Building Conceptual UnderstandingThrough 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.

Outline for today

1. Starting to Plan: Expectations 2. Prior Learning3. What’s My Goal?4. How to Plan … the PPQT4. Minds’ On5. Action: An investigation using

technology6. Consolidation: Reflecting and Practising7. Other approaches to this lesson8. Final thoughts

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 UnitSome 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 technologyare 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 equationfactored quadratic expressionssketched 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)

Expectations and Lesson Goals

Will My Students get it?

The Lesson Organizer

Organizing My ThoughtsLesson Title: Picturing Parabolas Course: 10,

Academic

The Lesson Organizer

Starting with the end in mind …

The Lesson Organizer

Mind’s On

Where’s the math?

Our Picture … Deconstructed

Action

In your groups, carry out the investigation, using the graphing calculator, by following the instructions provided.

Calculator Rep.Timer

RecorderPresenter

ConsolidationIn 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 …

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.

Where’s the Homework?

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).

(h, k)

x = h

y = (x – h)2 + ky = x2

• 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?