**Comprehensive 6-8 Curriculum**

UNDERSTANDS PATTERNS, RELATIONSHIPS, AND FUNCTIONS

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

Relate and compare different forms of representation for a relationship

Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.

REPRESENT AND ANALYZE MATHEMATICAL SITUATIONS AND STRUCTURES* *USING ALGEBRAIC SYMBOLS

Develop an initial conceptual understanding of different uses of variables

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

USE MATHEMATICAL MODELS TO REPRESENT AND UNDERSTAND QUANTITATIVE RELATIONSHIPS

Model and solve contextualized problems using various representations, such as graphs, tables, and equations

ANALYZE CHANGE IN VARIOUS CONTEXTS

Use graphs to analyze the nature of changes in quantities in linear relationships

SPECIFY LOCATIONS AND DESCRIBE SPATIAL RELATIONSHIPS USING COORDINATE GEOMETRY AND OTHER REPRESENTATIONAL SYSTEMS

Use coordinate geometry to represent and examine the properties of geometric shapes

Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides

ANALYZE CHARACTERISTICS AND PROPERTIES OF TWO - AND THREE- DIMENSIONAL GEOMETRIC SHAPES AND DEVELOP MATHEMATICAL ARGUMENTS ABOUT GEOMETRIC RELATIONSHIPS

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship

APPLY TRANSFORMATIONS AND USE SYMMETRY TO ANALYZE MATHEMATICAL SITUATIONS

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling

Examine the congruence, similarity, and line or rotational symmetry of objects using transformations

USE VISUALIZATION, SPATIAL REASONING, AND GEOMETRIC MODELING TO SOLVE PROBLEMS

Draw geometric objects with specified properties, such as side lengths or angle measures

Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume

Use visual tools such as networks to represent and solve problems

Use geometric models to represent and explain numerical and algebraic relationships

Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

UNDERSTAND MEASURABLE ATTRIBUTES OF OBJECTS AND THE UNITS, SYSTEMS, AND PROCESSES OF MEASUREMENT

Understand both metric and customary systems of measurement

Understand relationships among units and convert from one unit to another within the same system

Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume

APPLY APPROPRIATE TECHNIQUES, TOOLS, AND FORMULAS TO DETERMINE MEASUREMENTS

Use common benchmarks to select appropriate methods for estimating measurements

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders

Solve problems involving scale factors, using ratio and proportion

Solve simple problems involving rates and derived measurements for such attributes as velocity and density

FORMULATE QUESTIONS THAT CAN BE ADDRESSED WITH DATA AND COLLECT, ORGANIZE, AND DISPLAY RELEVANT DATA TO ANSWER THEM

Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plot

SELECT AND USE APPROPRIATE STATISTICAL METHODS TO ANALYZE DATA

Find, use, and interpret measures of center and spread, including mean and interquartile range

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatter plots

DEVELOP AND EVALUATE INFERENCES AND PREDICTIONS THAT ARE BASED ON DATA

Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken

Make conjectures about possible relationships between two characteristics of a sample on the basis of scatter plots of the data and approximate lines of fit

Use conjectures to formulate new questions and plan new studies to answer them

UNDERSTAND AND APPLY BASIC CONCEPTS OF PROBABILITY

Understand and use appropriate terminology to describe complementary and mutually exclusive events

Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations

Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models