Algebra

__**Objectives**__:
 * ===Simplify an algebraic expression.===
 * ===Multiply binomials mentally.===
 * ===Expand a binomial using the binomial theorem.===
 * ===Factor a polynomial.===
 * ===Evaluate an algebraic expression.===
 * ===Write spreadsheet expressions in ordinary algebraic notation.===
 * ===Use a spreadsheet to evaluate (including the replicate command).===
 * ===Use binomials to answer genetic applications.===
 * ===Solve equations (both linear and quadratic).===
 * ===Use a calculator to solve an equation.===
 * ===Solve linear inequalities.===
 * ===Solve applied problems; in particular, those involving number, distance, and Pythagorean relationships.===
 * ===Set up and simplify ratios.===
 * ===Compare the size of fractions, decimals, and radicals.===
 * ===Solve proportion problems.===
 * ===Be able to change forms: fractions/decimals/percents.===
 * ===Estimate percents.===
 * ===Solve applied percent problems.===
 * ===Be able to change forms: fractions/decimals/percents.===
 * ===Estimate percents.===
 * ===Solve applied percent problems.===
 * ===Use problem-solving methods to answer uncategorized questions.===

**Video:**

 * Adding and Subtracting Polynomials** (time: 7:47)
 * Multiplying Polynomials** (time: 1:53)
 * Binomial Theorem** (time: 9:40)



**Al-Khwarizmi:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html**



**Abel:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Abel.html**

**Reference Topic Sites**:

 * Introduction to polynomials.**
 * @http://www.purplemath.com/modules/polydefs.htm**


 * Introduction to multiplying polynomials.**
 * @http://www.purplemath.com/modules/polymult.htm**


 * Website discussing polynomials and areas.**
 * @http://argyll.epsb.ca/jreed/math9/strand2/2211.htm**


 * Website that provides some practice polynomial terminology, and with working with polynomials.**
 * @http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut25_poly.htm**


 * Website that provides interactive practice with the binomial theorem.**
 * @http://www.themathpage.com/aPreCalc/binomial-theorem.htm**


 * An interactive version of Pascal's Triangle.**
 * @http://mathforum.org/dr.cgi/pascal.cgi**

Video:

 * Factoring a trinomial** (time: 2:36)

**Galois:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Galois.html**



**Cauchy:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Cauchy.html**



**Fourier:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Fourier.html**

**Reference Topic Sites:**

 * Factoring with areas:**
 * @http://faculty.prairiestate.edu/skifowit/htdocs/manip/alg_tile.htm**

**Practice factoring trinomials using FOIL.** **@http://www.mathwizz.com/algebra/help/help3.htm**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**Practice factoring difference of squares:** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**@http://www.purplemath.com/modules/specfact.htm**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**Extra practice in factoring:** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**@http://www.saab.org/mathdrills/factor.cgi**

**Video:**

 * Evaluate** (time: 4:26)


 * Hardy:**
 * @http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hardy.html**

**Resource Topic Sites:**
<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Evaluation of polynomials.** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://www.purplemath.com/modules/evaluate.htm** <span style="color: #333333; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 11px;"> <span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**This interactive site gives practice with Punnett squares.**  <span style="color: #333333; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 11px;"> <span class="text" style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **http://biology.clc.uc.edu/courses/bio105/geneprob.ht** **m**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Spreadsheet basics:** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://mathforum.org/sum95/math_and/spreadsheets/basics.html**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **One of the most common spreadsheets is Excel (Excel tutorial):** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://www.usd.edu/trio/tut/excel/0.html**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **This cite collects information on spreadsheets with an emphasis of mathematics and statistics education.** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://sunsite.univie.ac.at/Spreadsite/spreaded.html**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Project ideas using a spreadsheet****:** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://mathforum.org/sum95/math_and/spreadsheets/intro.html**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> Equations
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<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Video:**
<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Solve Linear Equations** (time: 6:46) <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Solve Quadratic Equations** (time: 12:03)  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**Descartes:**
 * @http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Descartes.html**

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 * Fermat:**
 * @http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Fermat.html**

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<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">
 * Wiles:**
 * @http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Wiles.html**

** Reference Topic Sites: **
<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**This interactive site is excellent in giving practice solving linear equations with one variable.** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://www.hellam.net/algebra/linear2.html** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**This interactive site gives practice solving quadratic equations. It uses the quadratic formula, and if you input values for a, b, and c for which the expression under the radical (b^2 - 4ac) is less than 0, the quadratic formula will return a complex number (which is beyond the scope of this course). For our use, make sure b^2 - 4ac is not less than zero, and you will obtain the desired result.** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**@http://jblanco_60.tripod.com/**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> **Fermat's last theorem:** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**This is site from the PBS program, "The Proof":**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**@http://www.pbs.org/wgbh/nova/proof/**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;"> **Fermat's last theorem;** <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px; text-align: left;">**@http://www-history.mcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html**  <span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">

**Video:**
<span style="color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"><span style="font-family: arial,helvetica,sans-serif;">Linear Inequalities **(time: 6:25)**

<span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **Website discusses solving linear inequalities:**
 * @http://www.analyzemath.com/Linear_Inequalities/Linear_Inequalities_Tutor.html**

**Interactive site for practicing solving linear inequalities:**
 * http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_OneVariableSolvingInequalities.xm** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">

**Video:**
**Math Strategies** (time: 7:37)



<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">//Hypatia:// <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hypatia.html**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> //Bhaskara:// <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Bhaskara.html**

**Introduction to simple word problems:** **@http://www.algebrahelp.com/lessons/wordproblems/basics/index.htm**

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">**Translating word problems:** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> **@http://www.purplemath.com/modules/translat.htm** <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="display: block; font-family: Arial,Helvetica,sans-serif; font-size: 12px;">

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Ratios, Proportions and Problem Solving
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**Video:**

 * Ratios and Proportions** (time: 3:50)

** Reference Topic Sites: **
**http://www.purplemath.com/modules/ratio.htm**
 * Practice with ratios.**

**http://www.purplemath.com/modules/ratio2.htm**
 * Practice with proportions.**


 * Examples of working with proportions.**
 * @http://www.mathleague.com/help/ratio/ratio.htm**

**Video:**

 * Fractions/Decimals/Percents** (time: 4:59)

**Resource Topic Sites:**

 * Practice converting between decimals and fractions.**
 * @http://cstl.syr.edu/fipse/Decunit/convert/convert.htm**


 * Practice with percents and converting forms.**
 * @http://cstl.syr.edu/fipse/Decunit/percent/percent.htm**