1.0 NUMBER AND OPERATION

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

8.1.2 Understand operations and how they relate to one another

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

2.0 ALGEBRA

8.2.1 Understand patterns, relations, and functions.

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

8.2.3 Use mathematical models to represent and understand quantitative relationships.

8.2.4 Analyze change in various contexts.

3.0 GEOMETRY

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

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

8.3.3 Apply transformations and use symmetry to analyze mathematical situations.

  (Also 8.3.2)

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

4.0 MEASUREMENT

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

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

5.0 DATA ANALYSIS AND PROBABILITY

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

8.5.2 Select and use appropriate statistical methods to analyze data.

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

8.5.4 Understand and apply basic concepts of probability.

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Use a variety of models to demonstrate the relationships within the real num system  (real-rational, whole, natural, irrational) using Venn diagrams and webs

Define absolute value, opposite, and reciprocal.

Compare and order integers involving absolute value (£, ³)

Convert negative and positive improper fractions to mixed numbers

Convert between fractions, decimals (repeating and terminating), and percent forms.

Develop meaning for % greater than 100 and less than 1.

Evaluate a power with integer bases and exponents.  Negative exponents introduced this year, rational numbers to positive powers.

Convert numbers between standard and scientific notation (very large and very small numbers)

Recognize, understand and use the inverse relationships of +,-,*,/.

Determine square roots, inverse of squaring

Use the rule for order of operations to solve numerical expressions (grouping symbols, exponents, multiplication and division from left to right and addition/subtraction left to right)

Recognize and use the commutative, identity, associative properties of +, *

Recognize and use the distributive property

Estimate the results of rational number computations using a variety of strategies.

Define irrational numbers.  Estimate the square root of a number that is not a perfect square.

Add, sub, mult, div with decimals

Add and sub signed like, unlike, and mixed numbers including borrowing

Multiply and divide signed fractions, whole numbers, and mixed numbers using cross-canceling to simplify.

Add and subtract integers using models and rules

Multiply and divide integers using rules

Solve problems by setting up a proportion and using cross products to solve for an unknown. 

Identify and explain unit rates

Find percent, whole or part using the percent proportion or equation.

Solve real-world problems involving percentages

Read, plan, solve one and two-step real-world problems involving fracs, decs, whole, percents and check using act out, charts, pictures, guess&check, work backward, look for a pattern, etc..

Identify problems with too little or too much information and determine which info is needed/not needed.

Analyze numerical patterns to predict the next terms in a sequence or series

Write a numeric/algebraic rule for a given pattern.

Define arithmetic and geometric sequences.

Recognize and extend geometric patterns (rotations of figures, number of sides in a polygon, growing)

Develop understanding of particular patterns, relationships, and functions.

Define input and output

Identify functions as linear or nonlinear.

Graph a linear equation by plotting points and using slope-intercept form

Use a variety of forms to represent linear relationships.

Compare linear relationships to nonlinear relationships.

Define and use variables to replace unknowns.

Write a variable expression from a word form and vice-versa

Simplify variable expressions by combining like terms.

Evaluate expressions for a given variable.

Model and solve one and two-step equations (including variable on both sides of equal sign) using inverse operations +,-, *,/

Model and solve one-and two-step inequalities.

Relate, compare, & formulate different forms of multi-step equations that represent relationships and real-world situations.

Recognize and generate equivalent forms for simple algebraic expressions.

Use a variety of methods to solve real-world problems involving multi-step linear equations (manipulatives, technology, paper and pencil)

Apply given formulas to solve real-world problems.

Generate a chart of ordered pairs given a general rule.

Find a function rule given a table.

Identify the graphical representation of the solution to a one-variable linear inequality.

Model expressions with algebra tiles, etc..

Write an algebraic model to represent a real world problem.

Develop meaning for rate of change in real-world situations.

Construct tables and graphs to represent rates of change.

Use appropriate geometric vocabulary (polygons, base, height, prisms, cylinders, diameter, radius, NEW: chords, tangent to circle, inscribed angle, cones, etc..)

Use appropriate tools and methods to draw geometric objects with specified properties.

Classify triangles according to angles and sides.

Investigate the sum of all angles in a triangle.

Find missing angle measurements using sum of angles = 180 degrees.

Investigate, define, and apply the Pythagorean theorem.

Name different types of quadrilaterals.

Name different types of polygons (3 sides through 10)

Define and identify adjacent, vertical, complementary & supplementary angles, transversals, alternate interior and exterior.

Identify and distinguish among similar, congruent, and symmetric figures-name corresponding parts and prove triangle congruency.

Understand the basics of three dimensions figures.

Explore three-dimensional figures through surface area and volume of prisms and cylinders using nets (2-D representations of 3-D objects) and models.

(See algebra section for coordinate graphing and 8.3.3 below.)

Explore transformations using slides (translation), flips (reflection), turns (rotation), and dilations (enlargements/ reductions) in the coordinate plane.

Use visualization and special reasoning to solve real-world problems.

Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom-art, sci, everyday life.

Convert measures of length, weight, and time expressed in a given mixed unit (2ft 3 in) to other units in the given system.  (km to m, sm to mm, in-ft-yd-mi, ft/s, mi/h)

Select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles.

Identify the relationship between ratio and scale.

Use proportions to find missing side lengths in two simila