Math

Module 1: Expressions

Learning Targets

• Students write and evaluate numerical algebraic expressions

• Students explore order of operations

• Students write and evaluate algebraic expressions

• Students apply properties of real numbers to simplify expressions

• Students simplify expressions using distributive property

• Students evaluate absolute value expressions

• Students use quantities for descriptive modeling and report appropriate level of accuracy

 

Module 2: Equations in One-Variable

Learning Targets

• Students create and interpret equations that describe relationships

• Students solve equations by using addition, subtraction, multiplication and division

• Students solve multi-step equations for specific lettered coefficients by applying properties of equality

• Students solve equations with the variables on each side by applying the properties of equality and the distributive property

• Students solve absolute value equations

• Students solve equations involving proportions

• Students solve equations for specific variables and convert units of measure by applying the properties of equality

Module 3: Relations & Functions

Learning Targets

• Students represent relations with graphs, ordered pairs, tables, and mappings

• Students determine whether a relation is a function and find function values

• Students identify linear and nonlinear functions and continuous and discrete functions

• Students identify intercepts of functions and solve equations by graphing

• Students identify symmetry, extrema and end behavior functions

• Students sketch graphs of functions and compare two or more functions

 

Module 4: Linear & Nonlinear functions

Learning Targets

• Students graph linear functions by using tables and intercepts

• Students find and interpret the rate of change and slopes of lines

• Students graph equations in slope-intercept form

• Students identify the effects of transformations of graphs of linear functions

• Students write and graph equations of arithmetic sequences

• Students graph piecewise- defined and step functions

• Students identify the effects of transformations of the graphs of absolute value functions

Module 5: Creating Linear Equations

Learning Targets

• Students create linear equations in slope-form

• Students create linear equations in point-slope form and standard form

• Students use scatter plots to make and evaluate predictions

• Students determine whether a situation illustrates corrections or causation

• Students use best-fit lines and correlation coefficients to determine how well linear functions fit sets of data

• Students find inverses of functions

 

Module 6: Linear Inequalities

Learning Targets

• Students use addition, subtraction, multiplication, and division to solve inequalities

• Students solve inequalities by use of more than one step

• Students write and solve combinations of two inequalities joined by ‘and’ or ‘or’

• Students graph linear inequalities on the coordinate plane

 

Module 7: Systems of Linear Equations & Inequalities

Learning Targets

• Students solve systems of equations by graphing

• Students solve system of equations by substitution

• Students solve systems of equations by elimination with addition or subtraction

• Students solve system of equations by using elimination with multiplication

• Students solve systems of inequalities by graphing

Module 8: Exponents & Roots

Learning Targets

• Students apply the multiplication properties of exponents to simplify expressions

• Students apply the division properties of exponents to simplify expressions

• Students apply the properties of zero and negative exponents to simplify expressions

• Students apply the properties of rational exponents to simplify expressions

• Students simplify radical expressions

• Students solve expressions with radical expressions

• Students solve exponential equations

 

Module 9: Exponential Functions

Learning Targets

• Students graph exponential functions

• Students identify the effects of transformations of the graphs of exponential functions

• Students create exponential functions and solve problems involving exponential growth and decay

• Students use the properties of exponents to transform expressions for exponential functions

• Students write and graph equations of geometric sequences

• Students write geometric and arithmetic sequences recursively

Module 1: Tools of Geometry

Learning Targets

• Students use geometric notation and terminology

• Students draw and interpret geometric models

• Students find the distance between any two points

• Students locate any point along a segment, given a fraction of the distance

• Students locate the midpoint between any two points

• Students use algebra to solve for lengths of segments

 

Module 2: Angles & Geometric Figures

Learning Targets

• Students identify and use different kinds of angles

• Students figure out information based on complimentary and supplementary angles

• Students find measures of two dimensional figures

• Students model three-dimensional figures with two-dimensional representations

• Students apply the definitions of precision, accuracy, and error to data

• Students use significant figures

 

Module 3: Logical Arguments and Line Relationships

Learning Targets

• Students use inductive reasoning and counterexamples

• Students write and analyze compound statements by using logic

• Students apply the Laws of Detachment and Syllogism

Module 3: Logical Arguments & Line Relationships

Learning Targets

• Students analyze and construct viable arguments

• Students identify and use relationships between parallel lines and transversals

• Students classify lines as parallel, perpendicular, or neither

• Students identify and use parallel lines by using angle relationships

• Students use perpendicular lines to find distance

 

Module 4: Transformations & Symmetry

Learning Targets

• Students use rigid motions to reflect figures on the coordinate plane

• Students use rigid motions to translate figures on the coordinate plane

• Students use rigid motions to rotate figures about points on the coordinate plane

• Students complete compound transformations

• Students identify rotational and line symmetry

 

Module 5: Triangles & Congruence

Learning Targets

• Students solve problems using the Triangle Angle-Sum Theorem

• Students prove and use triangle congruence

Module 5: Triangles & Congruence

Learning Targets

• Students use triangle congruence theorems

• Students prove right triangles congruent

• Students solve problems involving isosceles and equilateral triangles

• Students write coordinate proofs for congruent triangles

 

Module 7: Quadrilaterals

Learning Targets

• Students prove and use theorems about the interior and exterior angles of polygons

• Students use the properties of parallelograms to solve problems

• Students determine whether quadrilaterals are parallelograms

• Students recognize and apply the properties of rectangles

• Students recognize and apply the properties of rhombi and squares

• Students solve problems using the properties of trapezoids and kites

 

Module 8: Similarity

Learning Targets

• Students draw and analyze dilated figures using tools or functions

• Students solve problems using the definition of similar polygons

• Students use triangle proportionality to solve problems and prove theorems

 

Module 9: Right Triangles & Trigonometry

Learning Targets

• Students solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse using the geometric mean

• Students solve problems using the Pythagorean Theorem and its converse

Module 9: Right Triangles & Trigonometry

Learning Targets

• Students solve problems by using the properties of 45°-45°-90° and 30°-60°-90° triangles

• Students solve problems using the trigonometric ratios and the inverse trigonometric ratios for acute angles

• Students solve application problems using the trigonometric ratios and their inverses

 

Module 10: Circles

Learning Targets

• Students find and apply the formulas for the circumference and area of a circle

• Students find measures of angles and arcs using the properties of circles

• Students solve problems using the relationships between arcs, chords, and diameters

• Students solve problems using inscribed angles

 

Module 11: Measurement

Learning Targets

• Students find areas of quadrilaterals by using the formulas they derive

• Students find areas of regular polygons by using the formulas they derive

• Students find areas of circles and sectors by using the formulas they derive

• Students find surface areas of prisms, cylinders, pyramids, cones, and spheres and composites of these shapes using the formulas they derive

• Students find measures of similar figures and solids by using scale factors

• Students solve application problems involving density by using area and volume

Module 1: Algebra I Review, Relations & Functions

Learning Targets

• Students determine the continuity of functions and whether functions are one-to-one

• Students determine linearity, intercepts and symmetry of functions

• Students identify extrema and end behavior of functions

• Students sketch graphs of functions and compare two functions represented in different ways

• Students graph linear functions and inequalities in two variables

• Students write and graph piecewise-defined, step and absolute value functions

• Students identify and use transformations of functions

 

Module 2: Linear Equations, Inequalities & Systems

Learning Targets

• Students solve linear equations and inequalities in one variable

• Students solve equations and inequalities involving absolute value algebraically and graphically

• Students write linear equations in standard, slope-intercept, and point-slope form

• Students solve systems of equations by graphing, substitution, and elimination

• Students solve systems of inequalities in two-variables

• Students use linear programming to find maximum and minimum values of a function

Module 3: Quadratic Functions

Learning Targets

• Students graph quadratic functions

• Students solve quadratic equations by graphing

• Students perform operations with pure imaginary and complex numbers

• Students solve quadratic equations by factoring

• Students simplify quadratic expressions by using the Square Root Property and completing the square

• Students use the quadratic formula and discriminant to solve quadratic equations and determine the number and type of roots

• Students solve a system of linear and quadratic equations

Module 4: Polynomials & Polynomial Functions

Learning Targets

• Students analyze polynomial functions by examining key features and graphing

• Students add, subtract, multiply polynomials

• Students divide polynomials using long and synthetic division

 

Module 5: Polynomial Equations

Learning Targets

• Students solve polynomial equations by graphing

• Students solve polynomial equations by factoring and by writing them in quadratic form

• Students evaluate and factor functions using the Remainder and Factor Theorem

• Students determine the number and types of roots of polynomial equations, find zeros of polynomial functions

 

Module 6: Inverse & Radical Functions

Learning Targets

• Students simplify operations of functions, and determine compositions of functions

• Students graph and find inverse functions

• Students simplify expressions involving radicals and rational exponents

• Students graph and analyze square root and cube root functions

• Students simplify and perform operations with radical expressions

• Students solve radical equations algebraically and by graphing

Module 7: Exponential Functions

Learning Targets

• Students graph exponential growth and decay functions

• Students solve exponential equations algebraically and by graphing

• Students analyze expressions and functions involving the natural base e

• Students generate geometric series and find their sums

• Students choose the best function type to model sets of data by using technology

 

Module 8: Logarithmic Functions

Learning Targets

• Students write and evaluate logarithms and graph logarithmic functions

• Students simplify logarithmic expressions  and solve logarithmic equations

• Students simplify natural logarithmic expressions and solve natural logarithmic equations

• Students write exponential growth and decay equations and solve them by using logarithms

 

Module 9: Rational Functions

Learning Targets

• Students add, subtract, multiply and divide rational expressions

• Students graph and analyze reciprocal and rational functions

• Students recognize and solve direct, joint, inverse and combined variation equations

• Students solve rational equations algebraically and graphically

Unit 1: Numbers and Number Sense

Learning Targets - 

• Students recognize and write whole numbers and understand their place value

• Students compare and order numbers effectively

• Students round numbers and estimate quantities

• Students represent numbers on a number line

 

Unit 2: Basic Operations and Problem Solving

Learning Targets

• Students add and subtract whole numbers, both with and without regrouping

• Students multiply and divide single-digit and two-digit numbers

• Students solve word problems using addition, subtraction, multiplication, and division

• Students apply these operations to real-life situations

Unit 3: Fractions and Decimals

Learning Targets

• Students identify, compare, and order fractions

• Students add and subtract fractions with like denominators

• Students convert fractions to decimals and vice versa

• Students relate fractions and decimals to real-world contexts

 

Unit 4: Measurement and Geometry

Learning Targets

• Students use units of measurement for length, weight, and capacity

• Students measure and convert using customary and metric units

• Students identify 2D and 3D shapes

• Students grasp basic geometry concepts such as lines, angles, and symmetry

Unit 5: Time and Money

Learning Targets - 

• Students tell time, both analog and digital, to the minute

• Students calculate elapsed time and perform time conversions

• Students identify and count money, including coins and bills

• Students make change and solve money-related problems effectively

 

Unit 6: Data and Graphs

Learning Targets - 

• Students collect and organize data systematically
• Students create and interpret bar graphs and pictographs

• Students read and analyze simple tables and charts

• Students predict and draw conclusions from data

Unit 7: Introduction to Pre-Algebra

Learning Targets - 

• Students solve variables and expressions

• Students evaluate simple algebraic expressions

• Students solve basic one-step equations

• Students apply pre-algebra concepts to real-life scenarios

 

Unit 8: Comprehensive Review and Reinforcement

Learning Targets - 

• Students review and consolidate previously learned mathematical concepts

• Students engage in targeted practice and reinforcement tailored to individual needs

• Students​​​​​​​ apply math skills to functional contexts and real-world situations

Chapter R: Review Topics

Learning Targets

• Students use interval and set notation

• Students manipulate polynomial expressions

• Students apply exponent rules

• Students solve any equation:  linear, quadratic, polynomial, absolute value, radical

• Students find and use the discriminant of a quadratic

• Students solve and interpret inequalities

 

Chapter 1: Functions & Relations

Learning Targets

• Students identify whether a relation is a function

• Students graph a circle given the general equation of a circle

• Students write the general equation of a circle

• Students name the domain and range limitations of a function

• Students find and use the average rate of change

• Students apply linear equations

• Students utilize linear regression to make predictions

• Students recognize and transform basic functions

• Students analyze piecewise-defined functions

• Students add/ subtract/ multiply/ divide functions with each other

• Students compose functions

Chapter 2: Polynomials & Rational Functions

Learning Targets

• Students analyze and use quadratic functions

• Students sketch the graph of a polynomial function

• Students divide polynomial expressions

• Students apply the Fundamental Theorem of Algebra

• Students use the equation of a rational function to identify asymptotes

• Students graph a rational function

 

Chapter 3: Exponential & Logarithmic Functions

Learning Targets

• Students find the inverse of a function

• Students graph, evaluate, and apply exponential functions

• Students evaluate and graph logarithmic functions

• Students apply the properties of logarithms

• Students apply the change of base formula for logarithms

• Students solve exponential and logarithmic equations

• Students create models for exponential growth and decay

 

Chapter 8: Systems of Equations & Inequalities

Learning Targets

• Students apply and solve systems of linear equations with two variables

• Students apply and solve systems of linear equations with three variables

• Students execute partial fraction decomposition

• Students apply and solve systems of nonlinear equations

• Students set up and solve linear programming applications

Chapter 9: Matrices & Determinants & Applications

Learning Targets

• Students write an augmented matrix and use it to solve problems

• Students identify inconsistent systems

• Students solve and apply systems with dependent equations

• Students execute arithmetic operations with matrices

• Students identify and use inverse matrices

• Students evaluate the determinant of a matrix

 

Chapter 4: Trigonometric Functions

Learning Targets

• Students use radians to study angles and circles

• Students apply trigonometric functions to the unit circle

• Students apply trigonometric functions to situations which translate to right triangles

• Students evaluate trigonometric functions of any angle

• Students graph sine and cosine functions, to include transformations

• Students graph secant, cosecant, tangent, and cotangent functions, to include transformations

• Students manipulate equations using the inverse trigonometric functions

Chapter 5: Analytic Trigonometry

Learning Targets

• Students use trigonometry in algebra

• Students apply the sum and difference formulas for trigonometry

• Students use the double angle, half angle, and power reducing formulas

• Students use identities to translate trigonometric function products to sums, and vice versa

• Students solve trigonometric equations

 

Chapter 6: Applications of Trigonometric Functions

Learning Targets

• Students solve applications of right triangles

• Students apply the Law of Sines

• Students apply the Law of Cosines

 

Chapter 7: Trigonometry Applied to Polar Coordinate Systems & Vectors

Learning Targets

• Students translate between polar and Cartesian coordinates

• Students graph polar equations

• Students manipulate complex numbers using polar form

• Students interpret vectors geometrically

• Students break vectors into components

• Students apply vector math

• Students compute and apply the dot product

Chapter 1: The Nature of Statistics

Learning Targets

• Students demonstrate knowledge of statistical terms

• Students differentiate between the two branches of statistics

• Students identify types of data

• Students identify measurement level for each variable

• Students identify four sampling techniques

• Students explain the difference between an observational and experimental study

• Students explain how statistics can be used and misused

• Students explain the importance of computers and calculators in statistics

 

Chapter 2: Frequency Distributions & Graphs

Learning Targets

• Students organize data using a frequency distribution

• Students represent data in frequency distributions graphically using histograms, frequency polygons and ogives

• Students represent data using bar graphs, Pareto charts, time series graphs, pie graphs, and dot plots

• Students draw and interpret a stem and leaf plot

Chapter 3: Data Description

Learning Targets

• Students summarize data using measures of central tendency such as mean, median, mode, and midrange

• Students describe data using measures of variation such as the range, variance, and standard deviation

• Students identify the position of a data value in a data set using various measures of position such as z scores, percentiles, deciles, and quartiles

• Students discover and describe various aspects of data using the techniques of exploratory data analysis including boxplots and five-number summaries

 

Chapter 4: Probability & Counting Rules

Learning Targets

• Students determine samples spaces and find the probability of an event using classical probability or empirical probability

• Students find the probability of compound events using addition rules

• Students find the probability of compound events using multiplication rules

• Students find the conditional probability of an event

• Students find the total number of outcomes in a sequence of events using the fundamental counting rule

• Students find the number of ways that r objects can be selected from n objects using the permutation rule

• Students find the number of ways that r objects can be selected from n objects without regard to order using the combination rule

• Students find the probability of an event using the counting rules

 

Chapter 5: Discrete Probability Distributions

Learning Targets

• Students construct a probability distribution for a random variable

• Students find the mean, variance, standard deviation, and expected value for a discrete random variable

• Students find the exact probability X successes in n trials of a binomial experiment

• Students find the mean, variance, and standard deviation for the variable of a binomial distribution

• Students find the probabilities for outcomes of variables using the Poisson, hypergeometric, geometric, and multinomial distributions

Chapter 6: The Normal Distribution

Learning Targets

• Students identify the properties of the normal distribution

• Students identify distributions and symmetric or skewed

• Students find the area under the standard normal distribution given various z values

• Students find probabilities for a normally distributed variable by transforming it into a standard normal variable

• Students find specific data values for given percentages using the standard normal distribution

• Students solve problems involving sample means for large samples using the central limit theorem

• Students compute probabilities for a binomial variable using the normal approximation

 

Chapter 7: Confidence Intervals & Sample Size

Learning Targets

• Students find the confidence interval for the mean when the population standard deviation is known

• Students determine the minimum sample size for finding a confidence interval of the mean

• Students find the confidence interval of the mean when the population standard deviation is unknown

• Students find the confidence interval for a proportion

• Students determine the minimum sample size for finding a confidence interval for a proportion

• Students find a confidence interval for a variance and a standard deviation

Chapter 8: Hypothesis Testing

Learning Targets

• Students demonstrate knowledge of terms used in hypothesis testing

• Students state the null and alternative hypothesis

• Students find critical values for the z test

• Students state the five steps used in hypothesis testing

• Students test means when population standard deviation is known using the z test

• Students test means when population standard deviation is unknown using the t test

• Students test proportions using the z test

• Students test variances or standard deviations using the chi-square test

• Students test hypotheses using confidence intervals

• Students explain the relationship between type I and type II errors and the power of a test

 

Chapter 9: Testing the Difference Between Two Means, Two Proportions, & Two Variances

Learning Targets

• Students test the difference between two means using the z test

• Students test the difference between two means for independent samples using the t test

• Students test the difference between two means for dependent samples

• Students test the difference between two proportions

• Students test the difference between two variances or standard deviations