1.1 Understand and use numbers.

Understand and use all rational numbers including fractions, decimals, and percents, & ratios to solve problems.

Understand and use real numbers, both rational and irrational.

Show a sense of magnitudes and relative magnitudes of real numbers using scientific notation (including negative exponents), fractions, decimals, and exponential numbers.

Develop and apply number theory concepts; e.g. primes, factors, and multiples in content problem situations.

Compare real numbers using <,>,=.

Understand the position of rational numbers on a number line.

Understand absolute value concepts on a number line.

Identify the lowest common multiple of numbers in their prime factored state.

Recognize pertinent information from word problems.

Use appropriate vocabulary.

1.2 Performs computations accurately

Consistently and accurately add, subtract, multiply, and divide rational numbers.

Understand and use both positive and negative exponents.

Apply absolute value concepts on number lines to write, order, or compare.

Calculate percent and percent of change.

Write equivalent forms of numbers using exponents, scientific notation, percent, decimals, and fractions.

Identify equivalent roots & radicals.

Estimate square roots using perfect squares.

Compute 2nd & 3rd degree exponents.

Evaluate numerical expressions using the order of operations involving integers, fractions, and decimals.

 Accurately use divisibility rules & factorization.

Select and use an appropriate method of computation from mental math, calculator, paper and pencil, or a combination of the three.

Use correct vocabulary and notation.

1.3 Estimates & judges reasonableness of results.

Estimate to predict computation outcomes using all rational numbers and all operations. 

Formulate conjectures and be able to defend your outcome.

Use a scientific calculator to solve complex pre-algebra problems.

Round to a given place value and determine if an estimate is an overestimate or underestimate.

 Recognize and explain when estimation is appropriate and understand the usefulness of an estimate as opposed to an exact answer.

Use appropriate vocabulary and notations.

1.1 Understand and use U.S. customary and metric measurements.

Select and use appropriate units and tools to make measurements in both systems.

Apply estimation of measurement to real world and content problems using standard measuring devices.

Understand the need for different units of measure within the same system.

Convert units of measurement within and between systems to solve problems.

Recognize and explain the differences between measures of length, area, circumference, surface area, and volume (capacity) in both systems.

Given formulas, find the perimeter, circumference, or area of triangles, circles, and quadrilaterals and other polygons.

Solve problems involving surface area and volume (capacity) of a variety of polyhedrons.

Compare the relationship of perimeter and area of a plane figure to the relationship of area and volume of a solid figure.

Use appropriate vocabulary and notations.

2.2 Apply concepts of rates, ratios, and proportions.

Use and explain rates and their relationships to ratios.

Reduce rates to unit rates.

Set up and solve simple proportions.

Use proportions to make indirect measurements with the help of a diagram.

Solve a variety of problems using proportional reasoning such as map scales, enlargements and reductions, and similar figures.

2.3 Apply dimensional analysis.

Understand units and their relationship to one another and to real world applications.

Properly identify and set up conversion problems involving single and multiple units and single and multiple conversions.

3.1 Use algebraic symbolism as a tool to represent mathematical relationships.

Understand and use variables in expressions, equations, and inequalities.

Interpret expressions, equations and polynomials using  

models and manipulatives.

Apply absolute value concepts in expressions and problem

solving.

Translate word statements and story problems into algebraic

expressions and equations.

Use appropriate symbols and notations.

3.2 Evaluate algebraic expressions.

Understand and use the following properties in evaluating algebraic expressions: multiplicative property of 1 & 0, associative, commutative, identity, substitution, inverse and distributive properties.

Understand and use the order of operations in evaluating basic algebraic expressions.

Simplify algebraic expressions.

Recognize and simplify like terms.

Multiply and divide exponential numbers with the same

base and whole number exponents.

Add, subtract, multiply, and divide monomials, binomials, and trinomials.

 Represent inequalities in various ways.

3.3 Solve algebraic equations and inequalities.

Solve one and two step equations and inequalities using inverse operations.

Solve word problems with equations and inequalities.

Write and solve equations and story problems with one variable and multiple operations.

Solve for the value of a variable in a two variable equation.

Use graphical representation to show linear equations.

Find the slope of a line.

Solve and graph linear equations using x/y intercepts or slope and y-intercept.

Use graphing to find the solution to two equations.

3.4 Understand the concept of functions.

Extend patterns involving rational numbers and describe the rule that generates the patterns.

Explain how a change in one quantity impacts a change in another quantity.

Use appropriate vocabulary and notations.

3.5 Represent equations, inequalities and 

      functions in a variety of ways.

Represent a set of data in a function table, as a graph, and as linear and nonlinear relationships.

3.6 Apply functions to a variety of problems.

Use patterns and linear functions to represent and solve problems.

4.1 Apply concepts of size, shape, and spatial relationships.

Describe and classify relationships among types of one-, two-, and three-dimensional geometric figures using their defining properties.

Draw and measure various angles and shapes using appropriate tools.

Understand and apply fundamental concepts, properties and relationships among points, lines, planes, angles (including complementary & supplementary) and shapes.

Recognize the specific circle terminology: chord, arc,   semicircle, and hemisphere.

Recognize transversals to parallel lines and the angles they create.

Know the definitions of perpendicular, parallel, and intersections.

Identify congruent triangles according to corresponding

parts (SSS,SAS,ASA).

Apply formulas for perimeter, circumference and area to polygons and circles.

 Apply formulas to measure volume & surface area.

Understand and apply the concept of surface area and volume (capacity).

Use appropriate vocabulary and notations.

Explain and model the effects reflections, translations, and rotations on various shapes.

Identify congruence, similarities, and line symmetry of shapes.

4.2 Apply the geometry of right triangles.

Investigate right triangle geometry using the Pythagorean Theorem and 30-60 & 45-45 right triangles.

Use triangle sum, property to calculate the value of a missing angle. (definition of hypotenuse)

4.3 Apply graphing in two dimensions.

Represent geometric figures on a coordinate grid.

Create, graph, and analyze ordered pairs.

5.1 Understand data analysis.

 Analyze and interpret tables, charts, and graphs, including; frequency tables, scatter plots, line plots, histograms, stem-and-leaf plots, box and whisker plots, broken and continuous line graphs, bar graphs (horizontal and vertical), venn diagrams, and circle graphs.

Explain conclusions drawn from tables, charts, and graphs.

Use appropriate vocabulary and notations.

5.2 Collect, organize, and display data.

Collect, organize, and display the data in tables, charts, and graphs, including; frequency tables, scatter plots, line plots, histograms, stem-and-leaf plots, box and whisker plots, broken and continuous line graphs, bar graphs (horizontal and vertical), venn diagrams, and circle graphs.

Use collected data to solve problems.

5.3 Apply simple statistical measurements.

Choose and calculate the appropriate measure of central tendency – mean, median, and mode

Solve practical problems involving the mean of a set of numbers.

Understand and discuss the significance of range, frequency, and informal distribution.

5.4 Understand basic concepts of probability.

Predict, perform, and record results of simple probability experiments.

Recognize equally likely outcomes.

Understand and discuss the difference between theoretical and experimental probability.

Explain that probability ranges from impossible to certain (0% to 100%)

Use a tree diagram to determine the number of possible outcomes of an event.

Recognize and know the difference between dependent and  independent events.

Find the probability of a dependent and independent event.

Define odds and understand the difference between odds and probability of a simple event.

Evaluate expressions with factorials.

Solve problems using permutations and combinations.

Use the language of probability.

5.5 Make predictions or decisions based on data.

Make predictions based on experimental and theoretical probabilities.

Predict and interpret results of statistical experiments using tables, charts, or graphs.

Use the language of probability.