On TargetBrought to you by:

You need a pencilpencil, calculatorcalculator &

scratch paperscratch 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

2200440066008800100100

Are these numbers

appropriate for the

difficulty of the task?

8800660044002020

How do we determine the difficulty of each section?

40%

20%

40%

Find the distance... Find the circumfe...

Find out how hard...

1.1. Find the distance you Find the distance you are from the target.are from the target.

2.2. Find the Find the circumference of each circumference of each circle.circle.

3.3. Find out how hard it is Find out how hard it is to hit each section to hit each section compared to the compared to the others.others.

What will help us find the difficulty of each color?

0%

47%

6%

47% 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?

A =

b•h

67%

0%

28%

6%

1.1. A = A = π•π•rr22

2.2. A = A = π•π•dd

3.3. A = 2A = 2π•π•rr

4.4. A = bA = b••hh

Which of the following is the radius?

A B C D

0% 0%

100%

0%

1.1. AA

2.2. BB

3.3. CC

4.4. DD

AA

BB

CC DD

• 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

ColorColor Area of Area of CircleCircle

Area of Area of TargetTarget

Percent of Percent of Total AreaTotal Area

GreenGreen

PurplePurple

OrangeOrange

BlueBlue

RedRed

Area of SectionArea of Section

Po

int

Val

ue

Po

int

Val

ue

Large Area,Large Area,Small Point Small Point

ValueValue

Small Area,Small Area,Large Point Large Point

ValueValue

How do you How do you describe this describe this relationship?relationship?

What is the relationship of the What is the relationship of the area to the point value?area to the point value?

0%

75%

25%

1.1. Negative trendNegative trend

2.2. Positive trendPositive trend

3.3. No trendNo 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 The midpoint is the half-way point on any line segment.point on any line segment.

What we need to remember.Each side of any Each side of any triangle has a midpoint.triangle has a midpoint.

Connecting the midpoints Connecting the midpoints creates the colored creates the colored (removed) part of the fractal.(removed) part of the fractal.

Each new white triangle Each new white triangle gives us a new triangle with gives us a new triangle with new midpointsnew midpoints

As long as we have triangles, As long as we have triangles, we can keep connecting we can keep connecting midpoints and keep coloring…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?

Red

Purp

le

Gre

en

Whi

te

0% 0%0%0%

Please pass your responders to the front of the roomPlease pass your responders to the front of the room

1.1. RedRed

2.2. PurplePurple

3.3. GreenGreen

4.4. WhiteWhite

Let’s Collect Some Data

Red:

Purple:

Green:

White:

Remember:Remember: Darts that miss Sierpinski’s Darts that miss Sierpinski’s Triangle do not count as white.Triangle do not count as white.

G t Game?• Can you design a new game with the Can you design a new game with the

appropriate scoring?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 It must be a fair game and each color

needs to be scored in relation to its needs to be scored in relation to its difficulty.difficulty.

• Let your creativity make it fun Let 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?Questions?Good-bye!Good-bye!