Coordinate Geometry Lesson 7

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Jessie Little
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1 Coordinate Geometry Name: Kelly Date: May 3, 004 Today s Lesson Construct a Concept: Parabolas Unit Topic: Coordinate Geometry Course: Math 1 NYS Mathematics, Science, and Technology Learning Standards Addressed Standard 1: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. Standard 3: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry. Standard 6: Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning. Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions. Objectives Materials Anticipatory Set Students will recall their previous knowledge about polynomials and linear equations. They will then compare several linear and quadratic equations that they have and have not seen before to distinguish the difference between their graphs. (Knowledge, Synthesis, Comprehension). Handout with examples and non-examples (one per student) Overhead of the same for teacher Handout with graphs for students (one per student) Overhead of same for teacher Overhead pens We have talked about graphing straight lines such as (write examples- x + 3 and x on board while explaining) with a table of values. But what happens when we change from only x s to x? (write new examples- x + 3 and x + 5 on board) Take a minute to talk about this with your group without the use of pencil, 1

2 pen or a calculator, remembering what you have already learned about polynomials earlier in the year. Lesson Body Sorting and Categorizing Distribute handout to class and give them 7-10 minutes to develop a conjecture within small groups. Have each person graph one equation and share the picture with their group. Tell the students to complete the worksheet through question 3. Circulate throughout the class and address any initial problems, but only if necessary. Reflecting and Explaining Bring group discussion to a close and begin a class discussion. Split the examples and non-examples evenly among the groups and have one person from each group graph their assignment on the overhead. Ask the students to share their first conjecture and write on side board. Be sure to ask what lead you to this conclusion? or how did your group justify this conjecture? Generalizing and Articulating Lead the discussion to analysis by asking what are similarities and differences of our conjectures? Make a list of the students observations on the board. Bring the class to a general consensus for a conjecture by asking what are the most important elements of our conjectures? Then bring the students to a final class definition by leading the students to formulate a collaborated conjecture. Lastly, talk about naming and defining this newly discovered concept. Verifying and Refining Now that the class has a definition for this concept, ask each small group to create their own example of an equation representative of the examples and graph it and present it to the class. If the students have trouble explaining their examples, ask how does your example fit our definition? and what were the essential elements you used to create this example? Once all groups have presented, complete formal definition of parabola as they understand it now on handout. Parabola: An equation which has a squared variable and whose graph is in a curved shape either concave up or down.

3 Closure Return to anticipatory set. Ask which equations are straight lines and which are parabolas? Over the next few days, we will learn much more about parabolas. We will discuss how to find whether it is concave up or concave down, find the axis of symmetry, find the maximum or minimum point, and find the x-intercepts. Homework/Assessment Complete attached assignment Extensions 3

4 Name: Task sheet- Parabolas Examples Non-Examples The graph of y = x + The graph of y = x The graph of y = x + 3x + 5 The graph of y = x The graph of y = x + 5 The graph of y = 3x 5 The graph of y = 3x + x The graph of y = 7x + 4x How are the examples alike?. How are the non-examples different from the examples? 3. Create a conjecture about the examples. 4. Write the definition of the examples. 4

5 Name Homework assignment- Parabolas 1. Create 5 examples of parabolas. Explain how each of these fits our definition.. An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x + 0x, where 0 =x =0 and all dimensions are expressed in feet. On the accompanying set of axes, sketch a graph of the arch and determine its maxi-mum height, in feet. 3. Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = t, where t is the number of seconds it takes the car to travel down to each point on the ride. How many seconds will it take Greg to reach the ground? Find an algebraic solution. Find a graphic solution. 5

Cal s Dinner Card Deals

Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help