IXL - Pennsylvania eighth-grade math standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2005 Pennsylvania Assessment Anchors 2005 Pennsylvania Assessment Anchors

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M8.A Numbers and Operations

M8.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.
M8.A.1.1 Represent numbers in equivalent forms.
M8.A.1.1.1 Represent numbers using scientific notation and/or exponential forms.
- Exponents and roots: Understanding exponents (Eighth grade - F.1)
- Scientific notation: Convert between standard and scientific notation (Eighth grade - G.1)
M8.A.1.1.2 Find the square or cube of a whole number (single digit) and/or the square root of a perfect square (without a calculator) and explain the relationship between the two (i.e. square and square root).
- Exponents and roots: Square roots of perfect squares (Eighth grade - F.13)
- Exponents and roots: Relationship between squares and square roots (Eighth grade - F.16)
M8.A.2 Understand the meanings of operations, use operations and understand how they relate to each other.
M8.A.2.1 Complete calculations by applying the order of operations.
M8.A.2.1.1 Simplify numeric expressions involving integers, using the order of operations. (May include all types of grouping symbols. No combining negatives with exponents [4 to the -3 power] or compound exponents.)
- Operations with integers: Simplify expressions involving integers and absolute values (Eighth grade - C.8)
M8.A.2.2 Represent or solve problems using rates, ratios, proportions and/or percents.
M8.A.2.2.1 Solve problems involving percents (e.g., tax, discounts, etc) Do not include percent increase or decrease.
M8.A.2.2.2 Represent or solve rate problems (e.g., unit rates, simple interest, distance, etc.) Students may be asked to solve for any term (formulas provided on the reference sheet for distance and interest).
M8.A.3 Compute accurately and fluently and make reasonable estimates.
M8.A.3.1 Determine the appropriateness of overestimating, underestimating or calculating an exact answer in problem-solving situations.
M8.A.3.1.1 Identify, use and/or explain when it is appropriate to round up or round down.
- Rational numbers: Round decimals and mixed numbers (Eighth grade - D.4)
M8.A.3.1.2 Identify, apply and/or explain when an exact answer is needed or when estimation is appropriate.
- Ratios and proportions: Estimate population size using proportions (Eighth grade - H.10)
M8.A.3.2 Use estimation strategies in problem-solving situations.
M8.A.3.2.1 Estimate answers to problems involving percents (percents will be limited to: 1%, 10%, 15%, 20%, 25%, 50% or 75%).
- Percents: Estimate percents of numbers (Eighth grade - J.5)
- Consumer math: Estimate tips (Eighth grade - K.9)
M8.A.3.3 Compute and/or explain operations with integers, fractions and/or decimals.
M8.A.3.3.1 Add, subtract, multiply and/or divide integers, fractions and/or decimals with and without a calculator (straight computation or word problems).

M8.B Measurement

M8.B.1 Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.
M8.B.1.1 Convert measurements.
M8.B.1.1.1 Convert among metric measurements (milli, centi, kilo using meter, liter and gram) (table of equivalency provided on the reference sheet).
- Measurement: Convert rates and measurements: metric units (Eighth grade - L.2)
M8.B.1.1.2 Convert customary measurements up to 2 units above or below the given unit (e.g., inches to yards, pints to gallons) (table of equivalency provided on the reference sheet).
- Measurement: Convert rates and measurements: customary units (Eighth grade - L.1)
- Measurement: Mixed customary units (Eighth grade - L.3)
M8.B.1.1.3 Convert time up to 2 units above or below given unit (e.g., seconds to hours).
M8.B.1.1.4 Convert from Fahrenheit to Celsius or Celsius to Fahrenheit (formulas provided on the reference sheet).
- Measurement: Convert between Celsius and Fahrenheit (Eighth grade - L.6)
M8.B.2 Apply appropriate techniques, tools and formulas to determine measurements.
M8.B.2.1 Determine the measurement of a missing side(s) or angle(s) in a polygon.
M8.B.2.1.1 Determine the total number of degrees in the interior angles of a polygon in 3 - 8 sided figures (formula provided on the reference sheet).
- Geometry: Interior angles of polygons (Eighth grade - Q.8)
M8.B.2.1.2 Determine the measurement of one interior angle of a regular polygon (3- 8 sided polygons, formula provided on the reference sheet).
- Geometry: Interior angles of polygons (Eighth grade - Q.8)
M8.B.2.1.3 Determine the number of sides of a polygon given the total number of degrees in the interior angles (3-8 sided polygons, formula provided on the reference sheet).
M8.B.2.2 Use, describe and/or develop procedures to determine measures of perimeter, circumference, area, surface area and/or volume.
M8.B.2.2.1 Calculate the surface area of cubes and rectangular prisms (formula provided on the reference sheet).
- Geometry: Surface area (Seventh grade - P.28)
M8.B.2.2.2 Calculate the volume of cubes and rectangular prisms (formulas provided on the reference sheet).
- Geometry: Volume (Seventh grade - P.29)
M8.B.2.2.3 Determine the appropriate type of measurement (circumference, perimeter, area, surface area, volume) for a given situation (e.g., which measurement is needed to determine the amount of carpeting for a room).

M8.C Geometry

M8.C.1 Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.
M8.C.1.1 Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.
M8.C.1.1.1 Match the three-dimensional figure with its net (cube, cylinder, cone, prism, pyramid). Any measurements used should be consistent in the stem and answer choices.
- Geometry: Nets of 3-dimensional figures (Eighth grade - Q.24)
M8.C.1.1.2 Define, identify and/or use properties of angles formed by intersecting lines (complementary, supplementary, adjacent and/or vertical angles).
- Geometry: Identify complementary, supplementary, vertical, adjacent, and congruent angles (Eighth grade - Q.1)
- Geometry: Find measures of complementary, supplementary, vertical, and adjacent angles (Eighth grade - Q.2)
M8.C.1.1.3 Define, identify and/or use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical corresponding).
- Geometry: Transversal of parallel lines (Eighth grade - Q.3)
M8.C.1.2 Compute measures of sides of right triangles using the Pythagorean Theorem.
M8.C.1.2.1 Use the Pythagorean Theorem to find the measure of a missing side of a right triangle (formula provided on the reference sheet - whole numbers only).
M8.C.2 Identify and/or apply concepts of transformations or symmetry.
M8.C.3 Locate points or describe relationships using the coordinate plane.
M8.C.3.1 Plot and/or identify ordered pairs on a coordinate plane.
M8.C.3.1.1 Plot, locate or identify ordered pairs on a coordinate plane (the point may be a vertex of a polygon).

M8.D Algebraic Concepts

M8.D.1 Demonstrate an understanding of patterns, relations and functions.
M8.D.1.1 Analyze, extend or develop descriptions of patterns or functions.
M8.D.1.1.1 Continue a numeric or algebraic pattern (pattern must show 3 repetitions - may include up to 2 operations, squares and square roots).
M8.D.1.1.2 Find missing elements in numeric or geometric patterns and/or functions (may be given a table or rule - pattern must show 3 repetitions).
M8.D.1.1.3 Determine the rule of a function (given elements in an input-output table, chart or list - limit to linear functions).
M8.D.2 Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.
M8.D.2.1 Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy.
M8.D.2.1.1 Solve one- or two-step equations and inequalities (should not include absolute values - one variable only).
M8.D.2.1.2 Use substitution to check the accuracy of a given value for an equation or inequality (simple inequalities with one variable).
M8.D.2.1.3 Determine the value of an algebraic expression by simplifying and/or substituting a number for the variable.
M8.D.2.2 Create and/or interpret expressions, equations or inequalities that model problem situations.
M8.D.2.2.1 Match a written situation to its numeric and/or algebraic expression, equation or inequality (up to two variables in equations or expressions - one variable with inequalities).
- Linear functions: Linear function word problems (Eighth grade - V.8)
M8.D.2.2.2 Write and/or solve an equation for a given problem situation (one variable only).
M8.D.3 Analyze change in various contexts.
M8.D.4 Describe or use models to represent quantitative relationships.
M8.D.4.1 Represent relationships with tables or graphs on the coordinate plane.
M8.D.4.1.1 Graph a linear function based on an x/y table (integers only).
- Linear functions: Graph a line from a function table (Eighth grade - V.6)
M8.D.4.1.2 Match the graph of a linear function to its x/y table (integers only).
M8.D.4.1.3 Match the linear equation (y = mx + b form) to the x/y table (integers only in the table).
- Linear functions: Write a rule for a function table (Eighth grade - V.4)

M8.E Data Analysis and Probability

M8.E.1 Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.
M8.E.1.1 Choose, display or interpret data (tables, charts, graphs, etc.).
M8.E.1.1.1 Choose and/or explain the correct representation (graph) for a set of data.
- Charts and graphs: Choose the best type of graph (Eighth grade - N.16)
M8.E.1.1.2 Analyze data and/or answer questions pertaining to data shown in multiple line graphs, circle graphs or histograms.
M8.E.1.1.3 Interpret data shown in stem-and-leaf or box-and-whisker plots.
- Charts and graphs: Interpret stem-and-leaf plots (Eighth grade - N.8)
- Charts and graphs: Interpret box-and-whisker plots (Eighth grade - N.12)
M8.E.2 Select and/or use appropriate statistical methods to analyze data.
M8.E.3 Understand and/or apply basic concepts of probability or outcomes.
M8.E.3.1 Calculate the probability of an event.
M8.E.3.1.1 Find the probability for a mutually exclusive or an independent event (written as a fraction in simplest form).
- Probability: Probability of simple events (Eighth grade - BB.1)
M8.E.3.2 Determine the number of combinations and/or permutations for an event.
M8.E.3.2.1 Determine/show the number of permutations and/or combinations for an event using up to four choices (e.g., organized list, etc.).
M8.E.4 Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.
M8.E.4.1 Draw conclusions, make inferences and/or evaluate hypotheses based on statistical and data displays.
M8.E.4.1.1 Fit a line to a scatter plot and/or describe any correlation between the two variables (positive, negative, strong, weak or none).
- Charts and graphs: Scatter plots (Eighth grade - N.13)
M8.E.4.1.2 Make predictions based on survey results or graphs (bar, line, circle, scatterplots, etc.).
- Probability: Make predictions (Eighth grade - BB.4)