Advanced+Algebra+Lesson+Objectives+DAA

Advanced Algebra Lesson Objectives

 * Semester 1 Semester 2 **

**In this chapter you will:**
 * Chapter 0 **
 * **solve problems both on your own and as a group**
 * **use pictures and graphs as problem-solving tools**
 * **learn a four-step process for solving problems with symbolic algebra**
 * **practice strategies for organizing information before you solve a problem.**

0.1The students will:
 * Learn and review multiple ways to solve problems.
 * Introduce a 4-step outline for solving problems
 * Use pictures, diagrams, and graphs as problem-solving tools
 * Find the slope of a line from a graph
 * Find the slope of a line from a pair of points
 * Learn to work in a cooperative group

0.2 The students will:
 * Learn and review symbolic representation in algebra.
 * Translate English phrases into algebraic symbols assigning a variable to each unknown quantity
 * Encounter absolute-value notation
 * Review solving equations and solving systems of equations

0.3 The students will:
 * Learn good ways to organize information
 * Practice using dimensional analysis and unit conversion
 * Solve logic problems
 * Improve at working cooperatively

**In this chapter you will:**
 * Chapter 2 **
 * **create, interpret, and compare graphs of data sets**
 * **calculate numerical measures that help you understand and interpret a data set**
 * **make conclusions about a data set and compare it with other data sets based on graphs and numerical values.**

2.1 The students will
 * Learn about measures of central tendency and box plots.
 * Review mean, median, and mode
 * Learn sigma notation for summation
 * Create box plots from 5-number summaries
 * Create 5-number summaries from box plots
 * Describe the shape and spread of a data set from box plots
 * Use box plots to compare the centers, shapes, and spreads of data sets
 * Construct a data set having various statistics

2.2 The students will
 * Learn about measures of spread
 * Develop a concept of spread (variability)
 * Use a calculator to find standard deviation
 * Derive formulas for standard deviation and variance - find standard deviation by hand
 * Understand deviation from the mean
 * Distinguish measures of spread relative to the mean from measures of spread relative to the median
 * Understand and apply definitions of outlier

2.3 The students will
 * Learn about histograms and percentile ranks
 * Distinguish bar graphs from histograms
 * Find the approximate number of data items, the range, and the median by studying a histogram
 * Understand the effect of different bin widths in histograms
 * Create box plots and histograms in order to analyze specific characteristics of a data set
 * Determine the percentile rank of a data item either from raw data or from a histogram
 * Connect percentile rank and standard deviation

**In this chapter you will:**
 * Chapter 1 **
 * **recognize and visualize mathematical patterns called sequences**
 * **write recursive definitions for sequences**
 * **display sequences with graphs**
 * **investigate what happens to sequences in the long run.**

1.1 The students will
 * Learn about recursively defined sequences
 * Introduce recursive formulas for sequences
 * Explore arithmetic sequences
 * Practice using recursive notation
 * Define and use geometric sequences
 * Use recursively defined sequences to model applications

1.2 The students will
 * Learn about modeling growth and decay
 * Use geometric sequences to model decay
 * Use geometric sequences to model growth

1.3 The students will
 * Learn about limits
 * Explore long run values
 * Begin to understand the concept of limit
 * Investigate shifted geometric sequences

1.4 The students will
 * Learn about graphing sequences
 * Recognize arithmetic and geometric sequences from their graphs
 * Use graphs to check whether a recursive formula is a good model for the data

1.5 The students will
 * Learn about loans and investments
 * Use a recursive formula to model a loan
 * Use a recursive formula to model an investment

**In this chapter you will:**
 * Chapter 3 **
 * **review linear equations in intercept form and point-slope form**
 * **explore connections between arithmetic sequences and linear equations**
 * **find lines of fit for data sets that are approximately linear**
 * **solve systems of linear equations.**

3.1 The students will
 * Learn about linear equations and arithmetic sequences
 * Given a recursive formula, find n for a given u n
 * Graph an arithmetic sequence to locate the intercept and determine the slope
 * Recognize slope as the common difference in an arithmetic sequence;
 * Use the intercept and slope to write a linear equation in x and y
 * Recognize that an arithmetic sequence is always linear

3.2 The students will
 * Learn about slope
 * Use recursion in application contexts
 * Define domain and range

3.3 The students will
 * Learn about fitting a line to data
 * Find a line of fit for data that are approximately linear
 * Use interpolation and extrapolation

3.4 SKIP The students will
 * Learn about the median-median line
 * Practice writing equations for lines through two points
 * Review how to determine the equation of a line parallel to another line
 * Introduce median-median line
 * Compare median-median line to other lines of fit

3.5 SKIP The students will
 * Learn about residuals
 * Define residual, root mean square error
 * Calculate the residual sum from a small number of data points
 * Use residuals to test the fit of a line
 * Calculate the root mean square error for a small number of data points
 * Use the root mean square error to find the error range in the context of a problem

3.6 The students will
 * Learn about linear systems
 * Examine problems involving multiple conditions that must be satisfied simultaneously
 * Understand the visual representation of a solution to a system of equations
 * Solve systems of equations graphically, using the transitive property of equality, and using a table

3.7 The students will
 * Learn about substitution and elimination
 * Solve systems of equations using substitution
 * Explore how the addition and multiplication properties of equations can be used to solve systems of equations by elimination

**In this chapter you will:**
 * Chapter 4 **
 * **interpret graphs of functions and relations**
 * **review function notation**
 * **learn about the linear, quadratic, square root, absolute-value, and semicircle families of functions**
 * **apply transformations - translations, reflections, stretches, and shrinks - to the graphs of functions and relations**
 * **transform functions to model real-world data**

4.1 The students will
 * Learn about interpreting graphs
 * Identify independent and dependent variables
 * Interpret features of a qualitative graph, including rates of change and x- and y-intercepts
 * Decide whether a graph (or a function) is discrete or continuous given a description of the variables
 * Draw a qualitative graph from a context scenario and create a context scenario given a qualitative graph
 * Distinguish between linear change and non-linear change.

4.2 The students will
 * Learn about function notation
 * Define function as "a relation with at most one y-value for any x-value"
 * Review function notation
 * Review the vertical line test for functions
 * Distinguish between functions and relations
 * Define the domain and range of a function.

4.3 The students will
 * Learn about lines in motion
 * Review linear equations
 * Describe translations of a line in terms of horizontal and vertical shifts
 * Write the equation of a translated line using h and k
 * Understand point-slope form as a translation of the line with its equation written in intercept form
 * Apply translations to functions.

4.4 The students will
 * Learn about translations and the quadratic family
 * Define the parent quadratic function y = x 2
 * Determine elements of equations that produce translations of the graphs of parent functions (h and k)
 * Introduce the (non-stretched) vertex form of the graph of a parabola, y = (x - h) 2 + k
 * Define //parabola//, //vertex of a parabola//, and //line of symmetry//.

4.5 The students will
 * Learn about reflections and the square root family
 * Define reflection
 * Define the parent square root function, y = x 1/2
 * Define the square root symbol and function as the positive root
 * Compare f(x), -f(x), f(-x), and -f(-x); Apply the square root function in context
 * Apply reflections to functions in general
 * Symbolically solve the equation a + (x + b) 1/2 = c for x.

4.6 The students will
 * Learn about stretches and shrinks and the absolute value family
 * Define absolute value and its notation, and use it to model distance
 * Define the parent absolute-value function, y = |x|, and the absolute-value family, y = a|x-h| + k
 * Calculate horizontal and vertical stretch or shrink factors from points on the image of a graph
 * Apply horizontal and vertical stretches and shrinks to functions in general.

4.7 The students will
 * Learn about transformations and the circle family
 * Define //unit circle// and derive the equation x
 * Express a circle as two semicircle functions
 * Define //ellipse// as "a vertical and/or horizontal dilation of a circle"
 * Transform a circle to get an ellipse
 * Apply transformations to relations and to a new function expressed in terms of f(x)
 * Summarize transformations - translations, reflections, rotations, and stretches and shrinks.

4.8 The students will
 * Learn about compositions of functions
 * Define composition of functions and learn the notation
 * See transformations of two or three steps as the composition of functions
 * Apply composition to real world contexts
 * Distinguish composition from the product of functions
 * Understand composition both graphically and numerically.

**Chapter 12** **In this chapter you will:**
 * **learn about randomness and the definition of probability**
 * **count numbers of possibilities to determine probabilities**
 * **determine expected values of random variables**

12.1 The students will:
 * Learn about randomness and probability.
 * Define experimental and theoretical probability
 * Simulate experimental probability on a calculator
 * Define and calculate geometric probability.

12.2 The students will:
 * Learn about counting outcomes and tree diagrams.
 * Use tree diagrams as an aid to counting possibilities for compound events
 * Use the multiplication rule for independent events
 * Explore conditional probability.

12.3 The students will
 * Learn about mutually exclusive events and Venn diagrams
 * Explore mutually exclusive events
 * Use Venn diagrams as a tool for breaking down compound events into mutually exclusive events
 * Understand the addition rule for finding the probabilities of events described by a Venn diagram
 * Differentiate between mutually exclusive events and independent events.