What does a student learn in StateTennessee,GradeGrade 10,SubjectMathematics?

Reason quantitatively and use units to understand problems.

Use units as a way to understand real-world problems.

Choose and interpret the scale and the origin in graphs and data displays,

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Reason quantitatively and use units to solve problems.

Use units as a way to understand real world problems.

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Extend the properties of exponents to rational exponents.

Extend the properties of integer exponents to rational exponents.

Develop the meaning of rational exponents by applying the properties of integer exponents.

Explain why x^1/n can be written as the n^th root of x.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Reason quantitatively and use units to understand problems.

Use units as a way to understand real-world problems.

Choose and interpret the scale and the origin in graphs and data displays.

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Perform operations on matrices and use matrices in applications.

Use matrices to represent data in a real-world context. Interpret rows, columns, and dimensions of matrices in terms of the context.

Perform operations on matrices in a real-world context.

Multiply a matrix by a scalar to produce a new matrix.

Add and/or subtract matrices by hand and using technology.

Multiply matrices of appropriate dimensions, by hand in simple cases and using technology for more complicated cases.

Describe the roles that zero matrices and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real number system.

Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.

Reason quantitatively and use units to understand problems.

Use units as a way to understand real-world problems.

Choose and interpret the scale and the origin in graphs and data displays.

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Perform operations on matrices and use matrices in applications.

Use matrices to represent data in a real-world context. Interpret rows, columns, and dimensions of matrices in terms of the context.

Perform operations on matrices in a real-world context.

Multiply a matrix by a scalar to produce a new matrix.

Add and/or subtract matrices by hand and using technology.

Multiply matrices of appropriate dimensions, by hand in simple cases and using technology for more complicated cases.

Describe the roles that zero matrices and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real number system.

Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.

Extend the properties of exponents to rational exponents.

Extend the properties of integer exponents to rational exponents.

Develop the meaning of rational exponents by applying the properties of integer exponents.

Explain why x^1/n can be written as the n^th root of x.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Reason quantitatively and use units to understand problems.

Use units as a way to understand real-world problems.

Choose and interpret the scale and the origin in graphs and data displays.

Use appropriate quantities in formulas, converting units as necessary.

Define and justify appropriate quantities within a context for the purpose of modeling.

Choose an appropriate level of accuracy when reporting quantities.

Use financial mathematics to make personal financial decisions.

Define common terms associated with finance (such as interest, compound interest, annuities, retirement funds, amortizations, future value, and present value) and know how each term is related to personal finance.

Calculate compound interest within the context of personal finance (such as credit card debt, home/car purchase, personal loans, and amortization schedules) and use the results to make decisions (for example, determine which home financing option is best).

Calculate net pay using gross pay (weekly, biweekly, monthly, or annual) and both fixed and variable deductions (such as withholding tax, Social Security tax, insurance costs, retirement investments and other contributory benefits).

Access and use published data (such as cost of city or state utilities, housing, city or state taxes, meals, and other costs of living) to estimate and compare monthly living expenses based on location, identified needs, and personal preferences or desired lifestyles.

Access and use published data (such as average life expectancy based on location and/or health issues, investment data, retirement funds, and annuity data) to calculate and compare retirement investments (such as total savings and monthly payouts) based on projected income.

Access and use published data to create depreciation schedules and analyze the depreciation of various assets (such as cars, business equipment, and store fixtures).

Access and use published data to calculate income tax based on projected gross annual income, returns on investments, tax deductions and tax credits, and other factors that affect calculations.

Develop a personal mid-term (three to five years) financial plan based on anticipated income, projected living expenses, projected retirement or other savings, and other factors that affect personal finances.

Use financial mathematics to make business decisions.

Compare the components of a small business plan to the components of a personal financial plan (i.e., identify components that are common to both plans and components that are unique to a small business plan).

Define common terms associated with business finance (such as assets, liabilities, revenue, expenses, net profit, net loss, profit margin, and return on investment) and know how each term is related to business finance.

Access and use published data to develop a three-year financial plan for starting and running a small business (including projected income and projected fixed and variable costs such as licenses, rent and utilities, city and state taxes, cost of goods sold, etc.).

Represent, interpret, compare, and simplify number expressions.

Use the laws of exponents and logarithms to expand or collect terms in expressions; simplify expressions or modify them in order to analyze them or compare them.

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Classify real numbers and order real numbers that include transcendental expressions, including roots and fractions of π and e.

Simplify complex radical and rational expressions; discuss and display understanding that rational numbers are dense in the real numbers and the integers are not.

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Perform complex number arithmetic and understand the representation on the complex plane.

Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Perform arithmetic operations with complex numbers expressing answers in the form a + bi.

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation (for example, (–1 + 3i)³ = 8 because (–1 + 3i) has modulus 2 and argument 120°).

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Use complex numbers in polynomial identities and equations.

Extend polynomial identities to the complex numbers (for example, rewrite x² + 4 as (x + 2i)(x – 2i).

Solve quadratic equations with real coefficients that have complex solutions.

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Represent and model with vector quantities.

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, <img src="http://purl.org/ASN/resources/images/D21321918/TN_Math_2023_PN-VM-A-1.gif"/>.

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Solve problems involving velocity and other quantities that can be represented by vectors.

Understand the graphic representation of vectors and vector arithmetic.

Add and subtract vectors.

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

Multiply a vector by a scalar.

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise (e.g., as c(v_x, v_y) = (cv_x, cv_y).

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Calculate and interpret the dot product of two vectors.

Perform operations on matrices and use matrices in applications.

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Interpret the structure of expressions.

Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Perform arithmetic operations on polynomials.

Add, subtract, and multiply polynomials. Use these operations to demonstrate that polynomials form a closed system that adhere to the same properties of operations as the integers.

Create equations that describe numbers or relationships.

Create equations and inequalities in one variable and use them to solve problems in a real-world context.

Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.

Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

Solve equations and inequalities in one variable.

Solve linear and absolute value equations and inequalities in one variable.

Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically.

Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically.

Solve quadratic equations and inequalities in one variable.

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has solutions that are not real numbers.

Solve quadratic inequalities using the graph of the related quadratic equation.

Solve systems of equations.

Write and solve a system of linear equations in real-world context.

Represent and solve equations and inequalities graphically.

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Find approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Interpret the structure of expressions.

Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Understand the relationship between zeros and factors of polynomials.

Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Create equations that describe numbers or relationships.

Create equations and inequalities in one variable and use them to solve problems in a real-world context.

Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations and inequalities with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

Solve radical equations in one variable, and identify extraneous solutions when they exist.

Solve systems of equations.

Write and solve a system of linear equations in a real-world context.

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically, graphically, and using technology.

Interpret the structure of expressions.

Interpret expressions that represent

quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Create equations that describe numbers or relationships

Create equations and inequalities in one variable and use them to solve problems in a real-world context.

Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.

Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

Solve equations and inequalities in one variable.

Solve linear and absolute value equations and inequalities in one variable.

Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically.

Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically.

Solve systems of equations.

Write and solve a system of linear equations in a real-world context.

Represent and solve equations and inequalities graphically.

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Find approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.

Interpret the structure of expressions.

Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Perform arithmetic operations on polynomials.

Add, subtract, and multiply polynomials. Use these operations to demonstrate that polynomials form a closed system that adhere to the same properties of operations as the integers.

Understand the relationship between zeros and factors of polynomials.

Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).

Create equations that describe numbers or relationships.

Create equations and inequalities in one variable and use them to solve problems in a real-world context.

Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

Solve equations and inequalities in one variable.

Solve quadratic equations and inequalities in one variable.

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has nonreal solutions.

Solve quadratic inequalities using the graph of the related quadratic equation.

Solve radical equations in one variable and identify extraneous solutions when they exist.

Solve systems of equations.

Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically, graphically, and using technology.

Represent and solve equations and inequalities graphically.

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Find approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

Use linear programming techniques to solve real-world problems.

Read, interpret, and solve linear programming problems graphically and by computational methods.

Solve real-world optimization problems.

Use linear programming to solve optimization problems (for example, optimizing profit for a small business).

Interpret the meaning of the maximum or minimum value in terms of the objective function.

Understand and use sequences and series.

Demonstrate an understanding of sequences by representing them recursively and explicitly.

Use sigma notation to represent a series; expand and collect expressions in both finite and infinite settings.

Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist.

Determine whether a given arithmetic or geometric series converges or diverges.

Find the sum of a given geometric series (both infinite and finite).

Find the sum of a finite arithmetic series.

Understand that series represent the approximation of a number when truncated; estimate truncation error in specific examples.

Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal's Triangle.

Solve systems of equations and nonlinear inequalities.

Represent a system of linear equations as a single matrix equation in a vector variable.

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solve rational and radical equations in one variable, and identify extraneous solutions when they exist.

Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, logarithmic, and rational) by graphing (solutions in interval notation if one-variable), by hand and with appropriate technology.

Solve systems of nonlinear inequalities by graphing.

Describe and use parametric equations.

Graph curves parametrically (by hand and with appropriate technology).

Eliminate parameters by rewriting parametric equations as a single equation.

Understand the properties of conic sections and model real-world phenomena.

Display all of the conic sections as portions of a cone.

Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics.

Transform equations of conic sections to convert between general and standard form.