8.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

8.1.1.e: work flexibly with fractions, decimals, and percents to solve problems;

8.1.1.f: compare and order fractions, decimals, and percents;

8.1.1.g: connect whole numbers, fractions, decimals, percents and integers to locations on the number line;

8.1.1.h: develop meaning for percents greater than 100 and less than one;

8.1.1.j: understand and use ratios and proportions to represent quantitative relationships;

8.1.1.o: apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime).

8.1.2: Understand operations and how they relate to one another.

8.1.2.a: understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;

8.1.2.b: apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals;

8.1.2.d: apply order of operations in computing with rational numbers;

8.1.2.e: understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

8.1.3: Solve problems, compute fluently, and make reasonable estimates.

8.1.3.b: develop and analyze procedures for computing with fractions, decimals, and integers;

8.1.3.c: develop and use strategies to estimate the results of rational number computations in real-world situations;

8.1.3.e: solve one-step real-world problems involving whole numbers, fractions, decimals, and percents;

8.1.3.g: solve multi-step real-world problems involving whole numbers, fractions, decimals, and percents;

8.1.3.h: develop, analyze, and explain methods for solving problems involving proportions (e.g., scaling, finding equivalent ratios);

8.2.1: Understand patterns, relations, and functions.

8.2.1.a: represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible symbolic rules;

8.2.1.b: develop understanding for arithmetic and geometric sequences;

8.2.1.c: relate and compare different forms of representation for a relationship;

8.2.1.d: identify functions as linear or nonlinear;

8.2.1.e: compare and contrast properties of functions from tables, graphs, or equations.

8.2.2: Represent and analyze mathematical situations and structures using algebraic symbols.

8.2.2.a: formulate multi-step equations that represent relationships and real-world situations;

8.2.2.b: develop meaning for intercept and slope;

8.2.2.d: use a variety of forms to represent linear relationships;

8.2.2.f: evaluate a first-degree algebraic expression given values for two or more variables;

8.2.2.g: solve one- and two-step linear equations involving integers;

8.2.2.h: use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper);

8.2.2.j: solve one-step linear inequalities;

8.2.2.k: identify the graph of a linear equation;

8.2.2.l: identify the graphical representation of the solution to a one-variable linear inequality;

8.2.2.m: develop understanding for particular values of patterns, relationships, and functions (e.g., x- and y- intercepts, slope, maximum and minimum values).

8.2.4: Analyze change in various contexts.

8.2.4.a: compare linear relationships to non-linear relationships;

8.2.4.b: develop meaning for rate of change in real-world situations.

8.3.1: Analyze characteristics and properties of two- and three-dimensional geometric figures.

8.3.1.a: describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;

8.3.1.b: understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding);

8.3.1.c: solve problems using angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding);

8.3.1.d: determine the measure of an angle of a triangle given the measures of the other two angles;

8.3.1.e: understand relationships among the angles and side lengths of similar geometric figures;

8.3.1.f: determine congruence of line segments, angles, and polygons by direct comparison of given attributes;

8.3.1.g: develop understanding of the Pythagorean theorem.

8.3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

8.3.2.a: graph points in the coordinate system.

8.3.3: Apply transformations and use symmetry to analyze mathematical situations.

8.3.3.a: describe sizes, positions, and orientations of shapes under transformations (e.g., rotations, translations, reflections, dilations);

8.3.3.b: relate symmetry and congruence to reflections about a line.

8.3.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.

8.3.4.b: use two-dimensional representations of three-dimensional objects to visualize;

8.3.4.c: use visualization and spatial reasoning to solve real-world problems;

8.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

8.4.1.c: understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume.

8.4.2: Apply appropriate techniques, tools, and formulas to determine measurements.

8.4.2.a: use a variety of strategies to estimate length, perimeter, circumference, area, and volume;

8.4.2.b: select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision;

8.4.2.c: apply formulas and/or other strategies to solve problems involving perimeter, circumference of circles, and the area of triangles, parallelograms, trapezoids, and circles;

8.4.2.e: apply given formulas to find volume of selected prisms and cylinders;

8.4.2.f: compare and contrast the volumes of a variety of geometric solids;

8.4.2.g: solve problems involving rate/time/distance (i.e., d = rt);

8.4.2.h: solve problems involving scale factors using ratio and proportion;

8.4.2.i: solve real-world problems using the Pythagorean Theorem;

8.4.2.j: construct tables and graphs to represent rates of change;

8.4.2.k: find measures using proportional relationships and properties of similar figures;

8.4.2.l: determine the measure of angles by applying angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding).

8.5.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

8.5.1.a: formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g., random sampling, simulations);

8.5.1.b: select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatterplots).

8.5.2: Select and use appropriate statistical methods to analyze data.

8.5.2.a: find, use, and interpret measures of center and spread (e.g., mean, interquartile range);

8.5.2.b: develop meaning for frequency, distribution, and outliers;

8.5.2.c: discuss and understand the relationship between data sets and their graphical representations (e.g., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots).

8.5.3: Develop and evaluate inferences and predictions that are based on data.

8.5.3.c: develop meaning for lines of best fit;

8.5.4: Understand and apply basic concepts of probability.

8.5.4.b: connect the symbolic representation of a probability to an experiment;

8.5.4.c: use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models);

8.5.4.d: distinguish between theoretical and experimental probability;

8.5.4.e: find the probability of dependent and independent events.

Correlation last revised: 7/7/2009

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.