Acquisition Lesson Planning Form - ciclt.net

1 Math 2 unit 1 Lesson 1 Quadratic Functions Page 1 acquisition lesson planning form Key Standards addressed in this Lesson : MM2A3a, MM2A3b, MM2A3c Time allotted for this Lesson : 5 hours Essential Question: Lesson 1 QUADRATIC FUNCTIONS How do you analyze and graph quadratic functions of the forms f(x) = ax2 + bx + c (standard form ) and f(x) = a(x - h)2 + k (vertex form )? Activating Strategies: (Learners Mentally Active) Use GO #1 Families of Quadratic Functions graphic organizer as a review of quadratic concepts from Math 1. Students work in collaborative pairs to complete the organizer, The teacher might need to discuss the y-intercept if the students were not taught this in Math 1. They should do the problems by hand, and check with a graphing calculator. Discuss with the entire group Use #2 #5 of the Protein Bar Learning Task, Part 1 as activating strategies/review problems on a subsequent day.

2 Acceleration/Previewing: (Key Vocabulary) Quadratic Function, standard form , vertex form , horizontal shift, vertical shift, reflection, vertical stretch, vertical shrink, vertex, axis of symmetry, domain, range, zeros, intercepts, extrema, intervals of increasing and decreasing, and rates of change (slope). Have the students make foldables with these words. Students can brainstorm all the things they remember from last year about these words. Teaching Strategies: (Collaborative Pairs; Distributed Guided Practice; Distributed Summarizing; Graphic Organizers) Note: Much of this is a review from Math 1. Review characteristics of the quadratic function, factoring methods for quadratics, simplifying square roots, and solving quadratics by factoring and by extracting roots. Use the graphic organizers #2 - #4 as needed for your class. Pairs complete parts 1- 6 of Henley s Chocolates Learning Task.

3 (Page 20) Choose pairs to explain each part. Ones share with twos the patterns noticed in Henley s Chocolates Learning Task #5 a-f. Small groups of 3-4 work on #6 and #7 of The Protein Bar Toss Learning Task, Part 1 . (Page 23) A mini Lesson on factoring trinomials with coefficients of x2 other than 1 and factoring four terms by grouping is needed before the students reach #8 in the task. The Matching Factors Activity beginning on page 10 can be used to reinforce the concepts of factoring. Groups complete The Protein Bar Toss, Part 1 . Then share parts with the entire class. Pairs complete The Protein Bar Toss, Part 2, Learning Task, #1 - #8. (Page 29) Pairs should explain each part. Math 2 unit 1 Lesson 1 Quadratic Functions Page 2 Mini Lesson , if needed, using Graphic Organizer #2: Properties of a Function, to illustrate the characteristics of a function, particularly stressing intervals of increase and decrease.

4 Pairs complete #9 from the Protein Bar Toss, Part 2, Learning Task. Discuss with the entire group. Mini Lesson using Graphic Organizers #5 and #6 on converting between forms before completing part #10 from the Protein Bar Toss, Part 2, Learning Task. Pairs complete the remainder of The Protein Bar Learning task. Think-Pair-Share. Share answers and answer questions. Distributed Guided Practice/Summarizing Prompts: (Prompts Designed to Initiate Periodic Practice or Summarizing) What are the differences between the transformations of f(x) when graphing a. f(-x) and f(x); b. f(x + a) and f(x) + a How does the height a ball rises when thrown into the air correspond to the equation of the function representing this motion? If it takes a ball t seconds to rise to its peak when tossed into the air, how long does it take before it hits the ground? If the point (-3, 5) is on the graph of a quadratic function with axis of symmetry x = 1, what is another point on the quadratic function?

5 Extending/Refining Strategies: Complete parts 7-10 of Henley s Chocolates Learning Task. Task: Protein Bar Toss (Question #13) Using what students have learned, students work in pairs to complete #13-15 to extend knowledge on solving quadratic equations algebraically in real-life situations. Summarizing Strategies: Learners Summarize & Answer Essential Question Ticket out the door. Teacher will put 2 quadratic equations such as y = x2 and y = (x + 3)2 on the board, and have students explain in writing the transformation that took place. Other TODs as needed on pages 20 and 21. GO #1: Do You Remember? Math 2 unit 1 Lesson 1 Quadratic Functions Page 3 . f(x) = x2 x f(x) -3 -2 -1 0 1 2 3 y-int = f(x) = 12x2 x f(x) -3 -2 -1 0 1 2 3 y-int = f(x) = -2x2 x f(x) -3 -2 -1 0 1 2 3 y-int = f(x) = (-x + 2)2 x f(x)

6 -3 -2 -1 0 1 2 3 y-int = Families of Quadratic Functions y Complete the table below for each of the indicated functions and draw each in a different color on the graph to the right. As you graph each function, discuss the following questions with your partner: x 1. How are the lines alike? 2. How are they different? 3. What transformation is occurring? f(x) = x2 - 2 x f(x) -3 -2 -1 0 1 2 3 y-int = f(x) = (x 2)2x f(x) -3 -2 -1 0 1 2 3 y-int = GO #2: Properties of a Function: f(x) = _____ What is the x-intercept?

7 What is the y-intercept? Domain: Range: Minimum: Decreasing: Increasing: Maximum: Reflection: Math 2 unit 1 Lesson 1 Quadratic Functions Page 4 GO #3: Parent Function: f(x) = _____ f(x) = ____ x f(x) VOCABULARY Domain Range y x x-intercepts (zeros) y-intercept Intervals of Increase/Decrease End Behavior Max or Min Describe: Math 2 unit 1 Lesson 1 Quadratic Functions Page 5 GO #4: Exploring Quadratic Functions -- Transformations How do the transformations relate to the parent graph? y = x2 + 2 y = x2 2 y = 2x2 y = 21x2 y = - x2 How does the graph change? What is the range? What is the domain? What is the end behavior? What is the maximum / minimum? Identify the intervals for which the function is increasing / decreasing.

8 What are the intercepts ? Math 2 unit 1 Lesson 1 Quadratic Functions Page 6 GO # 5: Quadratic Functions: Vertex form : f(x) = a(x h)2 + k Standard form : f(x) = ax2 + bx + c Converting Quadratic Equations from standard form into vertex form : Math 2 unit 1 Lesson 1 Quadratic Functions Page 7 f(x) = -2x2 + 16x 27 = -2 ( x2 + 8x ) - 27 = -2( x2 + 8x + 16 ) - 27 + 32 Add the opposite of that value to the constant. Take half the coefficient of x and square it. Add it inside the parentheses. Standard form : Factor the coefficient of x2 from the first two terms. Factor the trinomial, write it as a quantity squared, combine terms and you have Standard form = =2( x + 4 )2 + 5 GO #6: Quadratic Functions Vertex form : f(x) = a(x h)2 + k Standard form : f(x) = ax2 + bx + c Converting Quadratic Equations from vertex form into standard form : Math 2 unit 1 Lesson 1 Quadratic Functions Page 8 f(x) = -2(x 4)2 + 5 = -2(x2 8x + 16) + 5 = -2x2 + 16x 32 + 5 Distribute the coefficient of the Combine like terms.

9 Vertex form : Square the binomial. Standard form = -2x2 + 16x 27 GO #7: How do you graph quadratic functions? Math 2 unit 1 Lesson 1 Quadratic Functions Page 9 Vertex form f(x) = a(x-h)2 + k f(x) = 2(x + 5)2 4 f(x) = - x2 2x + 1 1. Find the vertex 2. Find and sketch the axis of symmetry. 3. Find two points on one side of the axis of symmetry. 4. Use symmetry to find two points on the opposite side of the axis of symmetry. 5. Connect with a smooth curve. Standard form f(x) = ax2 + bx + c Math 2 unit 1 Lesson 1 Quadratic Functions Page 10 Matching Factors Activity Match the factors with the special product. Copy the pages onto cardstock, laminate them and then cut out the cards before use. You could use different colored cards for different sets so they can be kept separate easily if you wish.

10 You might want to put the factors on one color and the products on a second color. The two sets of cards can be matched to practice multiplying polynomials and/or factoring quadratic expressions. This can be done by small groups of students, collaborative pairs, or by individual students working alone. Math 2 unit 1 Lesson 1 Quadratic Functions Page 11 Polynomial Set 1 4x + 6 3x 9 6x 8 2x 16 8x + 24 3x 36 6x 40 4x 44 12x + 80 4x 8 9x 9 3x 12 8x 42 12x 60 9x - 12 9x 6 16x 4 12x 8 Math 2 unit 1 Lesson 1 Quadratic Functions Page 12 Factors Set 1 2(2x + 3) 3(x 3) 2(3x 4) 2(x 8) 8(x + 3) 3(x 12) 2(3x 20) 4(x 11) 4(3x + 20) 4(x 2) 9(x 1) 3(x 12) 2(4x 21) 12(x 5) 3(3x 4) 3(3x 6) 4(4x 1) 4(3x 2) Math 2 unit 1 Lesson 1 Quadratic Functions Page 13 Polynomial Set 2 4x2 1 4x2 9 4x2 25 4x2 49 4x2 81 9x2 - 25 9x2 1 9x2 4 9x2 16 x2 10x + 25 4x2 + 4x + 1 4x2 4x + 1 9x2 + 6x + 1 9x2 6x + 1 4x2 + 12x + 94x2 12x + 9 9x2+30x+25 16x2 24x+9 Math 2 unit 1 Lesson 1 Quadratic Functions Page 14 Factors Set 2 (2x+1)(2x 1) (2x+3)(2x-3)(2x+5)(2x-5)(2x+7)(2x 7) (2x+9)(2x 9)(3x+5)