Numbers and Operations on Numbers
1. Use properties of operations with real numbers, including rational and irrational numbers (e.g., identify rational and irrational numbers, locate these numbers between two points on a number line, find the product and sum of rational and irrational numbers, and determine if the product or sum is rational or irrational).
2. Rewrite expressions involving radicals and rational exponents using the properties of exponents (e.g., find an equivalent expression to the cube root of 27x^5y^6). 13
3. Solve problems involving numbers written in scientific notation (e.g., add, subtract, multiply, and divide numbers in scientific notation form).
4. Reason quantitatively and use units to solve problems.
5. Choose a level of accuracy appropriate to limitations on measurement.
6. Solve multistep real-world and mathematical problems involving rational numbers and irrational numbers including proportional relationships (settings may include money, rate, percentage, average, estimation/rounding).
Measurement/Geometry
1. Understand transformations in the plane, including reflections, translations, rotations, and dilations. Describe a sequence of transformations to demonstrate that one two-dimensional figure is either congruent or similar to a second two-dimensional figure.
2. Use properties of two-dimensional figures, including formulas for area and perimeter and angle relationships. Develop a logical argument to show that such properties are valid.
3. Understand and apply the Pythagorean Theorem (e.g., find the distance between two points on a coordinate grid; find the third side of a right triangle given the lengths of two of the sides).
4. Demonstrate that two triangles are similar or congruent from criteria that is given. Use the fact that two triangles are congruent or similar to determine the values of unknown quantities. Solve realworld problems involving congruent and similar triangles.
5. Use volume formulas and problem-solving techniques to solve for the volume or surface area of 3-dimensional figures (e.g. cylinders, pyramids, cones, and spheres).
6. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
7. Solve problems involving supplementary, complementary, vertical, and adjacent angles (e.g., given two supplementary angles with measures of 7 x and 2 x, find the measure of one angle in degrees).
8. Know precise definitions of geometric terms (e.g., given three noncollinear points on a plane, determine which describes all the points between these points, including the points).
Data Analysis/Probability/Statistics
1. Use equations, graphs (dot plots, histograms, and box plots), and tables to understand, represent, and interpret data. For data displays, interpret shape, center, spread, and effects of outliers. Summarize data for two categories in two-way frequency tables to solve problems, including those of bivariate data, spread, and relative frequencies.
2. Identify line of best fit from a scatter plot. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
3. Use tables, lists, tree-diagrams and simulations to find the probabilities of compound events.
4. Approximate the probability of a chance event. Develop a probability model, and use it to find probabilities of events (e.g., using the results of an experiment, determine the probability of an event from those results).
5. Use measures of center (mean) to draw inferences about populations including summarizing numerical data sets and calculation of measures of center (e.g., compare the means of two data sets; determine the mean given a set of data).
6. Understand how to use statistics to gain information about a population, generalizing information about a population from a sample of the population (e.g., determine which method to use from a list of methods to select a random sample; using the outcome from a random sample, predict the outcome of the population).
Algebraic Concepts
1. Interpret parts of an expression, such as terms, factors, and coefficients in terms of its context.
2. Perform arithmetic operations on polynomials and rational expressions.
3. Write expressions in equivalent forms to solve problems, including factoring a quadratic expression to reveal the zeros of the function it defines, completing the square to determine the minimum or maximum value of a function, or transforming exponential equations.
4. Solve mathematical and real-world problems involving linear equations and inequalities, including equations with coefficients represented by letters.
5. Solve quadratic equations in one variable that have real or complex roots by taking square roots, completing the square, or using the quadratic formula. Derive the quadratic formula by completing the square.
6. Solve simple rational and radical equations in one variable.
7. Solve systems of two linear equations algebraically and graphically. Know when a system has 0, 1, or an infinite number of solutions.
8. Graph linear, quadratic, square root, cube root, piecewise, absolute value, polynomial, rational, logarithmic, and exponential functions. Identify any intercepts, minima, maxima, asymptotes, and end behavior.
9. Create equations and inequalities in one or more variables to represent relationships and use them to solve problems mathematically and in the real world.
10. Rearrange formulas/equations to highlight a quantity of interest.
11. Understand the concept of a function and use function notation; interpret key features of graphs and tables in terms of quantities. Evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Write a function that describes a relationship between two quantities (e.g., identify the graph of the function that shows y as a function of x). For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
12. Understand domain and range of a function (e.g., given a function in a real-world setting, determine which sets of numbers represent the domain of this function).
13. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
14. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate rate of change from a graph (e.g., estimate the rate of change from a graph of a function for a specified interval).