Mathematics
Algebra 1 | Algebra 1a | Geometry | Precalculus
Algebra 1 Course Number:451 Prerequisites: 438, 448
Algebra 1 is a first year course in algebra. It is designed for students who are entering high school with a substantial background in pre-algebra. Teachers design classroom experiences using an inquiry/ problem solving model of instruction that allows students to explore concepts from a variety of perspectives and representations. In each topic students learn to analyze and represent concepts numerically, algebraically, graphically, and linguistically. Students develop understanding of major topics in Algebra through a process that emphasizes communication, reasoning, and building connections between important algebraic concepts, additional strands of mathematics, and real world applications.
Topics:
Data and Statistics and Probability including: Students will…
Analyze 1-variable data using measures of central tendency and measures of spread.
Analyze 2-variable data using scatter plots and linear regression equations.
Analyze measures of spread using mean absolute deviation and standard deviation;
Algebra including: Students will…
Apply the commutative, associative, and distributive properties.
Apply scientific notation to simplify numerical expressions.
Apply laws of exponents to simplify expressions and solve problems.
Search for patterns of change that show relationships among variables.
Plot points on a coordinate system.
Understand relationships among tables, graphs, words, and symbolic rules.
Analyze and solve linear equations in the form of y=mx+b using tables, graphs, and equations including real world applications.
Find and interpret the slope of a line from a table, graph, and/or equation.
Analyze and solve linear equations, including real world applications.
Analyze and solve systems of two linear equations including real world applications.
Analyze and solve linear functions and step functions.
Analyze and solve exponential functions.
Solve problems involving the composition of functions including real world applications.
Instructional Time: The minimum time allocation is 235 minutes per week per school year.
Required Assessment:
Two formative assessments, in September and at mid-year
Eight open-response mathematics tasks, two each term;
One summative assessment in June
There is a benchmark for this course. All students must maintain a passing average for the course and pass five out of eight math tasks or pass the June summative assessment to receive credit for this course.
Instructional Materials:
Math Connections, 1a and 1b; published by It’s About Time
Graphing Calculator
Algebra 1a Course Number: 45a Prerequisites: None
Algebra 1a is a transition pathway first year course in algebra. It is designed for students who are entering high school without the prerequisites for a full algebra course. Teachers design classroom experiences using an inquiry/problem solving model of instruction that allows students to explore concepts from a variety of perspectives and representations. In each topic students learn to analyze and represent concepts numerically, algebraically, graphically, and linguistically. Students develop understanding of major topics in Algebra through a process that emphasizes communication, reasoning, and building connections between important algebraic concepts, additional strands of mathematics, and real world applications.
Topics:
Data and Statistics and Probability including: Students will…
• Analyze 1-variable data using measures of central tendency and measures of spread.
• Analyze 2-variable data using scatter plots and linear regression equations.
• Analyze measures of spread using mean absolute deviation and standard deviation;
• Analyze situations and compute probabilities involving independent events.
• Analyze probabilities using counting trees, lists, and the fundamental counting principle.
Algebra including: Students will…
• Apply the commutative, associative, and distributive properties.
• Apply scientific notation to simplify numerical expressions.
• Apply laws of exponents to simplify expressions and solve problems.
• Search for patterns of change that show relationships among variables.
• Plot points on a coordinate system.
• Understand relationships among tables, graphs, words, and symbolic rules.
• Analyze and solve linear equations in the form of y=mx+b using tables, graphs, and equations including real world applications.
• Find and interpret the slope of a line from a table, graph, and/or equation.
• Analyze and solve linear equations, including real world applications.
• Analyze and solve systems of two linear equations including real world applications.
Instructional Time: The minimum time allocation is 470 minutes per week per school year.
Required Assessment:
Two formative assessments, in September and at mid-year
Eight open-response mathematics tasks, two each term;
One summative assessment in June
There is a benchmark for this course. All students must maintain a passing average for the course and pass five out of eight math tasks or pass the June summative assessment to receive credit for this course.
Instructional Materials:
Math Connections, 1a and 1b; published by It’s About Time
Graphing Calculator
Geometry Course Number: 454 Prerequisites: 45a or 451 or 461
This is a full year, standards-based course of study in geometry with additional course work in probability. Teachers design classroom experiences using an inquiry/problem solving model of instruction that allows students to explore concepts from a variety of perspectives and representations. In each topic students learn to analyze and represent concepts numerically, algebraically, graphically, and linguistically. Students develop understanding of major topics in Geometry through a process that emphasizes communication, reasoning, and building connections between important geometric concepts, additional strands of mathematics, and real world applications.
Topics:
Probability including: Students will…
Analyze situations and compute probabilities involving independent events.
Analyze probabilities using tree diagrams, lists, and the fundamental counting principle.
Geometry including: Students will…
Construct, measure, and classify of polygons, including regular polygons
Identify lines of symmetry of polygons; use symmetry to classify polygons
Find perimeter and area of polygons using algebra, triangulation, and/or measurement
Use geometric representations to expand binomials and trinomials
Solve problems using the Pythagorean Theorem
Solve maximization problems involving volumes
Solve problems using proportionality, including scaling factors, scale drawings, and the effects of scaling on area and volume
Determine angle measure by degrees and slope with tan and arc tan functions, exemplifying inverse functions
Determine whether a set of lengths and angles determines 0, 1 or more triangle(s)
Solve geometric problems involving transversals of parallel lines
Solve geometric problems involving similarity and congruence of triangles
Analyze circles, including: area, circumference, arc length, sector area, segment area, inscribed angles, and the meaning and significance of pi.
Use logical justifications to write informal and formal proofs
Measure basic properties of figures in 3-space using both constructive and analytic methods
Instructional Time: The minimum time allocation is 235 minutes per week per school year.
Required Assessments:
Formative assessments in September and January;
Eight mathematics tasks, two each term;
Summative assessment in June.
Instructional Materials:
Math Connections: books 1b, 2a, 2b; published by It’s About Time
Geometry kits including rulers, compasses, patty paper, and protractors
Graphing calculators
Precalculus Course Number: 458 Prerequisites: 455 or 456 or 463
Precalculus is a challenging, standards based course in reasoning, applications, and problem solving associated with algebraic functions. The course introduces students to topics in calculus that are associated with these functions. The course is designed to prepare students for calculus and includes with an introduction to limits and continuity. In this course, teachers design classroom experiences using an inquiry/problem solving model of instruction that allows students to explore concepts from a variety of perspectives and representations. In each topic students learn to analyze and represent concepts numerically, algebraically, graphically, and linguistically. Students develop understanding of major topics in algebra through a process that emphasizes communication, reasoning, and building connections between important algebraic concepts, additional strands of mathematics, and real world applications.
Topics: Students will…
Evaluate quadratic functions including inverse functions and solving problems involving rates of change.
Evaluate polynomial and rational functions including the Fundamental Theorum of Algebra.
Solve polynomial functions and square root functions graphically and algebraically.
Find the composition of functions.
Determine the inverse of functions and/or relations.
Solve problems in analytic geometry including: parabolas, circles, ellipses, and hyperbolas.
Perform operations with rational expressions.
Recognize and solve direct, joint, and inverse variation problems.
Graph exponential functions and solve exponential equations and inequalities.
Evaluate logarithmic expressions and solve logarithmic equations and inequalities.
Simplify and evaluate expressions using the properties of logarithms.
Solve exponential equations and inequalities using common and natural logarithms.
Find values of trigonometric functions based right triangles and on the unit circle.
Solve problems by using right triangle trigonometry, the law of sines, and the law of cosines.
Graph trigonometric functions and determine amplitude, period, phase shifts and vertical shifts.
Use and verify trigonometric identities.
Use sum and difference formulas and double angle and half angle formulas.
Solve trigonometric equation by using inverse trigonometric functions.
Solve systems of equations including the use of matrix operations
Explore the limits of functions.
Solve problems involving the limits of functions.
Instructional Time: The minimum time allocation is 235 minutes per week per school year.
Required Assessment:
Two formative assessments, in September and at mid-year
Eight open-response mathematics tasks, two each term;
One summative assessment in June
Instructional Materials:
Precalculus, published by Holt Rinehart and Winston
Graphing Calculator