**Number Sense**

*Comparing and ordering real numbers (whole numbers, negative numbers, decimals, fractions)

*Estimating location of irrational numbers (like the square root of 7)

*Classifying numbers as natural/whole/integers/rational/irrational

*Absolute value

*Factors and multiples

*Divisibility and remainders (including problems on unit prices)

*Prime and composite numbers

*Describing the effect of multiplying a given number by other numbers (like a number between zero and one, a number less than zero, etc)

*Standard and scientific notation

*Order of operations

*Estimation

*Percent increase and decrease

*Simple interest

**Data Analysis, Probability, Discrete Math**

*Vertex-edge or directed graphs

*Creating and using displays of data (especially box and whisker and scatterplots, but really any type of graph or table)

*Summary statistics (mean, median, mode, range)

*Identifying biased information and evaluating effective representations of data

*Evaluating the design of an experiment

*Probability – theoretical and experimental, dependent and independent

*Counting problems, permutations and combinations

*Factorial

**Patterns, Algebra, and Functions**

*Rate Problems

*Numerical and geometric sequences in tables/graphs/words/symbols

*Identifying functions

*Identifying linearity

*Writing rules for simple functions

*x- and y- intercepts

*Slope

*Writing equations/expressions/inequalities for word problems

*Evaluating expressions with variables by substituting rational numbers for the variables

*Moving between equations/graphs/tables/words to represent linear relationships

*Graphing inequalities on number lines

*Sketch and/or interpret graphs modeling various situations

**Geometry and Measurement**

* Identify attributes of circles (radius, diameter, chord, tangent, secant, various angle and arc relationships, circumference, area

*Combining/subdividing/changing shapes of plane figures and solids

*Using proportional reasoning to determine congruence and similarity

*Pythagorean Theorem

*Rotations

*Reflections

*Translations

*Tesselations

*Rotational and reflectional symmetry

*Midpoint

*conversions between units of measurement

*Ratios and proportions in geometry (think scale factors, etc)

*Surface area and volume

**Structure and Logic**

*Analyze a problem to determine the question to be answered

*Analyze, compare and select most efficient mathematical strategies

*Identify relevant, missing, extraneous information

*Use multiple representations to solve problems

*Describe process used to solve problem

*Verify reasonableness of a solution

*Apply previously used strategy in new context

*Use appropriate representations and mathematical vocabulary to present answer

*Isolate and organize mathematical information taken from symbols, diagrams and graphs

*Describe when to use proportional reasoning

*Make and test conjectures based on information collected from experiments

*Solve logic problems involving multiple variables, conditional statements, conjectures, and negation using words, charts and pictures

*Identify simple valid arguments with if… then statements

*Make, validate and justify conclusions and generalizations about linear relationships

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