6th Grade Math · to solve problems and solve real world and mathematical problems involving ratios, ratios, and percents. ... trigonometry is used in careers such as construction,

SECONDARY MATH COURSE CONTENT

6th Grade Math

Unit Unit Title Key Learning(s)

1 The Number System Students will convert, compare, and order fractions, decimals, and percents. Students will find the percent of a number and interpret word problems involving fractions, decimals, and percents.

2 Compute with Multi-

Digit Numbers Students will use the four operations to solve problems with decimals.

3 Multiply & Divide

Fractions Students will use their knowledge of multiplication and division to multiply and divide fractions.

4 Integers & the

Coordinate Plane

Students will understand that positive and negative numbers are used to describe quantities, directions, or locations. Students will solve problems involving absolute value, rational numbers, integers on a number line and numbers on the coordinate plane.

5 Ratios & Proportional

Relationships Students will be able to find the GCF and LCM of two whole numbers, understand ratio concepts and use ratio reasoning to solve problems and solve real world and mathematical problems involving ratios, ratios, and percents.

6 Expressions Students will write and simplify expressions using properties, identify, write and evaluate numerical and algebraic expressions, and interpret word problems involving numerical and algebraic expressions.

7 Equations Students will create, solve and interpret one-variable equations and inequalities and interpret word problems involving equations and inequalities.

8 Functions & Inequalities Students will analyze the relationship between two quantities, represent functions and solve inequalities, and interpret word problems involving variables that represent two quantities.

9 Statistical Measures Students will find the measures of center and variability in a set of data, use data to describe patterns and variations within a set of data, and interpret word problems involving statistical measures.

10 Statistical Displays Students will display data using different displays, describe a set of data using measures of center and variability, and interpret word problems by describing and displaying data sets.

11 Area Students will find the area of shapes through the use of formulas, the area and side lengths of shapes on a coordinate plane, and the area of irregular and compound figures using formulas Students will solve word problems involving the area of triangles, quadrilaterals and irregular/compound polygons.

12 Volume & Surface Area Students will find the volume of shapes through the use of formulas, the surface area of prisms using formulas and represent three-dimensional figures using nets. Students will solve word problems involving volume, nets and surface area.


Pre-Algebra

Unit Number Unit Title Key Learnings

1 Part 1 Intro to the Tools of Algebra

Order of Operations and Substitution (when variables’ values are given) can be used to evaluate expressions, along with properties of numbers (commutative, associative, identity, etc.). Understanding what key words mean can allow students to translate verbal phrases and sentences into expressions and equations.

1 Part 2 Integers Compare and order integers and find absolute value. Select appropriate operations to solve problems involving rational numbers. Locate and name points on graph.

1 Part 3 Rational Numbers Using rational numbers to solve problems and justify solutions.

2 Part 1 Equations Solving one and two-step equations.

2 Part 2 Inequalities Write and solve inequalities and graph their solutions.

3 Part 1 Ratios, Rates, Proportions

and Direct Variation

Students learn the use of unit rate to determine best value when shopping. Proportions can be used to create scale drawings in architecture and to enlarge pictures. Direct variation can be used to describe proportional relationships. Both rate of change and y = kx have the ability to be used to make predictions and solve problems.

3 Part 2 Percents Percent can be used to calculate discounted prices, sales tax, and other percent of change, as well as for making predictions about data based on a sample.

4 Part 1 Geometry Concepts Relationships between angle measures in triangles and in figures containing parallel lines can be used to find missing angle measures. The formulas for the area, perimeter, or circumference of two-dimensional figures can be used to solve real-world problems.

4 Part 2 Three-Dimensional Figures Examine the different properties of three-dimensional figures and use these properties to solve problems.

4 Part 3 Statistics & Probability Students will write the probability of an outcome of an event. Given a situation students will determine which type of central tendency would be best to use. Students will use probability results to make predictions.

5 Part 1 Equations and Inequalities Write and solve multi-step equations/inequalities with variables on both sides and with grouping symbols.

5 Part 2 Functions and Graphing Use graphs and solutions to linear functions to solve problems.

5 Part 3 Monomials & Scientific

Notation Using powers and exponents.


HS PRE ALGEBRA


1 Language of Algebra Students will use the properties of various operations to generate equivalent expressions.

2 Integers Students will be able to compute with integers. Students will apply their knowledge of integers to real-world situations.

3 Rational Numbers Students will be able to compute with rational numbers. Students will apply their knowledge of rational numbers to real-world situations.

4 Powers and Roots Students will use the properties of various operations to generate equivalent expressions.

5 Algebraic Expressions Students will use the distributive property to generate equivalent expressions.

6 Algebraic Equations Students will use algebraic equations to solve real-world problems.

7 Inequalities Students will use algebraic inequalities to solve real-world problems.

8 Ratios and Proportional

Relationships Students will analyze, recognize, and represent proportional relationships when solving real-world problems.

9 Percentages Students will use proportions and equations to solve problems involving percents.

10 Linear Functions Students will be able to write, solve, graph, and interpret linear functions and systems of equations.

11 Probability & Statistics Students will use random samples and statistical measures to compare sets of data. Students will use different processes to develop, use, and evaluate probability models.


Algebra 1


1 Language & Tools of Algebra

Writing and evaluating expressions from real world information. Order of Operations and understanding properties can be used to evaluate and simplify expressions. Understanding what key words mean can allow students to translate verbal phrases and sentences into expressions and equations. Understanding all sets of numbers and how to write them in various forms help in comparing and ordering numbers. Simplest Radical Form is used to simplify radical expressions.

2 Solving Linear Equations Write and solve linear equations and use them to solve real world problems.

3 Solving Linear Inequalities Solve and graph linear inequalities and analyze the solutions. Solve absolute value equations and inequalities and analyze the solutions. Be able to compare and contrast equations and inequalities.

4 Polynomials Use various operations to simplify polynomials.

5 Factoring Recognize that factoring is the inverse of multiplying. Use different methods of factoring to solve equations.

6 Functions and Relations Represent and interpret relations and functions in various forms. Identify and interpret relationships between values.

7 Analyzing Linear Equations Represent real world situations by writing and graphing linear equations or inequalities.

8 Systems of Equations Write, solve, and graph systems of linear equations and inequalities. Compare and contrast the different methods for solving systems.

9 Statistics & Probability Using statistical techniques to find probability and graph data.


Geometry


0 Preparatory Students will solve real world situations using area and perimeter, surface area and volume, and Pythagorean Theorem

1 Tools of Geometry Students will solve real world situations using distance and midpoint formula Identifying points, segments, lines, planes and angles

2 Reasoning and Proofs Inductive reasoning, paragraph proofs, two-column algebraic and geometric proofs

3 Congruent Triangles Students will solve real world situations using relationships with angles and triangles in geometry, classifying triangles, congruence of triangles

4 Polygons Students will solve real world situations using polygons, parallelograms, rectangle, rhombus, square, trapezoid

5 Proving Statements Deductive reasoning, geometric proofs

6 Relationship in Triangles Students will solve real world situations using medians, bisectors and altitudes, and inequalities

7 Proportions and Similarity Students will solve real world situations using ratios and proportions, similar polygons, and proportional parts.

8 Right Triangles &

Trigonometry Radicals, Right Triangles, Trigonometry

9 Circles Students will solve real world situations using properties of arcs, chords, and angles of a circle and secants and tangents with circles.

10 Area & Perimeter Area and perimeter of plane figures (composite)

11 Surface Area & Volume Students will solve real world situations using surface area and volume formulas.


Honors Algebra II


1 Equations & Inequalities Students will solve real world situations using, absolute value, evaluating expressions, and properties of real numbers.

2 Linear Relations & Functions Students will solve real world situations using Linear Functions and their graphs.

3 Systems of Equations &

Inequalities Students will solve real world situations using linear systems.

4 Matrices Students will solve real world situations using matrix operations and matrices to solve systems.

5 Quadratics Students will solve real world situations using solving quadratic functions and graphical analysis of quadratics.

6 Polynomials Students will solve real world situations using properties of exponents, perform operations on polynomials, describe end behaviors, analyze polynomial graphs and find zeros of polynomial functions.

7 Radical Equations &

Inequalities Students will solve real world situations using radical equations and radical inequalities.

8 Rational Expressions &

Equations Students will solve real world situations using rational expressions and rational equations.

9 Exponential & Logarithms Students will solve real world situations using exponential properties and logarithmic properties.

10 Conics Using a quadratic equation to describe conic sections. Geometrically describing conic sections by slicing a double cone with a plane.

11 Sequences and Series Students will solve real world situations using sequences and series.

12 Trig Functions Using trigonometric functions to solve problems using indirect measurement. How trigonometry is used in careers such as construction, surveying, architecture, traffic control.

13 Trigonometric Graphs &

Identities Graph trigonometric functions; Determine period, amplitude, phase shift and vertical shifts; Use and verify trig identities; Solve trigonometric equations.


CP Algebra II



Inequalities Students will solve real world situations using linear systems.


4 Graphing Quadratics Students will solve real world situations by graphing quadratic functions and graphical analysis of quadratics.

5 Solving Quadratics Students will solve real world situations using solving quadratic

5 Polynomials Students will solve real world situations using properties of exponents, perform operations of polynomials, describe end behaviors, analyze polynomial graphs and use rational zero theorem.

6 Radical Equations &

Inequalities Students will solve real world situations using radical equations and radical inequalities.

7 Rational Expressions &

Equations Students will solve real world situations using rational expressions and rational equations.

8 Exponential & Logarithms Students will solve real world situations using exponential properties and logarithmic properties.

10 Sequences and Series Students will solve real world situations using sequences and series.

11 Probability & Statistics Students will solve real world situations using permutations and combinations and probability.



Honors Pre-Calculus


1 Equations & Inequalities Students will solve real world situations using functions, graph of functions and transforming graphs of functions.

2 Polynomials & Polynomial

Functions Students will solve real world situations using polynomial functions, complex numbers, finding zeros of polynomial functions and rational functions.

3 Exponential & Logarithmic

Functions Students will solve real world situations using exponential functions, logarithmic functions, properties of logarithms, and solving exponential equations.

4

Sequences, Series, Mathematical Induction,

Permutations/Combinations, Probability

Students will solve real world situations using explain the difference between geometric and arithmetic sequences, describe mathematical induction, and compare and contrast permutations and combinations.


6 Trigonometric Functions Students will solve real world situations using trig functions, unit circle and trig identities.

7 Graphing Trigonometric

Functions Students will graph trigonometric functions.

8 Analytic Trigonometry Students will verify trig identities and apply trig formulas.

9 Solving Trig Equations Students will solve Trigonometric Equations

10 Additional Topics in

Trigonometry Students will solve real world situations using law of sines, law of cosines, vectors and polar coordinates.


Inequalities Students will solve real world situations using linear systems, nonlinear systems, partial fraction and linear programming.



Pre-Calc/Trig A


1 Linear Relations & Functions Students will solve real world situations using linear functions.

2 Systems of Linear Equations

& Inequalities Students will solve real world situations using systems of equations.

3 Matrices Students will solve real world situations using matrix operations and properties.

4 The Nature of Graphs Students will solve real world situations using families of graphs.

5 The Nature of Graphs (II) Students will solve real world situations using families of graphs and variation.

6 Polynomial Functions Students will solve real world situations using polynomial functions.

7 Rational & Radical

Functions Students will solve real world situations using rational functions radical functions.

8 The Trigonometric Functions

Of Right Triangles Students will solve real world situations using trigonometric functions.

9 Solving Triangles Students will solve real world situations using trigonometric functions.

10 Graphs of Trig Functions Students will solve real world situations using radians and degree measures, linear and angular velocity, graphs of trigonometric functions and their inverses, and trigonometric functions to model given situations.

11 Trigonometric Identities &

Equations Students will solve real world situations using basic trigonometric identities, verifying trigonometric identities, normal form of a linear equation and distance from a point to a line.


Pre-Calc/Trig B


1 Trigonometric Identities &

Equations Students will solve situations using basic trigonometric identities, verifying trigonometric identities, normal form of a linear equation, and distance from a point to a line.

2 Vectors & Parametric

Equations Students will solve real world situations using geometric and algebraic vectors, vectors in 3-D space and perpendicular vectors.

3 Polar Coordinates & Complex Numbers

Students will solve real world situations using polar coordinates, complex numbers and polar graphs.

4 Conics Students will solve real world situations using analytic geometry and graphs and systems of conic sections.


Functions Students will solve real world situations using exponents, exponential growth and decay, logarithms, and common and natural logarithms.

6 Sequence & Series Students will solve real world situations using sequences and series, sigma notations, Pascal’s triangle and binomial expansion, iteration, and mathematical induction.

7 Combinatorics & Probability Students will solve real world situations using combinatorics and probability.

8 Statistics & Data Analysis Students will solve real world situations using statistics and data analysis.

9 Calculus Students will solve real world situations using limits, derivatives and antiderivatives and the Fundamental Theorem of Calculus.


CP Pre-Calculus


1 Functions, Inverses, and

Systems Students will be able to simplify expressions using operations on functions, find inverse of functions, and systems of equations

2 Exponential and Logarithms Students will be able to use exponent properties, graph exponential growth and decay, use logarithm properties, and use common and natural logarithms to solve equations

3 Rational Expressions and

Equations Students will be able to multiply and divide rational expressions, add and subtract rational expressions, and decompose partial fractions

4 Rational functions and their

graphs Students will be able to solve rational equation, graph rational equations, and model and apply the graphs of rational equations

5 Conics and Parametric

Equations Students will be able to graph and write equations for circle, ellipses, hyperbolas, and parabolas, find the intersections of conics, and graph parametric equations

6 Trigonometric Functions Students will be able to convert radians and degrees, derive and use the unit circle, solve right triangles, and calculate trig functions

7 Graphing Trigonometric

Functions Students will be able to graph trig functions and their inverses

8 Trigonometric Identities Students will be able to use trig identities to simplify expressions and verify trig identities

9 Trigonometric Equations Students will be able to use the product-to-sum and sum-to-product formulas and solve trig equations

10 Polar Coordinates Students will be able to convert between polar and rectangular coordinates, graph polar equations, simplify complex number in rectangular and polar form


AP Calculus


1 Prerequisites for Calculus Using trigonometric functions to solve problems using indirect measurement. How trigonometry is used in careers such as construction, surveying, architecture, traffic control.

2 Limits Students will solve real world situations using limits and continuity.

3 The Derivative Students will solve real world situations using differentiation properties, implicit differentiations and related rates.

4 Application of the Derivative Students will solve real world situations using curve sketching, optimization and differentials.

5 Integration Students will solve real world situations using integration, Reimann sums, and the Fundamental Theorem of Calculus.

6 Transcendental Functions Students will solve real world situations using derivatives/antiderivatives of transcendental functions and differential equations.

7 Applications of Integration Students will solve real world situations using area between curves, volume and arc length.

8 Additional Topics Students will solve real world situations using slope fields, Newton’s method and work.

Calculus I


1 Prerequisites for Calculus Using trigonometric functions to solve problems using indirect measurement. How trigonometry is used in careers such as construction, surveying, architecture, traffic control.

2 Limits Students will solve real world situations using limits and continuity.

3 The Derivative Students will solve real world situations using differentiation properties, implicit differentiations and related rates.

4 Application of the Derivative Students will solve real world situations using curve sketching, optimization and differentials.

5 Integration Students will solve real world situations using integration, Reimann sums, and the Fundamental Theorem of Calculus.

6 Transcendental Functions Students will solve real world situations using derivatives/antiderivatives of transcendental functions and differential equations.

7 Applications of Integration Students will solve real world situations using area between curves, volume and arc length.

8 Additional Topics Students will solve real world situations using slope fields, Newton’s method and work.


AP Calculus II


1 AB Calculus Review Topics Students will solve real world situations using curve sketching, optimization, related rates, hyperbolic functions and Euler’s method.

2 Application of Integration Students will solve real world situations using area between curves, volume, work, arc length and probability.

3 Techniques of Integration Students will solve real world situations using integration by parts, partial functions, trig substitution, L’Hospitals rule, and improper integral.

4 Series Students will solve real world situations using sequences, series, convergence/divergence, power series, Taylor/Maclaurin Series.

5 Parametric Functions & Vector Value Functions

Students will solve real world situations using parametric equations, arc length and vectors.

6 Polar Coordinates Students will solve real world situations using polar coordinates and conic sections.

7 BC Review Students will solve real world situations using calculus concepts.

8 Additional Topics Students will solve real world situations using three dimensional space & vectors.


Probability & Statistics


1 Introduction to Statistics What is statistics? Random samples and introduction to experimental design.

2 Frequency Distributions &

Graphs Bar graphs, circle graphs, pareto charts, and time-series graphs, frequency distributions, histograms, and ogives and stem-and-leaf displays

3 Averages & Variations Measures of central tendency; measures of variation; grouped data; percentiles and box-and whisker plots

4 Probability Basic probability concepts, compound probabilities, trees and counting techniques.

5 Binomial Probability

Distribution Random variables and probability distributions; Binomial probability distributions; Geometric probability distributions; Poisson probability distributions.

6 Normal Distributions Graph normal curves; Apply the empirical rule; Convert raw data to z scores; Compute probabilities of standardized events; Use the inverse normal to solve guarantee problems; Normal Approximation to the Binomial Distribution.

7 Sampling Distributions Explain the Central Limit Theorem; If the x distribution is normal, then the �̅� distribution is normal for any sample size; If the x distribution is not normal, then the sample size needs to be greater than or equal to 30.

8 Estimation Confidence level, error of estimate, and critical value, Degrees of freedom and Student’s t, Maximal margin of error given level of confidence, Interpret poll results and Sample size.

9 Hypothesis Testing (1) Students will decide whether to reject or fail to reject a claim by using hypothesis testing. Students will determine whether the data fits a mean or a proportion, and then utilize appropriate testing methods.

10 Hypothesis Testing (2)

Dependent/independent Samples

Perform a t-test for the difference between two population means using small independent samples Perform a two sample z-test for the difference between two means using large independent samples Perform a two prop z-test for the difference between two proportions.

11 Correlation & Regression The level of correlation between two pairs of ordered data can be evaluated; Correlation does not signify causation; High levels of linear correlation can be used to predict values for non-sampled situations using linear regression techniques

12 Chi-Square Students will decide whether to reject or fail to reject a claim by using hypothesis testing. Students will determine whether the data fits a mean or a proportion, and then utilize appropriate testing methods.


AP Statistics


1 Role of Statistics Distinguish between population and a sample Construct a frequency distribution, bar chart, and dot plot

2 Collecting Data Sensibly Understand bias in data; Understand key components of collecting a sample Understand components of an observational study and an experiment

3 Graphical Methods for

Describing Data

Construct pie charts, bar graphs, stem and leaf, histograms, relative frequency graphs, scatter plots, and a time series plot Interpret pie charts, bar graphs, stem and leaf, histograms, relative frequency graphs, scatter plots, and a time series plot

4 Averages and Variation Measures of Central Tendency; Measures of Variation; Grouped Data; Empirical Rule and Z-Scores

5 Bivariate Data How do you describe the relationship between two numerical variables in terms of form, strength, and direction?

6 Probability Basic Probability Concepts; Compound Probabilities; Trees and Counting Techniques

7 Random Variables and

Probability Distributions Random variables and probability distributions; Binomial probability distributions Geometric probability distributions; Poisson probability distributions

8 Sampling Variability and Sampling Distributions

Explain the Central Limit Theorem If the x distribution is normal, then the �̅� distribution is normal for any sample size If the x distribution is not normal, then the sample size needs to be greater than or equal to 30.

9 Estimation using single sampling Confidence level, error of estimate, and critical value; Degrees of freedom and Student’s t Maximal margin of error given level of confidence; Interpret poll results; Sample size

10 Hypothesis Testing Test Procedures; Type I and Type II Errors Hypothesis test for Proportion; Hypothesis for Mean

11 Hypothesis Testing Tests involving proportions; Tests involving paired differences (dependent samples) Testing differences of two means or two proportions

12 Chi-Square Recognize when a hypothesis test is a test of independence Recognize, when a hypothesis test is a goodness-of-fit test Analyze and carry out a goodness-of-fit hypothesis test; Analyze and carry out an independence test

13 Linear Regression and

Correlation Scatter Diagrams; Linear Regression and confidence bounds The linear correlation coefficient; Inferences concerning regression


Advanced Math Topics


1 P Factoring Students will solve real world situations using factoring trinomials, factoring with LCD, factoring by grouping, factoring difference of squares and factoring sum/difference of cubes.

2 Exponents & Radicals Simplify and/or solve problems containing exponents, radicals, and complex numbers.

3 Rational Expressions Solve and simplify rational equations and or expressions.

4 Modeling & Systems Modeling and interpreting real world situations using graphs of systems of equations.

5 Quadratics Apply quadratic equations to solve real world situations.

6 Graphs & Transformations Interpret the effects transformations have on functions and find the inverse of functions.


Functions Solve, simplify, graph, and apply exponential and logarithmic functions.

8 Advanced Geometry Solve right and non-right triangles.

9 Trigonometry Construct the unit circle. Apply trigonometric identities to prove equality. Graph periodic functions.

10 Sequences & Series Exploring sequences and series.

11 Probability Determine the number of outcomes for a situation. Determine probability.


Consumer Math


1 Gross Income Calculate straight-time, hourly, and weekly pay. Compute total pay for piecework employment. Determine the salary per pay period. Calculate straight and graduated commission.

2 Net Pay Your net income (take home pay) is found by subtracting all deductions from your gross pay.

3 Record Keeping Track finances and build a budget. Save money for future purchases.

4 Checking Accounts Keeping accurate records of the amount in a checking account is crucial to your financial success.

5 Savings Accounts Calculate balances of savings accounts. Complete deposit and withdrawal slips. Balance account statements. Find savings account interest.

6 Cash Purchases Know how to calculate a final sales price. Determine the final selling price. Decide if purchases are financially responsible.

Extra Taxes You must complete federal, state, and local income tax filings every year.

7 Charge Accounts & Credit

Cards Describe the pros and cons of owning a credit card. Determine what things affect your credit score.

8 Loans Single payment loan, Installment Loan, Simple Interest installment loans.

9 Vehicle Transportation Describe and defend the costs of vehicle ownership. Modify their plans of vehicle ownership to match their personal financial needs and requirements.

10 Housing Costs Knowing how to determine the cost of purchasing and maintaining a home.

11 Insurance Students will be able to compare and contrast the types of health insurance. And plan for the types of health and life insurance coverage and medical coverage their future needs may require.

12 Investments Knowing the various types of investments and what will be the best financial vehicle for you.

Documents

6th Grade Math · to solve problems and solve real world and mathematical problems involving ratios, ratios, and percents. ... trigonometry is used in careers such as construction,