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Mathematics Department Collaboration Outcome

Mathematics Department Collaboration Outcome. Brief Summary: Different math disciplines reviewed all District 4 benchmarks to see the growth. Although the growths were not very significant, yet the data revealed a steady improvement in every area.

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Mathematics Department Collaboration Outcome

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  1. Mathematics Department Collaboration Outcome • Brief Summary: Different math disciplines reviewed all District 4 benchmarks to see the growth. Although the growths were not very significant, yet the data revealed a steady improvement in every area. • Benchmark 4 data given by Ms. Gumucio were analyzed and disaggregated by math faculty • Algebra Essentials: 8 standards identified by the non-mastery item analysis were selected for re-teaching.Standards: 4,7,8,9,11,17,20,and 21. • ALGEBRAI: Non-Master range of 22% to 32% related to power Standards #:5,7,12,13,15,20,21, and 23 Were identified for re-teaching. • GEOMETRY:Standards # 4,7,16,17,18, 20, 21,and 22 were identified for re-teaching. • ALGEBRA II: Standards# 2,7,10,11.2, 12,18,and 19 were identified for re-teaching. • All teachers in different disciplines developed different exam questions based on the identified standards for re-teaching.

  2. Mathematics Department Plan: • All teachers shared and presented effective strategies for teaching identified standards .

  3. NEXT STEPS TO SOLVE THE EXIGENCE • Faculty based on the data unanimously decided to re- teach the designated standards starting Tuesday 4/20/2010 in order to be able to review all the concepts which were revealed as non-mastery areas. • New CST style power point lessons created by Curriculum Specialist were given to all disciplines as another venue to teach.

  4. TIMELINE • Math department will implement the remediation and intervention as of Tuesday 4/20/10.in order to have time to review all the identified standards and concepts. • Next year the starting date will be September.

  5. WHO IS RESPONSIBLE ? • Classroom Teacher • Math Curriculum Specialist • Discipline leader • Math department chair • AP Curriculum( Ms.Gumucio) • AP Testing (Ms. Rubio)

  6. To solve a quadratic eqn. by factoring, you must remember your factoring patterns!

  7. 5.2 Solving Quadratic Equations by Factoring Goals: 1. Factoring quadratic expressions 2. Finding zeros of quadratic functions What must be true about a quadratic equation before you can solve it using the zero product property?

  8. Zero Product Property • Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 or B=0. • This means that If the product of 2 factors is zero, then at least one of the 2 factors had to be zero itself!

  9. Example: Solve.x2+3x-18=0 x2+3x-18=0 Factor the left side (x+6)(x-3)=0 set each factor =0 x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

  10. Example: Solve.2t2-17t+45=3t-5 2t2-17t+45=3t-5 Set eqn. =0 2t2-20t+50=0 factor out GCF of 2 2(t2-10t+25)=0 divide by 2 t2-10t+25=0 factor left side (t-5)2=0 set factors =0 t-5=0 solve for t +5 +5 t=5 check your solution!

  11. Example: Solve.3x-6=x2-10 3x-6=x2-10 Set = 0 0=x2-3x-4 Factor the right side 0=(x-4)(x+1) Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4-1 -1 x=4 OR x=-1 Check your solutions!

  12. Finding the Zeros of an Equation • The Zeros of an equation are the x-intercepts ! • First, change y to a zero. • Now, solve for x. • The solutions will be the zeros of the equation.

  13. Example: Find the Zeros ofy=x2-x-6 y=x2-x-6 Change y to 0 0=x2-x-6 Factor the right side 0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions! If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).

  14. 5.2 Solving Quadratic Equations by Factoring Goals: 1. Factoring quadratic expressions 2. Finding zeros of quadratic functions What must be true about a quadratic equation before you can solve it using the zero product property?

  15. To solve a quadratic eqn. by factoring, you must remember your factoring patterns!

  16. Zero Product Property • Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 or B=0. • This means that If the product of 2 factors is zero, then at least one of the 2 factors had to be zero itself!

  17. Example: Solve.x2+3x-18=0 x2+3x-18=0 Factor the left side (x+6)(x-3)=0 set each factor =0 x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

  18. Example: Solve.2t2-17t+45=3t-5 2t2-17t+45=3t-5 Set eqn. =0 2t2-20t+50=0 factor out GCF of 2 2(t2-10t+25)=0 divide by 2 t2-10t+25=0 factor left side (t-5)2=0 set factors =0 t-5=0 solve for t +5 +5 t=5 check your solution!

  19. Example: Solve.3x-6=x2-10 3x-6=x2-10 Set = 0 0=x2-3x-4 Factor the right side 0=(x-4)(x+1) Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4-1 -1 x=4 OR x=-1 Check your solutions!

  20. Finding the Zeros of an Equation • The Zeros of an equation are the x-intercepts ! • First, change y to a zero. • Now, solve for x. • The solutions will be the zeros of the equation.

  21. Example: Find the Zeros ofy=x2-x-6 y=x2-x-6 Change y to 0 0=x2-x-6 Factor the right side 0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions! If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).

  22. 5.2 Solving Quadratic Equations by Factoring Goals: 1. Factoring quadratic expressions 2. Finding zeros of quadratic functions What must be true about a quadratic equation before you can solve it using the zero product property?

  23. To solve a quadratic eqn. by factoring, you must remember your factoring patterns!

  24. Zero Product Property • Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 or B=0. • This means that If the product of 2 factors is zero, then at least one of the 2 factors had to be zero itself!

  25. Example: Solve.x2+3x-18=0 x2+3x-18=0 Factor the left side (x+6)(x-3)=0 set each factor =0 x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

  26. Example: Solve.2t2-17t+45=3t-5 2t2-17t+45=3t-5 Set eqn. =0 2t2-20t+50=0 factor out GCF of 2 2(t2-10t+25)=0 divide by 2 t2-10t+25=0 factor left side (t-5)2=0 set factors =0 t-5=0 solve for t +5 +5 t=5 check your solution!

  27. Example: Solve.3x-6=x2-10 3x-6=x2-10 Set = 0 0=x2-3x-4 Factor the right side 0=(x-4)(x+1) Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4-1 -1 x=4 OR x=-1 Check your solutions!

  28. Finding the Zeros of an Equation • The Zeros of an equation are the x-intercepts ! • First, change y to a zero. • Now, solve for x. • The solutions will be the zeros of the equation.

  29. Example: Find the Zeros ofy=x2-x-6 y=x2-x-6 Change y to 0 0=x2-x-6 Factor the right side 0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions! If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).

  30. #1) Which statement must be true about the triangle? P Q R • P + R < Q • P + Q > R • Q + P < R • P + R = Q

  31. B. P + Q > R

  32. #2) For the figure shown below, lines m // l -which numbererd angles are equal to each other? • 1 and 2 • 1 and 5 • 3 and 7 • 5 and 7

  33. Corresponding angle D

  34. #3) If two consecutive angles of a parallelogram measure (2x + 10) º and (x-10)º, then what must be the value of x? • 20 • 60 • 90 • 120

  35. B. 60

  36. #4) Point x, y, and z are points on the circle. Which of the following facts is enough to prove that < XZY is a right angle? • XY is a chord of the circle • XZ = YZ • XY > XZ • XY is a diameter of the circle.

  37. D One side of the triangle is a diameter => opposite is a RIGHT angle

  38. ┴ #5) In the circle below, ABCD, AB is a diameter, and CD is a radius. • What is m < B? • 45º • 55º • 65º • 75º

  39. Inscribed angle Bis half of arc AC = 90º A. 45º

  40. #6 Which of the following translations would move the point (5, -2) to (7, – 4)? • (x , y)  (x + 2, y + 2) • (x , y)  (x – 2, y + 2) • (x , y)  (x – 2, y – 2) • (x , y)  (x + 2, y – 2)

  41. (5, -2) to (7, – 4)? D. (x , y)  (x + 2, y – 2)

  42. #7) Which drawing below shows a completed construction of the angle bisector of angle B? A. B. C. D.

  43. #8) Put the steps in order to construct a line perpendicular to line l from point P.

  44. Geometry CST prep

  45. #1) Which statement must be true about the triangle? P Q R • P + R < Q • P + Q > R • Q + P < R • P + R = Q

  46. B. P + Q > R

  47. #2) For the figure shown below, lines m // l -which numbererd angles are equal to each other? • 1 and 2 • 1 and 5 • 3 and 7 • 5 and 7

  48. Corresponding angle D

  49. #3) If two consecutive angles of a parallelogram measure (2x + 10) º and (x-10)º, then what must be the value of x? • 20 • 60 • 90 • 120

  50. B. 60

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