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- A. Mathematical process standards
- A.1. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- A.1A. Apply mathematics to problems arising in everyday life, society, and the workplace.
- Coordinates with Chess board
- Percent more and Percent Less
- Word problems on Discount
- Calculating Compound Interest
- When will you become a Millionaire?
- Interpret Pie Charts
- Model using a balance
- Find using proportions
- Unitary Method - Word Problems
- Comparison of Ratios
- A game for teaching integers
- Find the length of the shape
- Identify the shape
- Combination of Multiplication & Division
- Word Problems
- Let us calculate Simple Interest
- A.1B. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
- A.1C. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
- Divisibility Test for the number 2
- Divisibility Test for the number 4
- Divisibility Test for the number 5
- Divisibility Test for the number 10
- Divisibility Test for the number 8
- Divisibility Test for the number 3
- Divisibility Test for the number 6
- Divisibility Test for the number 9
- Divisibility Test for the number 11
- Estimate using ball
- Identify the missing number
- Arrange the integers in order
- Estimate the position of the balloon
- Place the given integers on the numberline
- Recognizing Patterns
- Identify Patterns and find the n^{th} term of a pattern
- Building blocks
- Estimation of square roots
- Identify Percentage
- Estimate the Percentage
- A.1D. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
- A game for teaching integers
- Integer addition with counters
- Integer subtraction using counters
- Integer Number Line
- Explore Addition
- Relate Ratios and Fractions
- Represent in a number line and compare
- Additive Inverse
- Coordinates with Chess board
- Find the missing puzzle pieces
- Represent a polynomial
- Represent a Cubic Polynomial
- A.1E. Create and use representations to organize, record, and communicate mathematical ideas.
- Explore Addition
- Addition chips
- Addition using a number line
- Subtraction chips
- Subtraction using a number line
- Integer Number Line
- Integer addition with counters
- Integer subtraction using counters
- Commutative Property of Addition (number line)
- Commutative Property of Subtraction (number line)
- Multiplication using flip over method
- Multiplication using array model
- Division using flip over method
- Represent on a grid
- Represent and Find Percentage
- Multiplication of Rational Numbers using area model
- A.1F. Analyze mathematical relationships to connect and communicate mathematical ideas.
- Absolute Value of a Rational Number
- Additive Inverse
- Square root of decimals
- Square root of fractions
- Cube roots of rational numbers
- Cube roots of decimals
- Skill Practice using laws of exponents
- Find the general term of an AP
- Relation between sum of 'n' natural numbers and area of rectangle
- Sum of 'n' natural numbers
- Sum of first 'n' odd numbers
- Sum of 'n' terms in an AP
- A.1G. Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- Commutative Property of Addition
- Associative property of addition
- Additive Inverse
- Associative property of subtraction
- Commutative Property of multiplication
- Associative property of multiplication
- Distributive Property of Multiplication
- Commutative Property of division
- Associative property of division
- A.1A. Apply mathematics to problems arising in everyday life, society, and the workplace.
- A.1. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- A. Linear functions, equations, and inequalities
- A.2. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
- A.2A. Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities.
- A.2B. Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points.
- A.2C. Write linear equations in two variables given a table of values, a graph, and a verbal description.
- A.2D. Write and solve equations involving direct variation.
- A.2E. Write the equation of a line that contains a given point and is parallel to a given line.
- A.2F. Write the equation of a line that contains a given point and is perpendicular to a given line.
- A.2G. Write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined.
- A.2H. Write linear inequalities in two variables given a table of values, a graph, and a verbal description.
- A.2I. Write systems of two linear equations given a table of values, a graph, and a verbal description.
- A.2A. Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities.
- A.3. The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.
- A.3A. Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1).
- A.3B. Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems.
- A.3C. Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems.
- A.3D. Graph the solution set of linear inequalities in two variables on the coordinate plane.
- A.3E. Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
- A.3F. Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
- A.3G. Estimate graphically the solutions to systems of two linear equations with two variables in real-world problems.
- A.3H. Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
- A.4. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.
- A.4A. Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
- A.4B. Compare and contrast association and causation in real-world problems.
- A.4C. Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
- A.4A. Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.
- A.5. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.
- A.5A. Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
- A.5B. Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.
- A.5C. Solve systems of two linear equations with two variables for mathematical and real-world problems.
- A.2. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
- A. Quadratic functions and equations
- A.6. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.
- A.6A. Determine the domain and range of quadratic functions and represent the domain and range using inequalities.
- A.6B. Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)² + k), and rewrite the equation from vertex form to standard form (f(x) = ax² + bx + c).
- A.6C. Write quadratic functions when given real solutions and graphs of their related equations.
- A.6A. Determine the domain and range of quadratic functions and represent the domain and range using inequalities.
- A.7. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
- A.7A. Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
- A.7B. Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
- Understanding Discriminant
- Finding the roots with Quadratic Formula
- Identify the quadratic equation from the graph
- Standard and Vertex forms of Quadratics
- Represent a Quadratic Polynomial and Find factors
- Zeroes of a Quadratic Polynomial
- Identify the factorized form
- Identify the zeroes and the factorized form
- Factorization of Quadratic Equations
- A.7C. Determine the effects on the graph of the parent function f(x) = x² when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
- A.8. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
- A.8A. Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
- Factorization by Completing the Square
- Understanding Discriminant
- Finding the roots with Quadratic Formula
- Word problems
- Factorizing Quadratic Equation
- Represent a Quadratic Polynomial and Find factors
- Zeroes of a Quadratic Polynomial
- Identify the factorized form
- Identify the zeroes and the factorized form
- Factorization of Quadratic Equations
- A.8B. Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
- A.8A. Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
- A.6. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.
- A. Exponential functions and equations
- A.9. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
- A.9A. Determine the domain and range of exponential functions of the form f(x) = ab^x and represent the domain and range using inequalities.
- A.9B. Interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^x in real-world problems.
- A.9C. Write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay.
- A.9D. Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.
- A.9E. Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.
- A.9A. Determine the domain and range of exponential functions of the form f(x) = ab^x and represent the domain and range using inequalities.
- A.9. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
- A. Number and algebraic methods
- A.10. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.
- A.10A. Add and subtract polynomials of degree one and degree two.
- A.10B. Multiply polynomials of degree one and degree two.
- A.10C. Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend.
- A.10D. Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
- A.10E. Factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two.
- A.10F. Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.
- A.11. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.
- A.11A. Simplify numerical radical expressions involving square roots.
- A.11B. Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
- Simplify radical expression
- Simplify using distributive property
- Simplify the identities
- Laws of exponents
- Law of Exponents 1: Multiply powers with same base
- Law of Exponents 2: Power of a Power
- Law of exponents 3: (a/b)^{10} = a^{10}/b^{10}
- Law of Exponents 4: Divide Powers with same base
- Skill Practice using laws of exponents
- A.12. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.
- A.12A. Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function.
- A.12B. Evaluate functions, expressed in function notation, given one or more elements in their domains.
- A.12C. Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes.
- Introduction to Arithmetic Progression
- Arithmetic Progression - Combat zone
- Arithmetic Progression in day to day life
- Find the general term of an AP
- Arithmetic Series
- Relation between sum of 'n' natural numbers and area of rectangle
- Sum of 'n' natural numbers
- Sum of first 'n' odd numbers
- Sum of 'n' terms in an AP
- Arithmetic Progression using polygons
- A.12D. Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms.
- A.12E. Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
- A.12A. Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function.
- A.10. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.