Skills Checklist

ASE MA 1: Algebraic Concepts and Expressions – Student Checklist

MA.1.1 Number and Quantity: The Real Number System and Quantities.

Learning Targets

Mastery Level %

Date

I can, using the properties of exponents, rewrite a radical expression as an expression with a rational exponent.

I can, using the properties of exponents, rewrite an expression with rational exponent as a radical expression.

I can calculate unit conversions.

I can recognize units given or need to solve problems.

I can use given units and the context of a problem as a way to determine if the solution to a multi-step problem is reasonable (e.g. length problems dictate different units than problems dealing with a measure such as slope).

I can choose appropriate units to represent a problem when using formulas or graphing.

I can interpret units or scales used in formulas or represented in graphs.

I can use units as a way to understand problems and to guide the solution of multi-step problems.

I can identify appropriate units of measurement to report quantities.

I can determine the limitations of different measurement tools.

I can choose and justify a level of accuracy and/or precision appropriate to limitations on measurement when reporting quantities.

I can identify important quantities in a problem or real-world context.

MA.1.2 Algebra: Seeing Structure in Expressions

Learning Targets

Mastery Level %

Date

I can, for expressions that represent a contextual quantity, define and recognize parts of an expression, such as terms, factors, and coefficients.

I can, for expressions that represent a contextual quantity, interpret parts of an expression, such as terms, factors, and coefficients in terms of the context.

I can identify ways to rewrite expressions, such as difference of squares, factoring out a common monomial, regrouping, etc.

I can identify ways to rewrite expressions based on the structure of the expression.

I can use the structure of an expression to identify ways to rewrite it.

I can classify expression by structure and develop strategies to assist in classification.

I can factor a quadratic expression to produce an equivalent form of the original expression.

I can explain the connection between the factored form of a quadratic expression and the zeros of the function it defines.

I can explain the properties of the quantity represented by the quadratic expression.

I can choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the original expression.

MA.1.3 Algebra: Arithmetic with Polynomials and Rational Expressions

Learning Targets

Mastery Level %

Date

I can identify like terms.

I can use the distributive property.

I can combine linear and quadratic polynomials with addition and subtraction.

I can multiply a constant by a linear or quadratic polynomial.

I can multiply two polynomials using the distributive property.

I can identify that the sum, difference, or product of two polynomials will always be a polynomial, which means that polynomials are closed under the operations of addition, subtraction, and multiplication.

I can define “closure.”

I can apply arithmetic operations of addition, subtraction, and multiplication to polynomials.

I can rewrite rational expressions using inspection or a computer algebra system.

ASE MA 2: Equations and Inequalities – Student Checklist

MA.2.1 Algebra: Creating Equations

Learning Targets

Mastery Level %

Date

I can solve linear and exponential equations in one variable.

I can solve inequalities in one variable.

I can describe the relationships between the quantities in the problem (for example, how the quantities are changing or growing with respect to each other); express these relationships using mathematical operations to create an appropriate equation or inequality to solve.

I can create equations (linear and exponential) and inequalities in one variable and use them to solve problems.

I can create equations and inequalities in one variable to model real-world situations.

I can compare and contrast problems that can be solved by different types of equations (linear and exponential).

I can identify the quantities in a mathematical problem or real-world situation that should be represented by distinct variables and describe what quantities the variables represent.

I can create at least two equations in two or more variables to represent relationships between quantities.

I can justify which quantities in a mathematical problem or real-world situation are dependent and independent of one another and which operations represent those relationships.

I can determine appropriate units for the labels and scale of a graph depicting the relationship between equations created in two or more variables.

I can graph one or more created equation on a coordinate axes with appropriate labels and scales.

I can recognize when a modeling context involves constraints.

I can interpret solutions as viable or nonviable options in a modeling context.

I can determine when a problem should be represented by equations, inequalities, systems of equations and/or inequalities.

I can represent constraints by equations or inequalities, and by systems of equations and/or inequalities.

I can define a “quantity of interest” to mean any number or algebraic quantity (e.g. 2(a/b) = d, in which 2 is the quantity of interest showing that d must be even; πr²h/3 = V_cone and πr²h = V_cylinder showing that V_cylinder = 3* V_cone) .

I can rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g. π * r² can be re-written as (π *r) *r which makes the form of this expression resemble b*h).

MA.2.2 Algebra: Reasoning with Equations and Inequalities

Learning Targets

Mastery Level %

Date

I can demonstrate that solving an equation means that the equation remains balanced during each step.

I can recall the properties of equality.

I can explain why, when solving equations, it is assumed that the original equation is equal.

I can determine if an equation has a solution.

I can choose an appropriate method for solving the equation.

I can justify solution(s) to equations by explaining each step in solving a simple equation using the properties of equality, beginning with the assumption that the original equation is equal.

I can construct a mathematically viable argument justifying a given, or self-generated, solution method.

ASE MA 2: Equations and Inequalities – Student Checklist, Page 2

I can solve radical equations in one variable.

I can solve rational equations in one variable.

I can give examples showing how extraneous solutions may arise when solving rational and radical equations.

I can recall properties of equality.

I can solve multi-step equations in one variable.

I can solve multi-step inequalities in one variable.

I can determine the effect that rational coefficients have on the inequality symbol and use this to find the solution set.

I can solve equations and inequalities with coefficients represented by letters.

I can use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)² = q that has the same solutions.

I can solve quadratic equations in one variable.

I can derive the quadratic formula by completing the square on a quadratic equation in x.

I can solve systems of linear equations by any method.

I can justify the method used to solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables.

I can recognize that the graphical representation of an equation in two variables is a curve, which may be a straight line.

I can explain why each point on a curve is a solution to its equation.

ASE MA 3: Algebraic Functions and Modeling – Student Checklist

MA.3.1 Understand the concept of a function and use function notation and degrees of functions.

Learning Targets

Mastery Level %

Date

I can explain the meaning of domain and range.

I can determine the difference between the domain and range of a function.

I can determine if a relation is a function.

I can recognize when a graph is a function.

I can use an equation and the values in the domain to calculate the values in the range, and then determine if the equation is a function.

I can graph a function on the coordinate plane.

I can evaluate functions using function notation.

I can use values from a context to evaluate a function.

I can solve real-world problems given in function notation.

I can determine the subset of the real numbers over which a function is defined.

I can identify a function’s intercepts and local minimums/maximums.

I can identify intervals where functions are increasing or decreasing.

 I can identify whether or not a graph has symmetries.

I can determine the end behavior of linear, quadratic, and exponential functions.

I can translate a verbal description of a graph’s key features into a graph.

I can give a verbal description of a graph’s key features.

 I can give intervals where the function is increasing and intervals where the function is decreasing.

I can give intervals where the function is positive and/or negative.

I can relate a table of values to its graph.

I can relate coefficients and constants to a function.

I can relate the domain of linear, exponential, and quadratic functions to their graphs.

I can relate coefficients and constants of a function to their real life meaning.

I can identify the domain of linear, exponential, and quadratic functions from their graphs.

I can determine appropriate domains in context.

I can identify reasonable values for the domain in a real-world context.

I can determine if the domain is continuous or discrete.

I can calculate the slope of a line.

I know that slope is a rate of change.

I can calculate the average rate of change for functions using a table over a given interval.

I can calculate the average rate of change for functions algebraically over a given interval.

I can use a graph of a function to estimate the average rate of change over a given interval.

I can properly assign units to the average rate of change in context.

I can explain the meaning of the average rate of change in context.

I can graph linear functions and show intercepts.

ASE MA 3: Algebraic Functions and Modeling – Student Checklist, Page 2

I can graph quadratic functions and show intercepts, maxima, and minima.

I know the properties of exponents.

I can differentiate between exponential growth and exponential decay.

I can identify the percent rate of change in exponential functions.

I can convert the two functions to a common representation or form for comparison.

I can interpret key features (e.g., end behavior, intercepts, maximum and minimum, slope) of functions represented as graphs, tables, or in equation form.

I can compare key features of two functions.

I can compare functions represented in different ways including algebraically, graphically, numerically in tables and by verbal descriptions.

MA.3.2 Build a function that models a relationship between two quantities.

Learning Targets

Mastery Level %

Date

I can combine two functions using the operations of addition, subtraction, multiplication, and division.

I can evaluate the domain of the combined function.

I can build standard functions to represent relevant relationships/quantities given a real-world situation or mathematical process.

I can determine which arithmetic operation should be performed to build the appropriate combined function given a real-world situation or mathematical process.

I can relate the combined function to the context of the problem.

MA.3.3 Construct and compare linear, quadratic, and exponential functions models and solve problems. Interpret expressions for functions in terms of the situation they model.

Learning Targets

Mastery Level %

Date

I can recognize that linear functions grow by equal differences over equal intervals.

I can recognize that exponential functions grow by equal factors over equal intervals.

I can distinguish between situations that can be modeled with linear functions and with exponential functions to solve mathematical and real-world problems.

I can identify, regardless of form, the y-intercept and vertical translation of an exponential function.

I can rewrite the base, b, of an exponential as 1 + r and identify r.

I can identify the slope and y-intercept of a line.

I can explain the meaning of an exponential function’s base, end behavior, and rate of growth in context.

I can explain the meaning of a linear function’s slope and intercepts in context.

I can explain the meaning of the coefficients, factors, exponents, and intercepts in a linear or exponential function.

ASE MA 4: Geometry, Probability, and Statistics – Student Checklist

MA.4.1 Geometry: Understand congruence and similarity.

Learning Targets

Mastery Level %

Date

I can define an angel based on my knowledge of a point, line, distance along a line, and distance around a circular arc.

I can define a circle based on my knowledge of a point, line, distance along a line, and distance around a circular arc.

I can define perpendicular lines based on my knowledge of a pint, line, distance, along a line, and distance around a circular arc.

I can define a line segment based on my knowledge of a pint, line, distance, along a line, and distance around a circular arc.

I can define parallel lines based on my knowledge of a pint, line, distance, along a line, and distance around a circular arc.

I can describe the relationship between similarity and congruence.

I can set up and write equivalent ratios.

I can identify corresponding angles and sides of two triangles.

I can determine a scale factor and use it in a proportion.

I can solve geometric problems using congruence and similarity.

I can prove relationships using congruence and similarity.

MA.4.2 Geometric Measure and Dimension: Explain formulas and use them to solve problems and apply geometric concepts in modeling situations.

Learning Targets

Mastery Level %

Date

I can apply the formula for the perimeter of a rectangle to solve problems.

I can apply the formula for the area of a rectangle to solve problems.

I can apply the formula for the area of a triangle to solve problems.

I can apply the formula for the volume of a cone to solve problems.

I can apply the formula for the volume of a cylinder to solve problems.

I can apply the formula for the volume of a pyramid to solve problems.

I can apply the formula for the volume of a sphere to solve problems.

I can find the surface area of right circular cylinders.

I can find the surface area of rectangular prisms.

I can use geometric shapes, their measures, and their properties to describe objects.

I can apply concepts of density based on area and volume in modeling situations.

MA.4.3 Summarize, represent, and interpret categorical and quantitative data on (a) a single count or measurement variable, (b) two categorical and quantitative variables, and (c) Interpret linear models.

Learning Targets

Mastery Level %

Date

I can classify data as either categorical or quantitative.

I can identify an appropriate scale needed for the data display.

I can identify an appropriate number of intervals for a histogram.

I can identify an appropriate width for intervals in a histogram.

I can select an appropriate data display for real-world data.

ASE MA 4: Geometry, Probability, and Statistics – Student Checklist, Page 2

I can construct dot plots.

I can create a frequency table.

I can construct histograms.

I can construct box plots.

I can identify a data set by its shape and describe the data set as symmetric or skewed.

I can use the outlier rule (e.g., Q1 – 1.5 x IQR and Q3 + 1.5 IQR) to identify outliers in a data set.

I can analyze how adding/removing an outlier affects measures of center and spread.

I can interpret differences in shape, center and spread in the context of data sets.

I can compare and contrast two or more data sets using shape, center, and spread.

I can organize categorical data in two-way frequency tables.

I can interpret joint frequencies and joint relative frequencies in the context of the data.

I can interpret marginal frequencies and marginal relative frequencies in the context of the data.

I can interpret conditional frequencies and conditional relative frequencies in the context of the data.

I can recognize possible associations between categorical variables in a two-way frequency or relative frequency table.

I can determine the y-intercept graphically and algebraically.

I can determine the rate of change by choosing two points.

I can determine the equation of a line using data points.

I can interpret the slope in the context of the data.

I can interpret the y-intercept in the context of the data.

I can differentiate between causation and correlation/association.

I can interpret paired data to determine whether correlation implies causation/association.

MA.4.4 Using probability to make decisions.

Learning Targets

Mastery Level %

Date

I can develop a probability distribution for a random variable defined for a sample space of theoretical probabilities.

I can calculate theoretical probabilities and find expected values.

I can develop a probability distribution for a random variable for a sample space of empirically assigned probabilities.

I can assign probabilities empirically and find expected values.

I can weigh the possible outcomes of a decision and find expected values.

I can assign probabilities to payoff values and find expected values.

I can evaluate strategies based on expected values.

I can compare strategies based on expected values.

I can explain the difference between theoretical and experimental probability.

I can compute theoretical and experimental probability.

I can determine the fairness of a decision based on the available data.

I can determine the fairness of a decision by comparing theoretical and experimental probability.

I can use counting principles to determine the fairness of a decision.

I can analyze decisions and strategies related to product testing, medical testing, and sports.