Copia di Transforming and Parameter Effects

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Transforming and Parameter Effects

Wendy Curtner and Dusty Burcham
Photo by moore.owen38

That's Me!

I teach in a TEKS Resource System District

I've got plans for a summer vacation.

I am an administrator or central office personnel.

I am an instructional coach.

I teach 8th grade, Algebra I, II, Geometry, Math Models, PreCal, AQR

My district uses the TI Nspire

I drove more than 3 hours to get here
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What does it mean to transform?

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Transformations in the Coordinate Plane
8th grade & Geometry

8th grade & Geometry teachers work on Transformations in the Coordinate plane Flip book
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Parameter Changes in Functions

Algebra I, II, and beyond work on Monster Function Foldable
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Debrief

Have 4 teachers (2 from each group) pair up to discuss their activity. How were they alike? How were they different?
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Geometric Transformations

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Are teachers using the ETCD to understand the specificity of the TEKS?

Translation – a transformation frequently described as a slide of a figure
Algebraic notation
Translation h units horizontally
(x, y) → (x + h, y)
Translation k units vertically
(x, y) → (x, y + k)
Translation h units horizontally and k units vertically
(x, y) → (x + h, y + k)

Reflection – a transformation frequently described as a flip or a mirror image of the original figure
Algebraic notation
Reflection across a vertical axis
(x, y) → (–x, y)
Reflection across a horizontal axis
(x, y) → (x, –y)

Rotation – a transformation frequently described as a turn of a figure around a designated point
Origin as center of rotation
Algebraic notation
Rotation of 90° counterclockwise or rotation of 270° clockwise
(x, y) → (–y, x)
Rotation of 180° counterclockwise or clockwise
(x, y) → (–x, –y)
Rotation of 270° counterclockwise or rotation of 90° clockwise
(x, y) → (y, –x)
Rotation of 360° counterclockwise or clockwise
(x, y) → (x, y)

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Thinking Blocks - Transformations from Math Playground
http://www.mathplayground.com/TransformationWorkshop/Workshop.html

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The function machine metaphor can also aid one in understanding how a function can depend on parameters. Parmameters are additional quantities that influence the behavior of the function.
The influence of parameters on a function is like the influence of dials on a machine. For a given setting of the dials, the machine processes the inputs in a certain way. If one leaves the dials fixed, then the function machine always spits out the same output value for a given fixed input value.
If one wishes to change how the machine is operating, one can adjust one of the dials, i.e., change one of the parameters. When the dials are changed, the machine still process the inputs and turns them into outputs. However, with new parameters, for the same fixed input value, the function machine may now spit out a different output value than it did before the parameters were changed.

Let's generalize!

Photo by pfis

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Precal Parent Functions