A: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems.

A.1: Students know how to represent and use real numbers.

A.1.b: Estimate the value(s) of roots and use technology to approximate them.

Square Roots

A.1.c: Compute using laws of exponents.

Dividing Exponential Expressions
Multiplying Exponential Expressions

A.1.d: Multiply and divide numbers expressed in scientific notation.

Unit Conversions

A.1.e: Understand that some quadratic equations do not have real solutions and that there exist other number systems to allow for solutions to these equations.

Roots of a Quadratic

B: Students make measurements and collect, display, evaluate, analyze, and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students: understand that most measurements are approximations and that taking repeated measurements reveals this variability; understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement; understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

B.2: Students understand correlation and cause and effect.

B.2.a: Recognize when correlation has been confused with cause and effect.

Correlation

B.2.b: Create and interpret scatter plots and estimate correlation and lines of best fit.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

B.2.c: Recognize positive and negative correlations based on data from a table or scatter plot.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

B.2.d: Estimate the strength of correlation based upon a scatter plot.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

B.3: Students understand and know how to describe distributions and find and use descriptive statistics for a set of data.

B.3.a: Find and apply range, quartiles, mean absolute deviation, and standard deviation (using technology) of a set of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

B.3.b: Interpret, give examples of, and describe key differences among different types of distributions: uniform, normal, and skewed.

Polling: City

B.3.c: For the sample mean of normal distributions, use the standard deviation for a group of observations to establish 90%, 95%, or 99% confidence intervals.

Polling: City

B.4: Students understand that the purpose of random sampling is to reduce bias when creating a representative sample for a set of data.

B.4.a: Describe and account for the difference between sample statistics and statistics describing the distribution of the entire population.

Polling: City
Polling: Neighborhood
Populations and Samples

B.4.b: Recognize that sample statistics produce estimates for the distribution of an entire population and recognize that larger sample sizes will produce more reliable estimates.

Polling: City
Populations and Samples

B.4.c: Apply methods of creating random samples and recognize possible sources of bias in samples.

Polling: City
Polling: Neighborhood
Populations and Samples

B.5: Students understand the relationship of probability to relative frequency and know how to find the probability of compound events.

B.5.b: Find the expected value of events.

Theoretical and Experimental Probability

B.5.c: Find the probability of compound events including independent and dependent events.

Independent and Dependent Events
Theoretical and Experimental Probability

C: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct two-dimensional and three-dimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures students use estimation to check the reasonableness of results.

C.1: Students justify statements about polygons and solve problems.

C.1.a: Use the properties of triangles to prove theorems about figures and relationships among figures.

Isosceles and Equilateral Triangles
Triangle Angle Sum
Triangle Inequalities

C.1.c: Use the Pythagorean Theorem in situations where right triangles are created by adding segments to figures.

Cosine Function
Sine Function
Tangent Function

C.1.d: Use the distance formula.

Circles
Distance Formula

C.2: Students justify statements about circles and solve problems.

C.2.a: Use the concepts of central and inscribed angles to solve problems and justify statements.

Chords and Arcs
Inscribed Angles

C.3: Students understand and use basic ideas of trigonometry.

C.3.a: Identify and find the value of trigonometric ratios for angles in right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

C.3.b: Use trigonometry to solve for missing lengths in right triangles.

Sine, Cosine, and Tangent Ratios

C.4: Students find the surface area and volume of three-dimensional objects.

C.4.a: Find the volume and surface area of three-dimensional figures including cones and spheres.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

C.4.b: Determine the effect of changes in linear dimensions on the volume and surface area of similar and other three-dimensional figures.

Surface and Lateral Areas of Prisms and Cylinders

D: Students use symbols to represent or model quantities, patterns, and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs, and verbal rules choosing the most effective representation and converting among representations.

D.1: Students understand and use polynomials and expressions with rational exponents.

D.1.a: Simplify expressions including those with rational exponents.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

D.1.b: Add, subtract, and multiply polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

D.1.c: Factor the common term out of polynomial expressions.

Factoring Special Products

D.1.d: Divide polynomials by (ax+b).

Dividing Polynomials Using Synthetic Division

D.2: Students solve families of equations and inequalities.

D.2.a: Solve systems of linear equations and inequalities in two unknowns and interpret their graphs.

Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

D.2.b: Solve quadratic equations graphically, by factoring in cases where factoring is efficient, and by applying the quadratic formula.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic

D.2.d: Solve absolute value equations and inequalities and interpret the results.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Compound Inequalities

D.2.e: Apply the understanding that the solution(s) to equations of the form f(x) = g(x) are the x-value(s) of the point(s) of intersection of the graphs of f(x) and g(x) and common outputs in table of values.

Solving Linear Systems (Slope-Intercept Form)

D.2.f: Explain why the coordinates of the point of intersection of the lines represented by a system of equations is its solution and apply this understanding to solving problems.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

D.4: Students understand and interpret the characteristics of functions using graphs, tables, and algebraic techniques.

D.4.a: Recognize the graphs and sketch graphs of the basic functions

D.4.a.2: f(x) = ax_ + bx + c ;

Addition and Subtraction of Functions
Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

D.4.a.3: f(x) = square root of x ;

Radical Functions

D.4.a.4: f(x) = |x| ;

Absolute Value with Linear Functions
Translating and Scaling Functions

D.4.a.6: f(x) = a to the x power ; and

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

D.4.a.7: f(x) = kx + b

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Linear Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

D.4.c: Use concepts such as domain, range, zeros, intercepts, and maximum and minimum values.

Cat and Mouse (Modeling with Linear Systems)
Introduction to Functions
Linear Functions
Logarithmic Functions
Modeling the Factorization of x²+bx+c
Points, Lines, and Equations
Polynomials and Linear Factors
Radical Functions
Roots of a Quadratic
Slope-Intercept Form of a Line

D.4.d: Use the concepts of average rate of change (table of values) and increasing and decreasing over intervals, and use these characteristics to compare functions.

Linear Functions
Points, Lines, and Equations

D.5: Students express relationships recursively and use iterative methods to solve problems.

D.5.a: Express the (n+1)st term in terms of the nth term and describe relationships in terms of a starting point and rule followed to transform one term to the next.

Arithmetic Sequences
Geometric Sequences