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8.M.1
Number and Operation
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8.M.1.1
Understand and use numbers.
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8.M.1.1.1
Compare magnitudes and relative magnitudes of rational numbers, including integers, fractions, decimals, percents, and absolute values.
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8.M.1.1.2
Use rational numbers, including percents and ratios, and pi to solve problems.
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8.M.1.1.3
Locate the position of rational numbers and positive real numbers on a number line.
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8.M.1.1.4
Convert between standard form, scientific notation, and exponential form.
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8.M.1.1.5
Apply number theory concepts (primes, composites, prime factorization, LCM, GCF).
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8.M.1.1.6
Recognize pertinent information for problem solving.
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8.M.1.1.7
Apply integers in one- and two-step common real-world situations.
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8.M.1.1.8
Use appropriate vocabulary.
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8.M.1.2
Perform computations accurately.
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8.M.1.2.1
Recall the common equivalent fractions, decimals, and percents of halves, thirds, fourths, fifths, and tenths.
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8.M.1.2.2
Add, subtract, multiply, and divide rational numbers.
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8.M.1.2.3
Evaluate numerical expressions with whole number exponents.
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8.M.1.2.4
Evaluate numerical expressions with rational numbers using the order of operations.
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8.M.1.2.5
Select and use an appropriate method of computation from mental math, paper and pencil, calculator, or a combination of the three.
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8.M.1.2.6
Use a variety of strategies including common mathematical formulas to compute problems drawn from real life situations.
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8.M.1.2.7
Use appropriate vocabulary and notations.
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8.M.1.3
Estimate and judge reasonableness of results.
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8.M.1.3.1
Estimate to predict computation results.
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8.M.1.3.2
Identify when estimation is appropriate and apply to problem solving situations.
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8.M.1.3.3
Identify whether a given estimate is an overestimate or underestimate.
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8.M.1.3.4
Use a four-function calculator to solve complex grade-level problems.
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8.M.1.3.5
Formulate conjectures and justify (short of formal proof) why they must be or seem to be true.
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8.M.1.3.6
Use appropriate vocabulary and notations.
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8.M.2
Concepts and Principles of Measurement
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8.M.2.1
Understand and use U.S. customary and metric measurements.
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8.M.2.1.1
Select and use appropriate units and tools to make formal measurements in both systems.
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8.M.2.1.2
Apply estimation of measurement to real-world and content problems using standard measuring devices.
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8.M.2.1.3
Compare the differences and relationships among measures of perimeter, area, and volume (capacity) within both systems.
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8.M.2.1.4
Given the formulas, find the circumference, perimeter, or area of triangles, circles, and quadrilaterals, and the volume and surface area of rectangular prisms.
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8.M.2.1.5
Convert units of measurement within each system in problem solving situations.
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8.M.2.1.6
Solve problems involving area of circles and the perimeter and area of rectangles and triangles.
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8.M.2.1.7
Use appropriate vocabulary and notations.
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8.M.2.2
Apply the concepts of rates, ratios, and proportions.
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8.M.2.2.1
Use rates, proportions, ratios, and map scales in problem-solving situations.
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8.M.2.2.2
Determine unit rates in real-world situations.
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8.M.2.3
Apply dimensional analysis.
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8.M.2.3.1
Illustrate the interrelationship of measurement units through dimensional analysis conversions.
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8.M.3
Concepts and Language of Algebra and Functions
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8.M.3.1
Use algebraic symbolism as a tool to represent mathematical relationships.
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8.M.3.1.1
Use variables in expressions, equations, and inequalities.
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8.M.3.1.2
Translate simple word statements and story problems into algebraic expressions and equations.
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8.M.3.1.3
Use symbols "<," ">," "=," "not equal to," "less than or equal to," and "greater than or equal to" to express relationships.
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8.M.3.2
Evaluate algebraic expressions.
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8.M.3.2.1
Use and apply the following properties in evaluating algebraic expressions: commutative, associative, identity, zero, inverse, distributive, and substitution.
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8.M.3.2.2
Use the order of operations in evaluating simple algebraic expressions.
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8.M.3.2.3
Simplify algebraic expressions.
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8.M.3.3
Solve algebraic equations and inequalities.
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8.M.3.3.1
Solve one-and two-step equations and inequalities.
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8.M.3.3.2
Match graphical representations with simple linear equations.
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8.M.3.4
Understand the concept of functions.
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8.M.3.4.1
Extend patterns and identify a rule (function) that generates the pattern using rational numbers.
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8.M.3.4.2
Use relationships to explain how a change in one quantity may result in a change in another, and identify the relationship as a positive, negative, or neither.
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8.M.3.4.3
Use appropriate vocabulary and notations.
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8.M.3.5
Represent equations, inequalities and functions in a variety of formats.
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8.M.3.5.1
Represent a set of data in a table, as a graph, and as a mathematical relationship.
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8.M.3.6
Apply functions to a variety of problems.
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8.M.3.6.1
Use patterns and linear functions to represent and solve problems.
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8.M.4
Concepts and Principles of Geometry
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8.M.4.1
Apply concepts of size, shape, and spatial relationships.
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8.M.4.1.1
Describe and classify relationships among types of one-, two-, and three-dimensional geometric figures, using their defining properties.
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8.M.4.1.2
Draw and measure various angles and shapes using appropriate tools.
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8.M.4.1.3
Apply the fundamental concepts, properties, and relationships among points, lines, rays, planes, and angles.
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8.M.4.1.4
Identify and model the effects of reflections, translations, rotations, and scaling on various shapes.
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8.M.4.1.5
Identify congruence, similarities, and line symmetry of shapes.
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8.M.4.1.6
Explain the concept of surface area and volume (capacity).
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8.M.4.1.7
Use appropriate vocabulary and symbols.
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8.M.4.2
Apply the geometry of right triangles.
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8.M.4.3
Apply graphing in two dimensions.
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8.M.4.3.1
Identify and plot points on a coordinate plane.
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8.M.5
Data Analysis, Probability, and Statistics
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8.M.5.1
Understand data analysis.
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8.M.5.1.1
Analyze and interpret tables, charts, and graphs, including frequency tables, scatter plots, broken line graphs, line plots, bar graphs, histograms, circle graphs, and stem-and-leaf plots.
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8.M.5.1.2
Explain and justify conclusions drawn from tables, charts, and graphs.
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8.M.5.1.3
Use appropriate vocabulary and notations.
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8.M.5.2
Collect, organize, and display data.
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8.M.5.2.1
Collect, organize, and display data with appropriate notation in tables, charts, and graphs, including scatter plots, broken line graphs, line plots, bar graphs, histograms, and stem-and-leaf plots.
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8.M.5.3
Apply simple statistical measurements.
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8.M.5.3.1
Choose and calculate the appropriate measure of central tendency - mean, median, and mode.
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8.M.5.3.2
Explain the significance of distribution of data, including range, frequency, gaps, and clusters.
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8.M.5.4
Understand basic concepts of probability.
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8.M.5.4.1
Model situations of probability using simulations.
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8.M.5.4.2
Recognize equally likely outcomes.
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8.M.5.4.3
Explain that probability ranges from 0% to 100% and identify a situation as having high or low probability.
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8.M.5.4.4
Use the language of probability.
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8.M.5.5
Make predictions or decisions based on data.
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8.M.5.5.1
Make predictions based on experimental and theoretical probabilities.
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8.M.5.5.2
Conduct statistical experiments and interpret results using tables, charts, or graphs.
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8.M.5.5.3
Use appropriate vocabulary and notations.
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IXL Learning. All rights reserved.