6 Define “ALGEBRA”The intensive study of the last three letters of the alphabet.using variables to replace something significant in a problemequations, formulas, numbers, headachesusing letters such as x to represent an unknown number and solving for that letterThe class between prealgebra and geometry
7 Traditional Definitions! Dolciani VerbsSolveSimplifyFactorRationalize
8 We need a BALANCE Traditional Algebraic Symbolic Manipulation Patterns & Algebraic ThinkingContextual problem solving
9 Patterns to Algebra Swimming Pool Walkway Given a 2 by 2 pool: How many 1 by 1concrete slabs (tiles)are needed forthe walkway?
14 Construct a TableFigureTotal Squares14273105x13163x+1
15 Growing Tilessize # of tiles size # of tiles size # of tiles34233432342332433x-12x+13x+2
16 Crossing the River8 adults and 2 children need to cross a river and they have one small boat only available. The boat can hold ONLY:One adultOne or two childrenHow many one-way trips does it take for all 8 adults and 2 children to cross?
17 8 adults and 2 children # of ad. + 2ch. One ways trips 1 5 2 9 3 13 1 52 93 134 175 21x 4x+1
18 8 adults and 3 children # of ad. + 3ch. One ways trips 1 7 2 11 3 15 1 72 113 154 195 23x 4x+3
19 a adults and c children a ad. + # ch. One ways trips 2 4a + 1 3 4a + 3 c 4a + ( )2c - 3
20 Scratch off game cardsA game card has 5 scratch off spots. Exactly two of them have a million dollar prize. The other three spots are blank.You can ONLY scratch off two spots.What is the probability that the two spots you scratch off have the million dollar prize?
21 Change the Number of Spots Spots Probability3 1/34 1/65 1/106 1/157 1/21x3141516
22 To Medicate or Not?Thursday at 9 PM, an athlete is considering taking a cold preparation medicine (16 gr. dose).He will be drug tested before competing on Saturday at 9 AM. The test can detect 1 gram or more or the drug.His body eliminates 1/4 of the drug every four hours.If he takes the 16 gr. dose, will he fail the test?
24 Back to 3rd grade13 x 17 = ?21031 3x 1 71 0 07 03 02 191132 2 1221
25 Algebra: (x + 3) (x + 7) = x2 3x 21 This approach leads to ? x 7 x 7x
26 Texas State Assessment Herman claimed that the square of a number is always greater than or equal to the number. Which of the following examples disproves Herman’s claim?A) A comparison of (-1.5)2 with -1.5B) A comparison of (-0.5)2 with -0.5C) A comparison of (0.5)2 with 0.5D) A comparison of (1.5)2 with 1.5The graph of y = 11x2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c?A) c > 0B) c < 0C) c = 0D) c = 11
27 Connecticut State Assessment Elena plans to rent a motorbike at the beach. She uses a rental service that charges a fixed fee of $25 plus $15 for each hour or part of an hour that she uses the bike. Fill in the table and extend the patterns to show the total charges if she works from 9:15 am to 5:40 pm.HoursCharges0 < h ≤ 11 < h ≤ 22 < h ≤ 33 < h ≤ 4
28 Massachusetts State Assessment The graph below shows the number of milligrams of a medication in the bloodstream from the time it was administered to 300 minutes after administration. Using the information from the graph, which of the following statements is true?A. The maximum amount ofmedication in the bloodstreamwas 12 milligrams.B. The minimum amount ofmedication was in the bloodstream300 minutes after administration.C. The amount of medication in the bloodstream increased at a faster rate than it decreased.D. The maximum amount of medication was in the bloodstream 100 minutes after administration.
29 Idaho State Assessment a. In the space provided, draw in the diagonals for the six-sided polygon.b. How many diagonals are there in an 8-sided polygon? Show or explain how you found your answer.c. Explain how you would determine the number of diagonals in a 15-sided polygon.9
30 Algebra PlacementDistricts should not encourage all students to take Algebra I in grade 8; students should be taking Algebra I in grade 8 only if they are highly motivated, have a strong foundation in middle school mathematics, receive high grades in previous courses, intend to study calculus in high school, and only if the Algebra I courses are taught by teachers with mathematics certification.
31 Summary Algebra Courses: Traditional Algebraic Symbolic Manipulation Patterns & Algebraic ThinkingContextual problem solving