Unit 3
Algebra II – Trig MA4300
2-1 Represent Relations & Functions
2-1 Objectives:
 Recall relations, functions, domain, & range.
 Recall ways to represent relations (graph, table, rule, mapping).
 Identifying the domain and range of functions using an equation & a graph.
 Evaluating functions for a given value of x (ex. f(3) = ?) and finding
elements of the domain when given values of the range (ex. f(x) = 8).
2-1 Activities:
 Use Sasinschool online activity to recall and take notes on relations &
functions.
 Evaluate functions algebraically and graphically.
 Use graphing calculator to graph functions and determine the domain,
range, and evaluate the function for given values
2-1 Assessments:
 Do-nows to assess student understanding of basic concepts.
 Homework assignments
2-1 Worksheets
 2-1 Quiz on Relations & Functions
 Ongoing Review Exercises to spiral learned concepts.
Web Resources
Tutorials
http://www.purplemath.com/modules/fcns.htm
http://www.themathpage.com/aprecalc/functions.htm
http://score.kings.k12.ca.us/lessons/functions.html (would be good intro for alg I)
http://archives.math.utk.edu/visual.calculus/0/functions.11/
http://www.regentsprep.org/Regents/math/algtrig/ATP5/indexATP5.htm
Interactive Lessons on functions
Explorelearning – Intro to functions
Sasinschool – new online curriculum for core curriculum standards
http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@functions&cf=activity
http://www.analyzemath.com/precalculus.html
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30_function.ht
m
http://www.coolmath.com/algebra/Algebra1/index.html#Algebra_1:_Functions
SAT Review of Functions with practice problems
http://www.collegeboard.com/student/testing/sat/prep_one/math_review_alg/pracStart.html
2-2 Find Slope & Rate of Change
2-2 Objectives:
 Recall finding slope of a line from a graph and given points on a line.
 Find missing coordinate when given slope and another point (backwards
slope problems).
 Recall parallel lines have the same slope and perpendicular lines have
slopes that are opposite reciprocals.
 Application of slope as rate of change in real-life problems.
 Use and find models that illustrate rate of change.
2-2 Activities:
 Take notes to recall basics of slope – provide online tutorials for review.
 Use graphing calculator with equations that model real-life situations to
find rate of change.
2-2 Assessments:
 Do-nows to assess understanding of basic concepts
 Homework assignments
2-2 Worksheets
 Quiz (content included in Quiz 2-2 & 2-3)
 Ongoing Review Exercises to spiral learned concepts
Web Resources
Slope tutorials
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Rate.htm
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Llines.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut
15_slope.htm
http://cs.selu.edu/~rbyrd/math/slope/ with self-quiz
http://golf.about.com/cs/rulesofgolf/a/hfaq_whyslope.htm (real-life question why is the slope rating called “slope”?)
Sasinschool – Audio explanation of slope of vertical & horizontal lines – Quick
Launch 1287
2-3 Graph Equations of Lines
2-3 Objectives:
 Recall graphing linear equations by using a table of values, x & yintercepts, and slope-intercept form.
 Use the graphing calculator to graph linear functions – discuss how to
locate x & y-intercepts, find given values for x, and set window for
specific situations.
2-3 Activities:
 Recall methods of graphing linear equations by taking notes and completing
sample problems from PowerPoint on Graphing Linear Equations.
 Use the graphing calculator and Grapher to check student graphs.
 Pairs – Share Activity to assess student understanding of all methods of
graphing.
 Green Globs
2-3 Assessments:
 Do-now WS to assess understanding of basic graphing concepts and their
applications.
 Homework assignments:
2-3 Worksheets
 Quiz 2-2 & 2-3 (Slope and Graphing Linear Equations)
 Communicator activities to review basic concepts.
 Ongoing Review Exercises to spiral learned concepts.
Web Resources
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Graphing Lines online activity with quiz
http://enlvm.usu.edu/ma/nav/toc.jsp?sid=__shared&cid=emready@eqns_lines
&cf=activity
http://www.terragon.com/tkobrien/algebra/ (with project)
Graphing Lines tutorials (some with online quizzes)
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines2.htm
http://www.math.com/school/subject2/lessons/S2U4L3GL.html
http://www.purplemath.com/modules/graphlin.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_a
lg_tut21_graph.htm
http://www.brainpop.com/math/algebra/graphinglinearequations/preview.weml
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearEqGraphin
g.xml
Using a graphing calculator
http://www.wonderhowto.com/how-to/video/how-to-graph-equations-on-theti-83-calculator-246434/view/ (video)
http://www.mathbits.com/MathBits/TISection/Algebra1/EquationsLines.htm
http://www.mathbits.com/MathBits/TISection/General/BasicGraphing.htm
http://www.mathbits.com/MathBits/TISection/General/GraphingTidbits.htm
2-4 Write Equations of Lines
2-4 Objectives:
 Write equations of lines using slope-intercept form and point-slope form.
 Write equations of lines in Standard & General form.
 Write equations for real-life applications of linear equations.
2-4 Activities:
 Guided practice to recall writing equations of lines using slope-intercept
form and point-slope form.
 Class work group activity – students use given information to write
equations for real-life applications and interpret the results of the
graphs.
2-4 Assessments:
 Do-now WS to assess understanding of basic concepts.
 Homework assignments
2-4 Worksheets
 Quiz 2-4 (Content included with Scatter Plots)
 Ongoing Review Exercises to spiral learned concepts.
 Linear Function Enrichment Project
Web Resources
 Quia Activity – Linear Equations (review of slope & writing linear
equations)
http://www.quia.com/rr/132867.html
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Algebra vs the Cockroaches
http://hotmath.com/hotmath_help/games/kp/kp_hotmath_sound.swf
2-6 Draw Scatter Plots & Best-Fitting Lines
2-6 Objectives:
 Fit lines to data in scatter plots.
 Determine if data has a positive, negative, or no correlation.
 Model real-life applications with scatter plots.
 Use graphing calculator to find a linear regression.
2-6 Activities:
 Find line of best fit by hand from given data.
 Find line of best fit using a graphing calculator to find a linear regression.
 Interpolate and extrapolate to make predictions about given data.
2-6 Assessments:
 Do-nows to assess understanding of basic concepts
 Homework assignments
1-3 Solving Equations WS
1-3 Word Problems WS
 Quiz 2-4 & 2-6 (Writing Equations of Lines & Scatter Plots)
 Ongoing Review Exercises to spiral learned concepts.
Web Resources:
 Websites for Scatter Plots
 http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/indexAD4.ht
m
 http://www.explorelearning.com
 http://www.purplemath.com/modules/scattreg.htm
 http://www.internet4classrooms.com/links_grades_kindergarten_12/scat
ter_plots_math_secondary.htm using excel for scatter plots
2-7 Use Absolute Value Functions & Transformations
2-7 Objectives:
 Graph absolute value functions using a table.
 Sketch absolute value functions recognizing vertical and horizontal
translations, reflections over the x-axis, and vertical stretches or shrinks.
2-7 Activities:
 Sketch graphs of absolute value functions using tables to recognize the
various transformations.
 Use graphing calculator to graph absolute value functions & their
transformations.
2-7 Assessments:
 Do-nows to assess understanding of basic concepts
 Homework assignments
2-7 Graphing Worksheets
 Quiz 2-7 (Include this content with graphing linear inequalities)
 Ongoing Review Exercises to spiral learned concepts.
Web Resources
Absolute Value Tutorials & Practice
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_AbsoluteValueGrap
hing.xml
http://www.purplemath.com/modules/graphabs.htm
http://www.joemath.com/applets/abs/
Using the Graphing Calc. for Abs. Value
http://mathbits.com/Mathbits/TISection/Algebra2/absolutevalue.htm
Ready-Made GSP for Absolute Value www.mathbits.com
2-8 Graph Linear Inequalities in Two Variables
2-8 Objectives:
 Recall graphing of linear inequalities.
 Use graphing calculator and Grapher to graph linear inequalities.
 Write linear inequalities to model real-life situations.
2-8 Activities:
 Graph linear inequalities and state possible solutions.
 Matching linear inequalities with graphs.
2-8 Assessments:
 Do-nows to assess understanding of basic concepts
 Homework assignments
2-8 Worksheets
 Quiz 2-7 & 2-8 (Graphing Absolute Value Equations & Linear Inequalities)
 Ongoing Review Exercises to spiral learned concepts.
Web Resources
 Graphing Linear Inequalities Tutorials & Practice
 http://www.explorelearning.com/index.cfm?method=cResource.dspView
&ResourceID=142
 http://www.purplemath.com/modules/ineqgrph.htm
 http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra
/beg_alg_tut24_ineq.htm
 http://www.regentsprep.org/Regents/math/ALGEBRA/AE85/indexAE85
.htm
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http://www.mathwarehouse.com/algebra/linear_equation/linearinequality.php
http://www.regentsprep.org/Regents/math/ALGEBRA/AE85/PracGr.ht
m
Using the Graphing Calc. for Graphing Linear Inequalities
http://mathbits.com/mathbits/tisection/Algebra1/linearinequ2.htm
Chapter 2 Review
Chapter 2 Test
2-5 – 8-1 Direct, Inverse, & Joint Variation
2-5 & 8-1 Objectives:
 Use equations for direct, inverse, & joint variation to find the constant of
variation.
 Use equations for direct, inverse, & joint variation to find unknown values.
 Use equations for direct, inverse, & joint variation to model real-life
situations and solve problems that involve varying quantities.
2-5 & 8-1 Activities:
 Graph data to illustrate the difference between direct & inverse
variation.
 Take guided notes using specific examples to illustrate which equation to
use to solve problems.
 Solve problems that illustrate applications of the three forms of
variation.
2-5 & 8-1 Assessments:
 Do-nows to assess understanding of basic concepts
 Homework assignments
2-5 & 8-1 Practice WS
 Quia Activity on Variation.
 Quiz 2-5 & 8-1 (Direct, Inverse, & Joint Variation)
 Ongoing Review Exercises to spiral learned concepts.
Web Resources
Variation tutorials & practice
 http://www.purplemath.com/modules/variatn.htm
 http://hotmath.com/help/gt/genericalg2/section_7_2.html (practice)
 http://teachers.henrico.k12.va.us/math/HCPSAlgebra2/9-2.htm
(includes PPTs, HW, and online review)
 http://emathlab.com/Algebra/Functions/InvJntVar.php (practice)
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http://sriamanmathblog.blogspot.com/2009/05/direct-and-inversevariation.html
http://www.regentsprep.org/Regents/math/ALGEBRA/AO4/indexAO4.h
tm
http://www.regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.ht
m
www.classzone.com (8.1 Animated Activites for Alg II book)
Variation Quia Activity http://www.quia.com/rr/154729.html
Variation PowerPoints – On webpage