On Target Brought to you by: You need pencil calculator a pencil, calculator & scratch paper scratch paper for today.

Your tasks are these: –Determine if the scoring is appropriate for the original game. –Use this knowledge to apply it to a new target. –Create a game with the new target. On Target

Are these numbers appropriate for the difficulty of the task?

How do we determine the difficulty of each section? 1.Find the distance you are from the target. 2.Find the circumference of each circle. 3.Find out how hard it is to hit each section compared to the others.

What will help us find the difficulty of each color? 1.Find the area of each color 2.Find the area of each dart tip 3.Find the perimeter of each color 4.Find the perimeter of each dart

How do you find the area of a circle? 1.A = πr 2 2.A = πd 3.A = 2πr 4.A = bh

Which of the following is the radius? 1.A 2.B 3.C 4.D A B C D

Finding the area –Each of you will be given a circle. –Your task is to find the area of all the parts of the dart board. –You should check your answers with others in the class. –With everyone working together, this task should only take 5 – 7 minutes.– On Target

Color Area of Circle Area of Target Percent of Total Area Green Purple Orange Blue Red

Area of Section Point Value Large Area, Small Point Value Small Area, Large Point Value How do you describe this relationship?

What is the relationship of the area to the point value? 1.Negative trend 2.Positive trend 3.No trend

Now let’s change the target…

Creating the new target –The new target is called Sierpinski’s Triangle. Each color is a removed triangle from the original white triangle. –It is a fractal. Fractals are made by a process called recursion – a series of similar steps which build on the previous steps. –Let’s build the Sierpinski’s Triangle using this process. –We’ll start with an equilateral triangle. On Target

Creating Sierpinski’s Triangle

The midpoint is the half-way point on any line segment. What we need to remember. Each side of any triangle has a midpoint. Connecting the midpoints creates the colored (removed) part of the fractal. Each new white triangle gives us a new triangle with new midpoints As long as we have triangles, we can keep connecting midpoints and keep coloring…

Sierpinski’s Triangle No matter how much you zoom, you still get the same picture.

Fractals are natural…

…and man-made.

Which color is hardest to hit? Please pass your responders to the front of the room 1.Red 2.Purple 3.Green 4.White

Let’s Collect Some DataData Red: Purple: Green: White: Remember: Darts that miss Sierpinski’s Triangle do not count as white.

G t Game? Can you design a new game with the appropriate scoring?Can you design a new game with the appropriate scoring? Your game can be a 2 or 3 player game.Your game can be a 2 or 3 player game. It must be a fair game and each color needs to be scored in relation to its difficulty.It must be a fair game and each color needs to be scored in relation to its difficulty. Let your creativity make it funLet your creativity make it fun Practice playing your game.Practice playing your game. We’ll report when we’re finished.We’ll report when we’re finished.

Questions? Good-bye!