GEOMETRY. What is Geometry??? Geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. Geometry is found.

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Presentation transcript:

GEOMETRY

What is Geometry??? Geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. Geometry is found everywhere: in art, architecture, engineering, robotics, land surveys, astronomy, sculptures, space, nature, sports, machines, cars and much more.

Euclid Euclid: “Father of Geometry” Wrote The Elements

Sarah is making a tile pattern with identical regular hexagons. She wants to outline the pattern with ribbon and needs to know its outer perimeter. What is the outer perimeter if she uses 4 hexagons? What is the outer perimeter if she uses 8 hexagons? What is the outer perimeter if she uses 30 hexagons?

Looking For Patterns Shawna liked to jog in the late afternoon. As she passed her neighbors’ house, their dog would hear her and start barking. After the dog had barked for 15 seconds, two other dogs would join in and bark. In another 15 seconds, each barking dog would inspire two more dogs to start barking. At the end of 1 minute, how many dogs were barking? At the end of 2 minutes, how many dogs were barking?

Looking for Patterns Find the distance around each figure. Organize your results in a table. Use your table to describe a pattern in the distances. Predict the distance around the twentieth figure in this pattern.

Starters What is the next number in the sequence? 1.1, 3, 9, 27… 2.81, 9, 3, … Draw the figure.

Conjecture- an unproven statement based on patterns or observations Conjectures are always written as complete sentences. Example: Shaking Hands- A group of n people shake each others hands, with no repeats, how many handshakes will occur? 6 people? 14 people?

Conjectures Make a conjecture given the following examples: A number sequence: 2, 5, 8, 11, … A number sequence: 16, 8, 4, 2, … The product of any 2 even numbers is ______________. The difference of any 2 odd numbers is ____________.

Counterexample- an example that shows a conjecture is false. A counterexample can be a picture, equation, list of numbers, or a sentence. What county do you live in? Example: Students at Madison High School live in Madison county.

Counterexamples

Problem Set Pg. 6 #16-31, (#32, 33 Bonus)