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Building Conceptual Understanding. Through The Effective Use of Technology. Your Learning Partners for Today …. Look at the numbered card you received. How many of the following properties does it possess?. prime even square cube. triangular Fibonacci deficient.
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Building Conceptual Understanding Through The Effective Use of Technology
Your Learning Partners for Today … Look at the numbered card you received. How many of the following properties does it possess? • prime • even • square • cube • triangular • Fibonacci • deficient Form a group with the people whose # possesses the same number of properties.
Setting the Stage Do these expectations build on concepts from previous grades or units in this course? How will these expectations impact my students in future mathematics courses?
Organizing a Unit • Some questions I need to ask myself as I plan: • If I want to know whether my students have achieved these overall expectations, what questions should I ask them? • Which of the specific expectations, that relate to each overall expectation, are more important in helping my students achieve that overall expectation? • What lessons do I need to create in order to teach these expectations? • How do I organize these lessons in a way that supports my students making connections about the math they’re learning?
Prior Learnings • My students have: • explored the graphs of quadratic relations in standard form using technology • are able to identify key aspects of a parabola, such as: • the axis of symmetry • the zeros of the parabola • the coordinates of the vertex • Investigated the effects of changing the values of parameters a, b, and c, in the standard form of a quadratic equation • factored quadratic expressions • sketched the graph of a quadratic relation in factored form
What’s My Lesson Goal? What do I want my students to have accomplished by the end of this lesson? • I want my students to: • understand the connection between the location of the vertex of a parabola and the equation of the quadratic relation in vertex form • recognize that mathematics plays a role in art & design (spatial intelligence)
Organizing My Thoughts Lesson Title: Picturing Parabolas Course: 10, Academic
Mind’s On Where’s the math?
Action In your groups, carry out the investigation, using the graphing calculator, by following the instructions provided. Calculator Rep. Timer Recorder Presenter
Consolidation In your math journal, write a reflection on today’s investigation, as you consider the following questions: Describe how changing the value of k, in the equation y = x2 + k, affects: i) the graph of y = x2 ii) the coordinates of each point on the parabola iii) the parabola’s vertex and axis of symmetry Describe how changing the value of h, in the equation y = (x – h)2 , affects: i) the graph of y = x2 ii) the coordinates of each point on the parabola iii) the parabola’s vertex and axis of symmetry For a parabola of the form y = (x – h)2 + k, describe the process you would use to sketch its graph, if you begin by drawing a graph of y = x2 .
Further Consolidation … Where’s the Homework? Create a graphic design, based on a set of parabolas that you enter into your graphing calculator. Transfer your picture from the graphing calculator to your PC, and using a “paint” program, give it some colour! Print a copy of your finished design, and submit it to your instructor along with the list of equations that you used to create your design.
(h, k) x = h How Else Could You Teach These Concepts? • Teacher introduces the vertex form of a quadratic relation as the equation: • y = (x – h)2 + k, where the vertex is the point (h, k). y = x2 y = (x – h)2 + k • Teacher demonstrates several examples. • Teacher assigns practice questions. • Teacher takes up practice questions and summarizes.
Which Approach Would You Take?Why? • Who’s doing the thinking? • What mathematical processes are students using? • Which approach is more likely to engage more of your students?
