
College Preparatory Mathematics (CPM) 20182019 Syllabus
Teacher: John S. Coulter
832.264.4017
As required by HB5 which was approved by Texas Legislation in 2013, the purpose of the College Preparatory Mathematics (CPM) course is to provide an opportunity for high school seniors to demonstrate college readiness in mathematics so they are able to begin taking creditbearing courses their first year of college without mandatory enrollment in developmental mathematics courses.
If, by the end of a student’s junior year, s/he has not yet demonstrated college readiness in mathematics via satisfactory performance on the Algebra I STAAR EOC, PSAT, SAT, ACT, TSI, or any other measurement accepted as a formal indicator of college readiness by the Houston Community College, the student will be offered enrollment in the CPM Course. The CPM course may count as a fourthyear mathematics course required for graduation starting the 201516 school year.
The prerequisite for enrollment in the CPM course is Algebra II. In order for a student to be deemed “college ready” by HCC – that is, ready for enrollment into MATH 1314 as a college freshman – the student must pass the HCCprovided final exam for each semester of the CPM course AND earn an overall grade of C or better for each semester of the CPM course.
The curriculum for the CPM course has been developed through a partnership involving Houston ISD mathematics teachers, the HISD Curriculum and Development Department, and the Houston Community College. The content of the course synthesizes concepts from the HCC developmental mathematics courses MATH 0409 and MATH 0312 and includes concepts from College Algebra MATH 1314.
(NOTE: although students may NOT use graphing technology on the final exam provided by HCC, the use of graphing technology as a discovery and analytical tool is highly encouraged.)
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs) The student will:
The Mathematical Process Standards are integrated throughout the course in all activities and lessons. Teachers should refer to these standards for instructional strategies and depth of rigor. Specific process standards have been highlighted for each unit, but these process standards should not be the only process standards associated with the daily lessons.
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Cycle 1
28 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Aug. 27 – Oct. 5, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 1: OneVariable Equations & Inequalities
Students solve and apply linear equations and inequalities in one variable
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to:
Ⓡ ALGI.5A Solve linear equations in one variable, including those for which the application of the distributive property is necessary and includes variables on both sides.
Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10A Add and subtract polynomials of degree one and degree two.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Unit 2: Linear Equations and Inequalities
Students analyze, graph, and write various forms of linear equations and inequalities using multiple representation in mathematical and realworld contexts.
5 class periods (90 minutes each)
or
10 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2A Determine the domain and range of a linear function in mathematical problems, determine reasonable domain and range values for realworld situations, both continuous and discrete and represent domain and range using inequalities.
Ⓢ ALGI.2B Write linear equations in two variables in various forms, including
y = mx + b, Ax + By = C, and y – y_{1} = m(x – x_{1}), given one point and the slope and given two points.Ⓡ ALGI.2C Write linear equations in two variables given a table of values, a graph, and a verbal description.
Ⓢ ALGI.2D Write and solve equations involving direct variation.
Ⓢ ALGI.2E Write the equation of a line that contains a given point and is parallel to a given line.
Ⓢ ALGI.2F Write the equation of a line that contains a given point and is perpendicular to a given line.
Ⓢ ALGI.2G Write an equation of a line that is parallel or perpendicular to the x or yaxis and determine whether the slope of the line is zero or undefined.
Ⓢ ALGI.2H Write linear inequalities in two variables given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓢ ALGI.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 – y_{1} = m(x – x_{1}).
Ⓡ ALGI.3B Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and realworld problems.
Ⓡ ALGI.3C Graph linear functions on the coordinate plane and identify key features including xintercept, yintercept, zeros, and slope in mathematical and realworld problems.
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3E Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Number and Algebraic Methods. The student applies mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Ⓢ ALGI.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 3: Systems of Equations & Inequalities
In realworld situations, students solve and analyze systems of linear equations and inequalities with two variables using graphs, tables, and algebraic methods.
(continued in cycle 2)
4 class periods
(90 minutes each)
or
8 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2I Write systems of two linear equations given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3F Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Ⓢ ALGI.3G Estimate graphically the solutions to systems of two linear equations with two variables in realworld problems.
Ⓢ ALGI.3H Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Cycle 2
25 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Oct. 8 – Nov. 9, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 3: Systems of Equations & Inequalities
In realworld situations, students solve and analyze systems of linear equations and inequalities with two variables using graphs, tables, and algebraic methods.
(continued from cycle 1)
4 class periods
(90 minutes each)
or
8 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2I Write systems of two linear equations given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3F Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Ⓢ ALGI.3G Estimate graphically the solutions to systems of two linear equations with two variables in realworld problems.
Ⓢ ALGI.3H Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Unit 4: Polynomials and Operations
Students evaluate, analyze, perform operations on, and apply properties of polynomials.
3 class
periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10A Add and subtract polynomials of degree one and degree two.
Ⓢ ALGI.10B Multiply polynomials of degree one and degree two.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7B Add, subtract, and multiply polynomials.
Unit 5: Polynomials and Factoring
Students explore various methods of factoring polynomials.
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10B Multiply polynomials of degree one and degree two.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓡ ALGI.11B Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
Unit 6: Quadratic Equations
Students analyze, graph, and solve quadratic functions and inequalities and connect the attributes and solutions to real world situations using multiple representations.
(continued in cycle 3)
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.6A Determine the domain and range of quadratic functions, and represent the domain and range using inequalities.
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.7A Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including xintercept, yintercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
Ⓢ ALGI.7B Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Ⓡ ALGI.7C Determine the effects on the graph of the parent function f(x) = x^{2} when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓡ ALGI.8A Solve quadratic equations, having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Cycle 3
24 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Nov. 12 – Dec. 20, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 6: Quadratic Equations
Students analyze, graph, and solve quadratic functions and inequalities and connect the attributes and solutions to real world situations using multiple representations.
(continued from cycle 2)
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.6A Determine the domain and range of quadratic functions, and represent the domain and range using inequalities.
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.7A Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including xintercept, yintercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
Ⓢ ALGI.7B Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Ⓡ ALGI.7C Determine the effects on the graph of the parent function f(x) = x^{2} when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓡ ALGI.8A Solve quadratic equations, having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 7: Rational Expressions and Equations
Students analyze, perform operations on, and solve equations and application problems involving rational expressions, including rational exponents.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.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.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓢ ALGI.11A Simplify numerical radical expressions involving square roots.
Ⓡ ALGI.11B Simplify numerical and algebraic expressions using the laws of exponents, including integral and rational exponents.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents
Unit 8: Radical Expressions and Equations
Students analyze, perform operations on, and solve equations and application problems involving radical expressions and equations.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓢ ALGI.11A Simplify numerical radical expressions involving square roots.
Ⓡ ALGI.11B Simplify numerical and algebraic expressions using the laws of exponents, including integral and rational exponents.
Cycle 4
29 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Jan. 7 – Feb. 15, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 9: Absolute Value Equations, Inequalities, and Functions
Students solve, analyze, and graph absolute value equations and inequalities.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓡ ALGII.2C Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain and which will restrict its range.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6D Formulate absolute value linear equations.
Ⓡ ALGII.6E Solve absolute value linear equations.
Ⓢ ALGII.6F Solve absolute value linear inequalities.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 10: Factoring Completely
Students use factoring techniques including factoring by grouping, completing the square, sum of two cubes, and difference of two cubes to factor polynomials.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, an the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7C Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two.
Ⓢ ALGII.7D Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.
Ⓡ ALGII.7E Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping.
Ⓡ ALGII.7F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and degree two.
Ⓡ ALGII.7H Solve equations involving rational exponents.
Unit 11: Transformations and Attributes of Quadratic Functions
Students analyze the transformation of a quadratic function in
f(x) = ax^{2}+bx+c and
f(x) = a(x – h)^{2}+k forms through multiple representations.3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.
Ⓢ ALGII.4D Transform a quadratic function f(x) = ax^{2} + bx + c to the form f(x) = a(x – h)^{2} + k to identify the different attributes of f(x).
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Cycle 5
30 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Feb. 18 – Apr. 5, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 12: Quadratic Equations, Inequalities, and Functions
Students write, and solve quadratic equations by factoring, completing the square, and applying the quadratic formula, and apply these methods to solving realworld problems.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, an the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.4A Write the quadratic function given three specified points in the plane.
Ⓡ ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.
Ⓢ ALGII.4F Solve quadratic and square root equations.
Ⓢ ALGII.4H Solve quadratic inequalities.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 13: Systems of Quadratic Equations and Linear Equations Inequalities
Students analyze a system of equations in two variables consisting of a linear equation and a quadratic equation.
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3C Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation.
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Unit 14: Operations with Complex Numbers
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.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.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical idea.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7A Add, subtract, and multiply complex numbers.
Ⓢ ALGII.7B Add, subtract, and multiply polynomials.
Ⓢ ALGII.7D Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.
Ⓡ ALGII.7E Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping.
Cycle 6
38 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Apr. 8 – May 31, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 15:
Root Functions
Students analyze, perform operations on, and solve equations and application problems involving radical expressions.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
ALGII.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.
ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, , f(x)=x^{3}, f(x)=b^{x}, , and f(x) = log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓢ ALGII.2B Graph and write the inverse of a function using notation such as
f ^{1}(x).Ⓡ ALGII.2C Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain and which will restrict its range.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4C Determine the effect on the graph of when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x  c) for specific positive and negative values of a, b, c, and d.
Ⓢ ALGII.4E Formulate quadratic and square root equations using technology given a table of data.
Ⓡ ALGII.4F Solve quadratic and square root equations.
Ⓢ ALGII.4G Identify extraneous solutions of square root equations.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions.
Ⓢ ALGII.6B Solve cube root equations that have real roots.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents
Unit 16: Rational Equations and Functions
Students analyze rational equations and functions through graphs, tables, and algebraic methods.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, , f(x)=x^{3}, f(x)=b^{x}, , and f(x) = log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓢ ALGII.2B Graph and write the inverse of a function using notation such as
f^{1}(x).Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6H Formulate rational equations that model realworld situations.
Ⓡ ALGII.6I Solve rational equations that have real solutions.
Ⓢ ALGII.6J Determine the reasonableness of a solution to a rational equation.
Ⓢ ALGII.6K Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation.
Ⓡ ALGII.6L Formulate and solve equations involving inverse variation.
Unit 17: Exponential and Logarithmic Functions
Students graph, analyze, and solve exponential and logarithmic functions and equations.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Exponential Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.9A Determine the domain and range of exponential functions of the form f(x) = ab^{x} and represent the domain and range using inequalities.
Ⓢ ALGI.9B Interpret the meaning of the values of a and b in exponential functions of the form f(x) = a·b^{x} in realworld problems.
Ⓡ ALGI.9C Write exponential functions in the form f(x) = a·b^{x} (where b is a rational number) to describe problems arising from mathematical and realworld situations including growth and decay.
Ⓡ ALGI.9D Graph exponential functions that model growth and decay and identify key features, including yintercept and asymptote, in mathematical and realworld problems.
Exponential and Logarithmic Functions and Equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:
Ⓡ ALGII.5A Determine the effects on the key attributes on the graphs of
f(x) = b^{x} and f(x) = log_{b}(x), where b is 2, 10 and e when f(x) is replaced by a f(x), f(x) + d, and f(x  c) for specific positive and negative real values of a, c, and d.Ⓢ ALGII.5B Formulate exponential and logarithmic equations that model realworld situations including exponential relationships written in recursive notation.
Ⓡ ALGII.5D Solve exponential equations of the form y = a∙b^{x }where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 18: Data Analysis, Statistics, and Probability
Students analyze data, statistical models, and probability situations and evaluate models of regressions in realworld contexts.
3 class periods
(90 minutes each)
or
6 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on realworld data. The student is expected to:
Ⓢ ALGI.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.
Ⓢ ALGI.4B Compare and contrast association and causation in realworld problems.
Ⓢ ALGI.4C Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for realworld problems.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.8B Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for realworld problems.
Exponential Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.9E Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for realworld problems.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4C Determine the effect on the graph of when f(x) is replaced by a f(x), f(x) + d, f(bx), and f(x  c) for specific positive and negative values of a, b, c, and d.
Ⓢ ALGII.4E Formulate quadratic and square root equations using technology given a table of data.
Exponential and Logarithmic Functions and Equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:
Ⓡ ALGII.5A Determine the effects on the key attributes on the graphs of
f(x) = b^{x} and f(x) = log_{b}(x), where b is 2, 10 and e when f(x) is replaced bya f(x), f(x) + d, and f(x  c) for specific positive and negative real values of a, c, and d.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6A Analyze the effect on the graphs of f(x) = x^{3} and when f(x) is replaced by a· f(x), f(bx), f(x  c), and f(x) + d for specific positive and negative real values of a, b, c, and d.
Ⓢ ALGII.6G Analyze the effect on the graphs of when f(x) is replaced by a· f(x), f(bx), f(x  c), and f(x) + d for specific positive and negative real values of a, b, c, and d.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Data. The student applies mathematical processes to analyze data, select appro
College Preparatory Mathematics (CPM) 20182019 Syllabus
Teacher: John S. Coulter
832.264.4017
As required by HB5 which was approved by Texas Legislation in 2013, the purpose of the College Preparatory Mathematics (CPM) course is to provide an opportunity for high school seniors to demonstrate college readiness in mathematics so they are able to begin taking creditbearing courses their first year of college without mandatory enrollment in developmental mathematics courses.
If, by the end of a student’s junior year, s/he has not yet demonstrated college readiness in mathematics via satisfactory performance on the Algebra I STAAR EOC, PSAT, SAT, ACT, TSI, or any other measurement accepted as a formal indicator of college readiness by the Houston Community College, the student will be offered enrollment in the CPM Course. The CPM course may count as a fourthyear mathematics course required for graduation starting the 201516 school year.
The prerequisite for enrollment in the CPM course is Algebra II. In order for a student to be deemed “college ready” by HCC – that is, ready for enrollment into MATH 1314 as a college freshman – the student must pass the HCCprovided final exam for each semester of the CPM course AND earn an overall grade of C or better for each semester of the CPM course.
The curriculum for the CPM course has been developed through a partnership involving Houston ISD mathematics teachers, the HISD Curriculum and Development Department, and the Houston Community College. The content of the course synthesizes concepts from the HCC developmental mathematics courses MATH 0409 and MATH 0312 and includes concepts from College Algebra MATH 1314.
(NOTE: although students may NOT use graphing technology on the final exam provided by HCC, the use of graphing technology as a discovery and analytical tool is highly encouraged.)
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs) The student will:
The Mathematical Process Standards are integrated throughout the course in all activities and lessons. Teachers should refer to these standards for instructional strategies and depth of rigor. Specific process standards have been highlighted for each unit, but these process standards should not be the only process standards associated with the daily lessons.
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Cycle 1
28 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Aug. 27 – Oct. 5, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 1: OneVariable Equations & Inequalities
Students solve and apply linear equations and inequalities in one variable
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to:
Ⓡ ALGI.5A Solve linear equations in one variable, including those for which the application of the distributive property is necessary and includes variables on both sides.
Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10A Add and subtract polynomials of degree one and degree two.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Unit 2: Linear Equations and Inequalities
Students analyze, graph, and write various forms of linear equations and inequalities using multiple representation in mathematical and realworld contexts.
5 class periods (90 minutes each)
or
10 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2A Determine the domain and range of a linear function in mathematical problems, determine reasonable domain and range values for realworld situations, both continuous and discrete and represent domain and range using inequalities.
Ⓢ ALGI.2B Write linear equations in two variables in various forms, including
y = mx + b, Ax + By = C, and y – y_{1} = m(x – x_{1}), given one point and the slope and given two points.Ⓡ ALGI.2C Write linear equations in two variables given a table of values, a graph, and a verbal description.
Ⓢ ALGI.2D Write and solve equations involving direct variation.
Ⓢ ALGI.2E Write the equation of a line that contains a given point and is parallel to a given line.
Ⓢ ALGI.2F Write the equation of a line that contains a given point and is perpendicular to a given line.
Ⓢ ALGI.2G Write an equation of a line that is parallel or perpendicular to the x or yaxis and determine whether the slope of the line is zero or undefined.
Ⓢ ALGI.2H Write linear inequalities in two variables given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓢ ALGI.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 – y_{1} = m(x – x_{1}).
Ⓡ ALGI.3B Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and realworld problems.
Ⓡ ALGI.3C Graph linear functions on the coordinate plane and identify key features including xintercept, yintercept, zeros, and slope in mathematical and realworld problems.
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3E Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Number and Algebraic Methods. The student applies mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Ⓢ ALGI.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 3: Systems of Equations & Inequalities
In realworld situations, students solve and analyze systems of linear equations and inequalities with two variables using graphs, tables, and algebraic methods.
(continued in cycle 2)
4 class periods
(90 minutes each)
or
8 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2I Write systems of two linear equations given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3F Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Ⓢ ALGI.3G Estimate graphically the solutions to systems of two linear equations with two variables in realworld problems.
Ⓢ ALGI.3H Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Cycle 2
25 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Oct. 8 – Nov. 9, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 3: Systems of Equations & Inequalities
In realworld situations, students solve and analyze systems of linear equations and inequalities with two variables using graphs, tables, and algebraic methods.
(continued from cycle 1)
4 class periods
(90 minutes each)
or
8 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
Linear Functions, Equations, and Inequalities. 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. The student is expected to:
Ⓡ ALGI.2I Write systems of two linear equations given a table of values, a graph, and a verbal description.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards when using graphs of linear functions, their key features, and their related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:
Ⓡ ALGI.3D Graph the solution set of linear inequalities in two variables on the coordinate plane.
Ⓢ ALGI.3F Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist.
Ⓢ ALGI.3G Estimate graphically the solutions to systems of two linear equations with two variables in realworld problems.
Ⓢ ALGI.3H Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Unit 4: Polynomials and Operations
Students evaluate, analyze, perform operations on, and apply properties of polynomials.
3 class
periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10A Add and subtract polynomials of degree one and degree two.
Ⓢ ALGI.10B Multiply polynomials of degree one and degree two.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7B Add, subtract, and multiply polynomials.
Unit 5: Polynomials and Factoring
Students explore various methods of factoring polynomials.
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.10B Multiply polynomials of degree one and degree two.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓡ ALGI.11B Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
Unit 6: Quadratic Equations
Students analyze, graph, and solve quadratic functions and inequalities and connect the attributes and solutions to real world situations using multiple representations.
(continued in cycle 3)
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.6A Determine the domain and range of quadratic functions, and represent the domain and range using inequalities.
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.7A Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including xintercept, yintercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
Ⓢ ALGI.7B Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Ⓡ ALGI.7C Determine the effects on the graph of the parent function f(x) = x^{2} when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓡ ALGI.8A Solve quadratic equations, having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Cycle 3
24 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Nov. 12 – Dec. 20, 2018
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 6: Quadratic Equations
Students analyze, graph, and solve quadratic functions and inequalities and connect the attributes and solutions to real world situations using multiple representations.
(continued from cycle 2)
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.6A Determine the domain and range of quadratic functions, and represent the domain and range using inequalities.
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓡ ALGI.7A Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including xintercept, yintercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
Ⓢ ALGI.7B Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Ⓡ ALGI.7C Determine the effects on the graph of the parent function f(x) = x^{2} when f(x) is replaced by a·f(x), f(x) + d, f(x – c), f(b·x) for specific values of a, b, c and d.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓡ ALGI.8A Solve quadratic equations, having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:
Ⓢ ALGI.12B Evaluate functions, expressed in function notation, given one or more elements in their domains.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 7: Rational Expressions and Equations
Students analyze, perform operations on, and solve equations and application problems involving rational expressions, including rational exponents.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms, and perform operations on polynomial expressions. The student is expected to:
Ⓢ ALGI.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.
Ⓢ ALGI.10D Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property.
Ⓡ ALGI.10E Factor, if possible, trinomials with real factors in the form
ax^{2} + bx + c, including perfect square trinomials of degree two.Ⓢ ALGI.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.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓢ ALGI.11A Simplify numerical radical expressions involving square roots.
Ⓡ ALGI.11B Simplify numerical and algebraic expressions using the laws of exponents, including integral and rational exponents.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents
Unit 8: Radical Expressions and Equations
Students analyze, perform operations on, and solve equations and application problems involving radical expressions and equations.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents.
Number and Algebraic Methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:
Ⓢ ALGI.11A Simplify numerical radical expressions involving square roots.
Ⓡ ALGI.11B Simplify numerical and algebraic expressions using the laws of exponents, including integral and rational exponents.
Cycle 4
29 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Jan. 7 – Feb. 15, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 9: Absolute Value Equations, Inequalities, and Functions
Students solve, analyze, and graph absolute value equations and inequalities.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓡ ALGII.2C Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain and which will restrict its range.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6D Formulate absolute value linear equations.
Ⓡ ALGII.6E Solve absolute value linear equations.
Ⓢ ALGII.6F Solve absolute value linear inequalities.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 10: Factoring Completely
Students use factoring techniques including factoring by grouping, completing the square, sum of two cubes, and difference of two cubes to factor polynomials.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, an the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Quadratic Functions and Equations. 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. The student is expected to:
Ⓢ ALGI.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) = ax^{2} + bx + c).
Ⓢ ALGI.6C Write quadratic functions when given real solutions and graphs of their related equations.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7C Determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two.
Ⓢ ALGII.7D Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.
Ⓡ ALGII.7E Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping.
Ⓡ ALGII.7F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and degree two.
Ⓡ ALGII.7H Solve equations involving rational exponents.
Unit 11: Transformations and Attributes of Quadratic Functions
Students analyze the transformation of a quadratic function in
f(x) = ax^{2}+bx+c and
f(x) = a(x – h)^{2}+k forms through multiple representations.3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.
Ⓢ ALGII.4D Transform a quadratic function f(x) = ax^{2} + bx + c to the form f(x) = a(x – h)^{2} + k to identify the different attributes of f(x).
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Cycle 5
30 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Feb. 18 – Apr. 5, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 12: Quadratic Equations, Inequalities, and Functions
Students write, and solve quadratic equations by factoring, completing the square, and applying the quadratic formula, and apply these methods to solving realworld problems.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, an the workplace.
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.4A Write the quadratic function given three specified points in the plane.
Ⓡ ALGII.4B Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening.
Ⓢ ALGII.4F Solve quadratic and square root equations.
Ⓢ ALGII.4H Solve quadratic inequalities.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 13: Systems of Quadratic Equations and Linear Equations Inequalities
Students analyze a system of equations in two variables consisting of a linear equation and a quadratic equation.
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.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.
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Systems of Equations and Inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, to use a variety of methods to solve, and to analyze reasonableness of solutions. The student is expected to:
Ⓢ ALGII.3C Solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation.
Ⓢ ALGII.3E Formulate systems of at least two linear inequalities in two variables.
Ⓢ ALGII.3F Solve systems of two or more linear inequalities in two variables.
Unit 14: Operations with Complex Numbers
3 class periods (90 minutes each)
or
6 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1B Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
CPM.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.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical idea.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7A Add, subtract, and multiply complex numbers.
Ⓢ ALGII.7B Add, subtract, and multiply polynomials.
Ⓢ ALGII.7D Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.
Ⓡ ALGII.7E Determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping.
Cycle 6
38 Days
The recommended number of class periods is less than the number of days in the grading cycle to accommodate differentiated instruction, extended learning time, and assessment days. Complete instructional planning information and support are in the HISD Curriculum documents.
Apr. 8 – May 31, 2019
Unit
# Class Periods
Texas Essential Knowledge and Skills/Student Expectations (TEKS/SEs)
The student will:
Unit 15:
Root Functions
Students analyze, perform operations on, and solve equations and application problems involving radical expressions.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
ALGII.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.
ALGII.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, , f(x)=x^{3}, f(x)=b^{x}, , and f(x) = log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓢ ALGII.2B Graph and write the inverse of a function using notation such as
f ^{1}(x).Ⓡ ALGII.2C Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain and which will restrict its range.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4C Determine the effect on the graph of when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x  c) for specific positive and negative values of a, b, c, and d.
Ⓢ ALGII.4E Formulate quadratic and square root equations using technology given a table of data.
Ⓡ ALGII.4F Solve quadratic and square root equations.
Ⓢ ALGII.4G Identify extraneous solutions of square root equations.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions.
Ⓢ ALGII.6B Solve cube root equations that have real roots.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7G Rewrite radical expressions that contain variables to equivalent forms.
Ⓡ ALGII.7H Solve equations involving rational exponents
Unit 16: Rational Equations and Functions
Students analyze rational equations and functions through graphs, tables, and algebraic methods.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, , f(x)=x^{3}, f(x)=b^{x}, , and f(x) = log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Ⓢ ALGII.2B Graph and write the inverse of a function using notation such as
f^{1}(x).Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6H Formulate rational equations that model realworld situations.
Ⓡ ALGII.6I Solve rational equations that have real solutions.
Ⓢ ALGII.6J Determine the reasonableness of a solution to a rational equation.
Ⓢ ALGII.6K Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation.
Ⓡ ALGII.6L Formulate and solve equations involving inverse variation.
Unit 17: Exponential and Logarithmic Functions
Students graph, analyze, and solve exponential and logarithmic functions and equations.
4 class periods (90 minutes each)
or
8 class periods (45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
CPM.1E Create and use representations to organize, record, and communicate mathematical ideas.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Exponential Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.9A Determine the domain and range of exponential functions of the form f(x) = ab^{x} and represent the domain and range using inequalities.
Ⓢ ALGI.9B Interpret the meaning of the values of a and b in exponential functions of the form f(x) = a·b^{x} in realworld problems.
Ⓡ ALGI.9C Write exponential functions in the form f(x) = a·b^{x} (where b is a rational number) to describe problems arising from mathematical and realworld situations including growth and decay.
Ⓡ ALGI.9D Graph exponential functions that model growth and decay and identify key features, including yintercept and asymptote, in mathematical and realworld problems.
Exponential and Logarithmic Functions and Equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:
Ⓡ ALGII.5A Determine the effects on the key attributes on the graphs of
f(x) = b^{x} and f(x) = log_{b}(x), where b is 2, 10 and e when f(x) is replaced by a f(x), f(x) + d, and f(x  c) for specific positive and negative real values of a, c, and d.Ⓢ ALGII.5B Formulate exponential and logarithmic equations that model realworld situations including exponential relationships written in recursive notation.
Ⓡ ALGII.5D Solve exponential equations of the form y = a∙b^{x }where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Unit 18: Data Analysis, Statistics, and Probability
Students analyze data, statistical models, and probability situations and evaluate models of regressions in realworld contexts.
3 class periods
(90 minutes each)
or
6 class periods
(45 minutes each)
Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
CPM.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
CPM.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
CPM.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Linear Functions, Equations, and Inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on realworld data. The student is expected to:
Ⓢ ALGI.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.
Ⓢ ALGI.4B Compare and contrast association and causation in realworld problems.
Ⓢ ALGI.4C Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for realworld problems.
Quadratic Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.8B Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for realworld problems.
Exponential Functions and Equations. 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 realworld data. The student is expected to:
Ⓢ ALGI.9E Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for realworld problems.
Attributes of Functions and Their Inverses. The student applies mathematical processes to understand that functions have distinct key attributes and to understand the relationship between a function and its inverse. The student is expected to:
Ⓡ ALGII.2A Graph the functions, f(x)=x^{3}, f(x)=b^{x}, , and f(x)=log_{b}x where b is 2, 10, and e and when applicable analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum.
Quadratic and Square Root Functions, Equations, and Inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓡ ALGII.4C Determine the effect on the graph of when f(x) is replaced by a f(x), f(x) + d, f(bx), and f(x  c) for specific positive and negative values of a, b, c, and d.
Ⓢ ALGII.4E Formulate quadratic and square root equations using technology given a table of data.
Exponential and Logarithmic Functions and Equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:
Ⓡ ALGII.5A Determine the effects on the key attributes on the graphs of
f(x) = b^{x} and f(x) = log_{b}(x), where b is 2, 10 and e when f(x) is replaced bya f(x), f(x) + d, and f(x  c) for specific positive and negative real values of a, c, and d.
Cubic, Cube Root, Absolute Value and Rational Functions, Equations, and Inequalities. The student applies mathematical processes to understand that cubic, cube root, rational, and absolute value functions and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:
Ⓢ ALGII.6A Analyze the effect on the graphs of f(x) = x^{3} and when f(x) is replaced by a· f(x), f(bx), f(x  c), and f(x) + d for specific positive and negative real values of a, b, c, and d.
Ⓢ ALGII.6G Analyze the effect on the graphs of when f(x) is replaced by a· f(x), f(bx), f(x  c), and f(x) + d for specific positive and negative real values of a, b, c, and d.
Number and Algebraic Methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:
Ⓢ ALGII.7I Write the domain and range of a function in interval notation, inequalities and set notation.
Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:
Ⓢ ALGII.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.
Ⓢ ALGII.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.
Ⓡ ALGII.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
priate models, write corresponding functions, and make predictions. The student is expected to:
Ⓢ ALGII.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.
Ⓢ ALGII.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.
Ⓡ ALGII.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.