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ALGEBRA I Formulas and Applications

ALGEBRA I Formulas and Applications. Presented by: Sheree Horton. Chapter 111. TEKS for Mathematics Subchapter C. High School.

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ALGEBRA I Formulas and Applications

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  1. ALGEBRA IFormulas and Applications Presented by: Sheree Horton

  2. Chapter 111. TEKS for MathematicsSubchapter C. High School 111.32 (c) 3: Algebra I-The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. Performance descriptions: • The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. • The student investigates methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities. • For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities.

  3. Chapter 111. TEKS for MathematicsSubchapter C. High School(continued) 111.32 (c) 4: Algebra I-The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. Performance descriptions: • The student analyzes situations and formulates systems of linear equations to solve problems. • The student solves systems of linear equations using concrete models, graphs, tables, and algebraic methods. • For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations.

  4. Resources Content • http://wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/indes.htm • http://www.amt.canberea.edu.au/polya.html • http://www.ccm.net/~jsruiz/rsteps.html Clip Art • Wave Sound-Applause Microsoft Office/MEDIA/CAGCAT10/j0214098.wav • Arithmetic j0332680.wmf • Academics j0292112.wmf • Academics j0332680.wmf

  5. Learning Objectives After completing this lesson, you should be able to: • Translate an English phrase into an algebraic expression. • Use Polya’s four step process to solve word problems. • Solve a formula for a given variable.

  6. George Polya • Born in Budapest on December 13, 1887 • Earned doctorate from University of Budapest • Took up a position at Eidgenossische Technische Hochschule (ETH) in Zurich (Einstein & Roentgen are amongst its graduates) • Spent a year in England in 1924 in Oxford-ending in a publication (in collaboration with Hardy and Littlewood) of Inequalities • Published the Polya Enumeration Theorem in 1937 • 1940 left for the US-started at Brown University, then went to Stanford in 1942 • Retired from teaching in 1953, living at Palo Alto until his death, as a Professor Emeritus

  7. 4 Steps to Problem Solving • Step 1. Understand the Problem • Read the problem carefully • List the components and data involved • Assign your variable • Step 2. Devise a plan (translate). • Set up an equation and/or • Draw a diagram and/or • Make a chart • Step 3. Carry out the plan (solve). Solve the equation you came up with in ‘Devise a plan’ step. • Step 4. Look back (check and interpret). Go back and check that you used all of your information.

  8. Key Words • Addition: sum, plus, add to, more than, increased by, total • Subtraction: difference of, minus, subtracted from, less than, decreased by, less • Multiplication: product, times, multiply, twice, of • Division: quotient, divide, into, ratio

  9. Solve: Three times the difference of a number and 4 is 8 more than that number. Find the number. • Step 1. Understand the problem. Let x = a number

  10. Solve: Three times the difference of a number and 4 is 8 more than that number. Find the number. • Step 2. Devise a plan (translate). 3(x - 4) = x + 8

  11. Solve: Three times the difference of a number and 4 is 8 more than that number. Find the number. • Step 3. Carry out the plan (solve). 3(x - 4) = x + 8 3x - 12 - x = x + 8 - x 2x - 12 = 8 2x - 12 + 12 = 8 + 12 2x = 20 2x/2 = 20/2 x = 10

  12. Solve: Three times the difference of a number and 4 is 8 more than that number. Find the number. • Step 4. Look back (check and interpret). Take three times the difference of 10 & 4 - that is the same as 8 more than 10. FINAL ANSWER: The number is 10. The answer is correct.

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