1. UNIT ONE  MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.  a. Represent functions using function notation. b. Graph the basic functions f(x) = x(n), where n = 1 to 3, f(x) = √x, f(x) = |x|, and f(x) = 1/x. c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes. d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior. e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior. f. Recognize sequences as functions with domains that are whole numbers. g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.  MM1G2. Students will understand and use the language of mathematical argument and justification.  a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate. b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

2. UNIT TWO  MM1A2 Students will simplify and operate with radical expressions, polynomials, and rational expressions.  a. Simplify algebraic and numeric expressions involving square root. b. Perform operations with square roots. c. Add, subtract, multiply, and divide polynomials. d. Expand binomials using the Binomial Theorem e. Add, subtract, multiply, and divide rational expressions. f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.  (x + y) 2 = x 2 + 2xy + y 2 (x - y) 2 = x 2 - 2xy + y 2 (x + y)(x - y) = x 2 - y 2 (x + a)(x + b) = x 2 + (a + b)x + ab (x + y) 3 = x 3 + 3 x 2 y + 3xy 2 + y 3 (x - y) 3 = x 3 - 3 x 2 y + 3xy 2 – y 3  g. Use area and volume models for polynomial arithmetic.  MM1A3. Students will solve simple equations.  a. Solve quadratic equations in the form ax² + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

3. UNIT THREE  MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.  a. Determine the sum of interior and exterior angles in a polygon. b. Understand and use the triangle inequality, the side- angle inequality, and the exterior-angle inequality. c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL). d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite. e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

4. The slope of a line passing through point (1,3) is (-3). Write the rule (or equation) of this line. Start-upActivity m = y2 – y1 x2 – x1 -3 = y – 3 x - 1 y – 3 = (-3)(x – 1) y – 3 = -3x + 3 y = - 3x + 6 y = -3(x – 2)

5. True for all Real Numbers a, b, c Important Properties AdditionMultiplication Commutativea + b = b + aab = ba Associative(a+b) + c = a+(b+c)(ab)c =a(bc) Distributivea(b+c) = ab + ac and (b+c)a = ba + ca

6. Adding & Subtracting Expressions Adding ExpressionsSubtracting expressions  Remove the parentheses  Use Commutative & Associative Properties to Rearrange and Group “like terms”  Simplify by combining “like terms”  Change the subtracted expression to its opposite  Add the expressions (3x + 4) + (2x - 1) (4d – 2) – (5d – 3) (4d – 2) + (-5d + 3) 4d – 2 + 3 – 5d 4d – 5d – 2 + 3 - d + 1 3x + 4 + 2x – 1 3x + 2x +4 -1 5x +3

7. Multiplying & Dividing Expressions Multiplying ExpressionsDividing Expressions  ab = ba  (ab)c = a(bc)  a(b + c) = ab + ac

8. Dividing by Fractions - NASCAR  Distance = Rate * Time  Distance /Rate = Rate *Time/Rate  Time = Distance/Rate  Time = 1 Miles/ x Miles/Minute  Time = 1 Miles * Minute/ x Miles  f(x) = (1/x ) Minutes

9. Ticket Out The Door 9/17  Write a Paragraph containing at least 3 complete sentences:  The most interesting thing I learned in Math since school started. What was it about this topic that you liked most?  What I hope to learn more about this week.

10. Typical Binomial Squares  (a + b) 2 = a 2 + 2ab + b 2  (a - b) 2 = a 2 – 2ab + b 2  Prove using F.O.I.L.  (a + b) (a + b) = a 2 + ab + ab + b 2  = a 2 + 2ab + b 2  Sum and Difference Pattern (Conjugates)  (a + b) (a - b) = a 2 - ab + ab - b 2  = a 2 – b 2

11. Binomial Theorem & Pascal’s Triangle  (a + b) 0 = 1  (a + b) 1 = 1a + 1b  (a + b) 2 = 1a 2 + 2ab + 1b 2  (a + b) 3 = 1a 3 + 3a 2 b +3ab 2 + 1b 3 1 1 1 2 1 1 3 3 1

12. Solving Polynomial Equations In Factored Form  Factoring and the Zero-Product Property  If ab = 0, then:  a = 0, or  b = 0, or  Both a and b = 0  If (x + 1) (x – 2) = 0, then  (x + 1) = 0, or  (x - 2) = 0, or  Both are zero

13. Solving Polynomial Equations (cont.)  Factor x 2 + bx + c  Factor ax 2 + bx + c  Factor Special Products  a 2 – b 2  ( a + b) 2  (a - b) 2  Factor Polynomials Completely  Written as a product of unfactorable polynomials with integer coefficients

14. Mid-Term Assessment 1. How do you convert Miles per Hour to Miles per Minute? 2. In the NASCAR problem, it was discovered that the Rational Function, f(x) = 1/x, was a good fit to reflect the relationship described in the problem. Identify f(x), 1, and x in this problem. 3. In what units was time to be measured in #2, above? 4. After an accident on the track which caused a 5-minute delay, (a) reflect this delay in a new f(x) relationship. (b) What impact will this have on the original graph? 5. The problem then changed the venue to Daytona, which has a 2.5 mile track. (a) Write a new f(x) which reflects this change. (b) What impact does this distance change have on the original graph? 6. In the Tiling Task, what is the relationship between Mario’s Figure No. and (a) number of rows? (b) Number of tiles in each figure? 7. Mario has 5,000 tiles and wants to know how many rows he needs to use them. How should he proceed? 8. How many rows will he use to place the maximum number of available tiles? 9. How were Triangular Numbers defined in the problem? 10. What do you get when you add two Triangular Numbers?

15. NASCAR Task DAY 1 MPHMPMMinutes Dale Earnhardt, Jr.1803.000.33 Mark Martin601.00 Jeff Gordon2404.000.25 Kasey Kahne1202.000.50 Tony Stewart300.502.00 Jimmie Johnson901.500.67 Jeff Burton1502.500.40 Matt Kenseth150.254.00

16. Mario’s Tiling Vision Figure No. 123456 No. Rows 1357911 No. Tiles 149162536

17. Latasha’s Tiling Vision Figure No. 123456 No. Rows 24681012 No. Tiles 2612203042

18. Triangular Numbers....... …... … ….... … …. ….. Fig12345 T.N.1361015 Sum of the Numbers 1 through n is:

19. YE OLDE VILLAGE SHOPPE  Define the Variables  Draw a Picture  Define Relationships  Construct a Table  Graph the Results  Draw Conclusions x ww

21. Ladder Length Learning Task

22. Warm-up Simplify using the Distributive Property.  1. 4(x – 3)  2. -2(x + 5)  3. x(x + 10)  4. -x(x – 7)

23. Warm-up  Simplify using the Distributive Property.  1. 4(x – 3)  A) 4x – 3B) 4x + 12C) x – 12D) 4x – 7E) 4x - 12  2. -2(x + 5)  A) -2x + 3B) -2x – 10C) 2x – 10D) -2x + 5 E) x - 10  3. x(x + 10)  A) 2x + 10xB) 2x + 10xC) x 2 + 10D) x 2 + 10xE) 10x 2  4. -x(x – 7)  A) -7B) 7x 2 C) -x 2 + 7x D) x 2 - 7xE) 7x

24. Number Magic  Think of a number less than 10  Double it  Add 10  Divide it in half  Subtract the 1 st number you thought of from the answer  Your final answer is 5!  (or you did something wrong!!!)

25. I’ve Got Your Number  Pattern 1: (x+a)(x+b) = x 2 + (a + b)x + ab  (72)(76)  A. (70 + 1)(75 + 1)B. (70 +2)(70 + 6) C. (68 +3)(70 + 6)D. (70 + 2)(72 + 3)   (31)(39)  A. (30 + 1)(30 + 9)B. (27 + 5)(35 + 3) C. (29 + 4)(30 + 9)D. (30 + 1)(32 + 5)   (52)(48)  A. (43 + 8)(40 + 8)B. (50 +2)(50 - 2) C. (43 + 9)(43 + 6)D. (40 + 12)(40 + 8) 

26. I’ve Got Your Number Pattern 1 HW  ( x+a)(x+b) = x 2 + (a+b)x + ab 1. (x + 3)(x + 4)  x 2 + 7x + 12 2. (x + 5)(x + 2)  x 2 + 7x + 10 3. (x + 9)(x + 1)  x 2 + 10x + 9 4. (x + 7)(x + 6)  x 2 +13x + 42

27. I’ve Got Your Number Pattern 1 HW #5 1 x 2x 2 (x+2)(x+1) = x 2 + 3x + 2 x2x2 2x 1x

28. I’ve Got Your Number Problem #1, a. b. c.  Case 1: a positive, b positive: Figure A  Case 2: a positive, b negative: Figure D  Case 3: a negative, b positive: Figure B  Case 4: a negative, b negative Figure C

29. Problem #1, a. b. c.  Case 1: a positive, b positive: Figure A  Case 2: a positive, b negative: Figure D  Case 3: a negative, b positive: Figure B  Case 4: a negative, b negative Figure C I’ve Got Your Number

30. I’ve Got Your Number #2. Use Pattern 1 to calculate each of the following products.  (a) (52)(57) =  (50 + 2 ) (50 + 7) = 50 2 + (2 + 7) (50) + (2)(7) = 2500 + 450 + 14 = 2964  (b) (16)(13) =  (10 + 6)(10 + 3) = 10 2 + (6 + 3)(10) + (6)(3) = 100 + 90 + 18 = 208  (c) (48)(42) =  (40 + 8)(40 + 2) = 40 2 + (8 + 2)(40) + (8)(2) = 1600 + 400 + 16 = 2016  (d) (72)(75) =  (70 + 2)(70 + 5) = 70 2 + (2 + 5)(70) + (2)(5) = 4900 + 490 + 10 = 5400

31. I’ve Got Your Number #3.  (a) (34)(36) =  1224  (b) (63)(67) =  4221  (c) (81)(89) =  7209  (d) (95)(95) =  9025 Verify with Pattern 1  = 900 + 10(30) + 24 = 1224 Verify with Pattern 1  = 3600 + 10(60) + 21 = 4221 Verify with Pattern 1  = 6400 + 10(80) + 9 = 7209 Verify with Pattern 1  = 8100 + 10(90) + 25 = 9025

32. I’ve Got Your Number #3a.-f.  To represent two-digit numbers with the same ten’s digit  start by using n to represent the ten’s digit.  So, n is 3 for part (a) What is n for parts (b), (c), and (d)?  Next, represent the first two-digit number as 10 n + a and the second one as 10 n + b.  In part (a): (32)(38) = (30 + 2)(30 + 8) = (10n + a)( 10n + b) for n = 3, a = 2, and b = 8.  Now figure (b), (c), & (d)

33. I’ve Got Your Number #3h  (32)(38) = (30 + 2)(30 + 8) =  (10n + a)( 10n + b) for n = 3, a = 2, and b = 8  Since a + b = 10,  = 100n 2 + (10)(10n) + ab  = 100n 2 + 100n + ab  = 100(n 2 + n) + ab  Let k = (n 2 + n)  = 100k + ab  Therefore, (32)(38) = 100(3)(4) + 16 = 1216 n 2 + n = n(n+1)

34. I’ve Got Your Number #4 How much Bigger?  How much bigger is the area of a square if you add 4 to its length and width?  (x+4)(x+4)  = x 2 + 8x + 16  How much bigger if you add y to length and width?  (x + y)(x + y)  x 2 + 2xy + y 2  Pattern 2: Square of a Sum x2x2 x x 4 4 x + 4

35. I’ve Got Your Number #5 1. 302 2 =  (300 + 2) 2 = (300) 2 + 2(300)(2) + 2 2 = 90000 + 1200 + 4 = 91204 2. 54 2 =  (50 + 4) 2 = (50) 2 + 2(50)(4) + (4) 2 = 2500 + 400 + 16 = 2916 3. 85 2 =  (80 + 5) 2 = (80) 2 + (80)(5) + (5) 2 = 6400 + 800 + 25 = 7225 4. 2.1 2 =  (2 + 0.1) 2 = (2) 2 + 2(2)(0.1) + (0.1) 2 = 4 + 0.4 + 0.01 = 4.41

36. I’ve Got Your Number #6 What is the Volume?  If Length = Width = Height = x  How much larger if sides increase by 4?  (x + 4)(x 2 + 8x + 16)  = x 3 + 12x 2 + 48x + 64  How much larger is sides increase by y?  (x+y) 3 = x 3 +3x 2 y+3xy 2 +y 3  Pattern 3: Cube of a Sum x x x x3x3

37. I’ve Got Your Number #6e 1. 11 3 =  (10 + 1) 3 = 10 3 + 3(10) 2 (1) + 3(10)(1) 2 + 1 3 = 1000 + 300 + 30 +1 = 1331 2. 23 3 =  (20 + 3) 3 = 20 3 + 3(20) 2 (3) + 3(20)(3) 2 + 3 3 = 4000 + 3600 + 180 + 27 = 7807 3. 101 3 =  (100 + 1) 3 = 100 3 + 3(100) 2 (1) + 3(100)(1) 2 + 1 3 = 1000000 + 30000 + 300 + 1 = 1030301

38. I’ve Got Your Number #6f  Use the cube of the sum pattern to simplify the following expressions.  (t + 5) 3 =  t 3 + 3(t 2 )(5) + 3(t)(5 2 ) + 5 3 = t 3 + 15t 2 + 75t + 125  (w + 2) 3 =  w 3 + 3(w 2 )(2) + 3(w)(2 2 ) + 2 3 = w 3 + 6w 2 + 12w + 8

39. I’ve Got Your Number #7-9  Pattern 2: Square of a Sum  (x + y) 2 = x 2 + 2xy + y 2  Pattern 4: Square of a Difference  (x – y) 2 = x 2 - 2xy + y 2  Pattern 5: Cube of a Difference  (x - y) 3 = x 3 - 3x 2 y + 3xy 2 - y 3  Pattern 6: Conjugates  (x + y)(x – y) = x 2 – y 2

40. I’ve Got Your Number #7-10 1. (101)(99) =  (100 + 1)(100 – 1) = 100 2 – 1 2 = 10000 – 1 = 9999 2. (22)(18) =  (20 + 2)(20 – 2) = 20 2 – 2 2 = 400 – 4 = 396 3. (45)(35) =  (40 + 5)(40 – 5) = 40 2 – 5 2 = 1600 – 25 = 1575