear equation from a graph (8-Y.8) Write a linear equation from a slope and a point (8-Y.9) Write a linear equation from two points (8-Y.10) Identify functions (8-Z.1) Evaluate a linear function (8-Z.6) Complete a table for a linear function (8-Z.7) Complete a table and graph a linear function (8-Z.8) Interpret the graph of a linear function: word problems (8-Z.9) Write a linear function from a table (8-Z.10) Interpret linear functions (8-Z.13) Identify linear and nonlinear functions (8-Z.14) 8.15 The student will 8.15.a solve multistep linear equations in one variable with the variable on one and two sides of the equation; Solve one-step equations (8-W.6) Solve two-step equations (8-W.7) Solve multi-step equations (8-W.8) Solve equations involving like terms (8-W.9) Solve equations with variables on both sides (8-W.10) Solve equations: word problems (8-W.12) 8.15.b solve two-step linear inequalities and graph the results on a number line; and Solutions to inequalities (8-X.1) Write inequalities from number lines (8-X.3) Solve one-step inequalities (8-X.4) Solve two-step inequalities (8-X.6) Solve multi-step inequalities (8-X.8) 8.15.c identify properties of operations used to solve an equation. Properties of addition and multiplication (8-V.10) Multiply using the distributive property (8-V.11) Write equivalent expressions using properties (8-V.12) Properties of equality (8-W.5) 8.16 The student will graph a linear equation in two variables.

7 Graph a line from an equation (8-Y.6) 8.17 The student will identify the domain, range, independent variable, or dependent variable in a given situation. Identify independent and dependent variables (8-Z.3) For more information about IXL, go to or send an to orders@ixl.com.

Skills available for New York eighth grade math standards

Skills available for New York eighth grade math standards Standards are in bold, followed by a list of the IXL math skills that are aligned to that standard. Students can practice these skills online at