# Properties of Exponents Worksheets by obr77693

VIEWS: 195 PAGES: 4

• pg 1
```									Enriched Algebra A      September - Linear Models                              October - Linear Graphing                                          November - Linear Inequalities
Essential Questions     How do you use scatter plots to find                   How do we create graphs given the equation of a line?              What is the difference between equations and
correlations between variables? How do                 How can we find the linear equation for a specific                 inequalities? How can real-life situations be
you write the equation of a line? How do               graph? How can we use graphs to model real world                   modeled through the use of inequalities? How
you use an equation to make predictions                scenarios? What is a function, and how can it be                   does absolute value relate to linear equations?
about data?                                            evaluated?                                                         How do you make and use a stem & leaf plot
and a box & whisker plot to order data and
find measures of central tendency?

Content                1) Scatter Plots showing:                               1) Graph an equation with one & two variables (slope –             1) Solving & graphing simple and compound
 no correlation                                          intercept graphs)                                                 inequalities in one variable
 positive correlation                                2) Write the equation of the line for a given graph                2) Problem solving using inequalities and
 negative correlation                                3) Determine the intercepts for an equation                           compound inequalities
2) Data Collection                                      4) Sketch graphs using intercepts                                  3) Graphing linear inequalities in two variables
3) Use scatter plots to make predictions                5) Determine possible solutions for an equation                    4) Solving absolute value equations and
4) Draw the line of best fit                            6) Parallel & Perpendicular Lines                                     inequalities
5) Calculate the slope of a line from a table, from     7) Functions & Relations                                           5) Number line graphs for absolute value
a graph and from the formula                         8) Evaluating functions                                               inequalities
6) Write the equation of a line:                        9) Identify the Domain & Range of a function                       6) Graphs of absolute value equations
 given point & slope                                 10) TI – 84 Usage                                                  7) Stem & Leaf Plots
 given 2 points                                                                                                         8) Box & Whisker Plots
7) Interpolation & Extrapolation within data                                                                               9) Measures of Central Tendency
8) TI – 84 Training/Navigator Training

Skills                 1) Create graphs of scatter plots (by hand at first,    1) Graph equations in one variable                                 1) Solve and graph inequalities in one variable
then mainly on the TI-84) & make general             2) Write the equation for the vertical or horizontal graph         2) Solve and graph compound inequalities
predictions about trends                             3) Sketch a 2 variable equation using slope-intercept form         3) Use and write inequalities to model real life
2) Determine the correlation between the                    (check graphs using the TI-84)                                    situations
variables                                            4) Write the equation of the line given the graph                  4) Create graphs for 2 variable inequalities
3) Draw the line of best fit                            5) Find the intercepts of an equation                              5) Solve & graph absolute value equations
4) Find the slope of the best fitting line, using 2     6) Create a graph using only the intercepts                        6) Solve & graph absolute value inequalities
data points                                          7) Determine possible solutions for an equation or modeled         7) Organize data using a stem & leaf plot
5) Write the equation of the best fitting line (by          situation                                                      8) Determine the mean, median & mode of a set of
hand & using calculator)                             8) Use intercepts, and intercept graphs, to model real world          numbers
6) Make predictions using interpolation &                   scenarios                                                      9) Arrange data using a box & whisker plot
extrapolation with the equation                      9) Explore relationships between parallel & perpendicular
7) Collect data, create graphic models of data,             lines using graphic & algebraic means
compute & graph trend line, use line to make         10) Identify relations that are functions, graphically and
predictions for data                                     using a set of ordered pairs (vertical line test)
11) Evaluate functions for a given variable
12) Identify the restrictions of a function or relation (domain
& range)
13) Apply domain & range concepts to determining the
appropriate window for equations & data
CH                      3.11 (3,4,6,7); 3.14 (5,6,10); 3.17 ( 2-5); 3.15       3.11 (3,5); 3.14 (1,2); 3.15 (4); 3.17 (2,3); 3.18 (1,2,4,7);      3.14 (8,9); 3.11 (3,5); 3.17 (1,2,3); 3.18 (1,2,4,6,7);
Standards/Benchmarks    (1,6); 3.12 (7,13,15); 3.13 (13-20)                    3.19 (1,2)                                                         3.19;(1,2,3)
Assessments            1) Chapter Test & Quizzes                              1)   Chapter Test & Quizzes                                        1) Chapter test & Quizzes
2) TI-84/Navigator Activities                          2)   TI-84/Navigator Activities                                    2) TI-84/Navigator Activities
3) Homework & Practice Worksheets                      3)   Barbie Bungee Lab                                             3) Homework & Practice Worksheets
4)   Homework & Practice Worksheets
Enriched Algebra A      December - Linear Systems                            January - Exponential Functions                                 February / March - Polynomials
Essential Questions     How do you solve a system of linear                  How do you use the properties of exponents in                   How do you recognize and apply the sum,
systems by: graphing, substitution, & linear         algebra? How do you use exponential growth and                  difference, and product of polynomials in
combination? How do you use linear                   decay to model real-life situations? What is the                real-life situations? How do you break a
systems to model and compare real life               difference between a linear and exponential model?              polynomial into factors? How do you use
problems?                                            How do you write the equation for an exponential                factoring to solve a quadratic function?
trend?
Content                1)   Solving a system by graphing.                   1)   Multiplication properties of exponents.                    1) Adding, subtracting, & multiplying polynomials
2)   Solving a system by substitution.               2)   Negative and Zero exponents                                2) Multiplying polynomials, including special cases
3)   Solving by linear combination.                  3)   Division properties of exponents                           3) Perimeter & Area of geometric figures with
4)   Problem solving using systems.                  4)   Growth and Decay Graphs                                       unknown sides
5)   Solving Special Types of systems.               5)   Problem solving                                            4) Factoring using GCF
6)   Solving systems of linear inequalities.                                                                         5) Factoring special products and quadratic
trinomials (a = 1 & a ≠ 1)
6) Factoring by grouping
Skills                 1) Solving systems by graphing (by hand and          1) Evaluate powers                                              1) Classify polynomials by degree & number of
using a TI-84 – intersection function)            2) Simplify algebraic expressions using properties of              terms
2) Solving systems by substitution (check               exponents                                                    2) Add & Subtract Polynomials
solution graphically on TI-84)                        Product of powers                                          3) Multiply Polynomials by 3 methods:
3) Solving systems by linear combination (check          Power of a power                                              distribution, sum & difference, & square of a
solution graphically on TI-84)                        Power of a product                                            binomial
4) Special Systems – graphic representations             Negative exponents                                             Distribution
 1 solution (2 intersecting lines)                   Zero as an exponent                                            Sum & Difference
 no solution (2 parallel lines)                      Quotient of powers                                             Binomials Squared
 infinitely many solutions (2 coinciding             Power of a quotient                                        4) Factoring special products and quadratic
lines)                          3) Exponential Growth & Decay Models                               trinomials
5) Special Systems – algebraic representation            Real life applications (i.e. dosage of medication in           GCF
 1 solution (a specific point of intersection)        bloodstream, savings account, population growth,               Difference of 2 squares
 no solution (false statement)                        depreciation of value, increase & decrease in company          Perfect square trinomials
 infinitely many solutions (true statement)           sales, etc.)                                                   Quadratic trinomials (a = 1 & a ≠ 1)
6) Identifying the number of solutions of a linear   4) Graphing exponential functions                               5) Factoring by grouping
system                                                T chart (x values of -2, -1, 0, 1, 2)
7) Solving a system of linear inequalities               TI – 84
(graphically by hand & on TI-84)                      Identifying if functions model growth or decay
8) Analyze, write and solve systems of equations         Trend of y values, as x increases & as x decreases, for
and inequalities                                       the graphs
 Using slope intercept form
 Using standard form                              5) Given a graph, write the exponential model (   y  a bx )
CH                      3.11 (3,5,7); 3.14 (3,8,9); 3.17 (2,3,4,5);          3.11 (3,5);3.12 (3); 3.17 (1,2,3); 3.18 (1,2,4,6,7);            3.11 (2,3);3.14 (11,12); 3.17 (2,3); 3.18
Standards/Benchmarks    3.18 (1,2,3,4,7); 3.19 (1,2,3,4)                     3.19 (1,2); 3.20 (1,2)                                          (1,2,4,7); 3.19 (1,2,3)
Assessments            1)   Chapter test & Quizzes                          1) Chapter test & Quizzes                                       1) Chapter test & Quizzes
2)   TI-84/Navigator Activities                      2) TI-84/Navigator Activities                                   2) TI-84/Navigator Activities
3)   CBL Lab- Meet You at the Intersection           3) Homework & Practice Worksheets                               3) Homework & Practice Worksheets
4)   Homework & Practice Worksheets
Enriched Algebra A      March / April - Quadratic Functions                 April / May - Rational Expressions                               June - Radicals & Geometric Ideas
Essential Questions      How can real-life situations be modeled            How do you simplify, multiply/divide, add/subtract,              How do you find the distance between two
with quadratic equations? How do you                and solve rational expressions?                                  points? How do you find the mid-point of a
create graphic models of quadratics? How                                                                             segment? How do you find the length of a
do you solve & graph quadratic equations                                                                             side using a right triangle?
without factoring? How you do you
Content                1) Operations with Radicals                        1) Solving proportions (that create both linear & quadratic       1) Pythagorean Theorem
2) Square roots, square root method for solving        equations)                                                    2) Distance Formula
quadratics                                      2) Simplifying rational expressions                               3) Mid-Point Formula
3) Graphs of quadratic equations, by finding       3) State domains for original & simplified expressions
specific characteristics                        4) Geometric Probability
4) Quadratic formula                               5) Multiplying & Dividing Rational Expressions
5) Vertical Motion Models                          6) Writing & using rational models with multiplication &
6) Using the discriminate                              division
8) Writing & using rational models with addition &
subtraction
9) Dividing polynomials
10) Solving rational equations
Skills                 1) Operations with Radicals                        1) Solving proportions (that create both linear & quadratic       1)   Pythagorean Theorem
Addition & Subtraction, Multiplication,        equations)                                                    2)   Real Life application for Pythagorean Theorem
Division, Rationalizing denominators (with 2) Simplifying rational expressions – using GCF, special          3)   Distance Formula
and without conjugate)                        cases, & trinomial factoring                                  4)   Real Life application for Distance Formula
2) Evaluating square roots in two ways: exact & 3) State domains for original & simplified expressions in set        5)   Mid-Point Formula
calculator                                         notation                                                      6)   Real Life application for Mid-Point Formula
3) Solving quadratic equations by square roots     4) Geometric Probability (using rectangles, circles &
(i.e. 3(2 x  4)  6  21 )                      triangles)
2
5) Real world application for geometric probability
4) Solving using the quadratic formula
6) Multiplying & Dividing Rational Expressions (include
5) Standard & Vertex forms of quadratic
functions                                                                        3  x x2  9
difficult simplification i.e.                )
6)       Graphs of quadratic equations, by finding                                        4x2        2
     Vertex                                         7) Writing & using rational models with multiplication &
     Concavity & Max/Min identification                 division (i.e. rational models for averages, total sales,
X-intercepts (by factoring, square root            number of units, etc.)
method, & quadratic formula)                   8) Adding & Subtracting rational expressions (finding LCD)
     Y-intercept                                    9) Writing & using rational models with addition &
     Axis of symmetry                                   subtraction (perimeter, total distance traveled, total time
     Point symmetrical to y-intercept                   traveled, etc.)
     Domain & Range                                 10) Dividing polynomials (monomial & long division)
7) Vertical Motion models                          11) Solving rational equations (finding LCD)
8) Using the discriminate, determine the
possibilities of solutions for a quadratic
9) Use real life applications to model and solve