Using Cabri Jr. on the TI-83 or 84. WHAT HAPPENS IN A RIGID TRANSFORMATION 1.The shape changes size and position 2.The shape changes size but not position.

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Presentation transcript:

Using Cabri Jr. on the TI-83 or 84

WHAT HAPPENS IN A RIGID TRANSFORMATION 1.The shape changes size and position 2.The shape changes size but not position 3.The shape changes position but not size

WHAT ARE THE THREE TYPES OF RIGID TRANSFORMATIONS? 1. Rotation, Reduction, Reflection 2. Translation, Reflection, Dilation 3. Rotation, Reflection, Translation 4. Reflection, Rotation, Dilation

WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE? 1. Rotation 2. Reflection 3. Translation

WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE? 1. Rotation 2. Reflection 3. Translation

WHAT TYPE OF TRANSFORMATION WAS ILLUSTRATED IN THE PICTURE? 1. Rotation 2. Reflection 3. Translation

Discover what happens in each type of transformation. Use graphing calculators to make our discoveries Create fractals using transformations TODAY WE WILL……

CABRI JR. IMPORTANT KEYS ∏π∫ª º Arrows move the cursor a AU

LETS PRACTICE

Follow the directions on your sheet Record all measurements in journal Determine a definition Draw an illustration NOW IT’S YOUR TURN

RECORD INFORMATION IN YOUR JOURNAL

WHAT DID WE DISCOVER?

Distance: A,A’ _____ B,B’ _____ C,C’ _____ Dragging the point what happened? TRANSLATION

A transformation that _______ each point of a figure the same _________ and in the same _______. TRANSLATION slides distance direction

CAN YOU FIND A TRANSLATION IN THE TILE?

Distance: A,A’: _____ B,B’: _____ C,C’: _____ ROTATION ANGLES: <ADA’: _____ <BDB’: _____ <CDC’: _____

A transformation that _______ a figure ________ a point. The angle measurement between ____________________ and the _________________ are the _____. ROTATION turns around corresponding points center of rotation same

CAN YOU FIND A ROTATION IN THE TILE?

LETS CREATE THE REFLECTION TOGETHER

Distance: A,A’: _____ B,B’: _____ C,C’: _____ REFLECTION ANGLES: <ADA’: _____ <BDB’: _____ <CDC’: _____

REFLECTION A transformation that _____ a figure across the line of _________ forming a _____________ bisector with the segment joining the ___________________. flips reflection perpendicular corresponding points

CAN YOU FIND A REFLECTION IN THE TILE?

TRANSFORMATION GAME Player 1 spins and arrow lands on red a. Look at key b. Reflect up one block c. Rotate 90 counter- clockwise d. Translate diagonally

FRACTAL TILES

Geometric figures built up from a simple shape by repeating the same changes at smaller and smaller scales. (recursion) WHAT ARE FRACTALS?

Self-similar objects that look the same no matter to what stage you zoom. WHAT ARE FRACTALS?

FRACTALS CAN BE FOUND IN … MOVIES TECHNOLOGY ARCHITECHTURE NATURE

Creating stage 1 Translation Translate one tile up Translate one tile right

Creating stage 1 Rotation Rotate the top 90 degrees clockwise Rotate the bottom right 90 degrees clockwise

Creating stage 2 Translation Translate one grid up and one grid to the right

Rotate top 90 Rotate bottom right 90

To create Stage 3 repeat the process

STAGE Number of Tiles ??

What are some examples of transformations in the real world?