Warm Up

From OER Commons Wiki

Background:

Each morning, we will have some fun warm up exercises for the first hour or so. This is a chance to shake off the cobwebs and get your brain in gear in an individual and group setting.

These exercises typically consist of estimation or sizing problems. For example, last year we poured a BUNCH of popsicle sticks on the table and asked the boot camp students to estimate (not count) the number of sticks. You will be surprised about how much math and science you can use here to improve on your estimates.

We want each student to make their own best estimate first and log it in the computer (we will show you how), and then work in small teams to improve on their estimates by brainstorming and using some equipment in the library (tape measures, scales, etc). You can use the discussion section here to capture your ideas.

Finally, we will post a photo of the "problem" on the internet so that many others outside our class (possibly around the world!) can provide some guesses (this is called the Wisdom of Crowds). This is the theory that a larger group of diverse people can make better decisions, and display more intelligence than any smaller collection of experts.

At the end of the day, we will all get together and discuss our individual, group, and crowd sourcing results.

Tuesday, we will be estimating the value of a jar of coins that have a random number of quarters, nickels, dimes, and pennies. Enter your individual and group estimates on this form here

Students estimates:

• Subal $8.4
• Rahul $27.55
• Robby $27.07
• Isaac $7.64
• Victor $26.92
• Sandra $20
• Ahmed $20
• Ananya $12.75
• Maura $9.25
• Meghan $13.25
• Xander $8
• Tony $10
• Kevin $13.74
• Isaac $12.5
• Jennifer $21.64
• Lance $5.61

Stats: Average = $15.27

The real value is $36.40, which is much higher than any of the estimates. The best estimate used a sampling method: determine the value of coins in the sample jar, then take the ratio of the weight of the sample coins to the unknown coins. The estimate is the multiplication of that ratio by the value in the sample jar. This method yielded $27. Why does this work sometimes and what assumptions does it make?

Wednesday, we will be estimating the number of ping-pong balls in a container. The tricky part is that you can only see through a small window into the container. How can you use math to help get a better estimate?

Student estimates:

• Rahul 96 balls
• Tony 65 balls
• Robby 32
• Sandra 44
• Meghan 43
• Isaac 90
• Lance 106.395506
• Jennifer 105
• Victor 44
• Ananya 32
• Subal 36
• Ahmed 40
• KEVIN! 64

Stats: average = 61

The actual value is 87. Methods used included:

• count the number of balls along the three axes and multiplying them together
• measure the volume of one ball and the volume of the container, then divide to get the number of balls
• others ...

Thursday, diving right into Robot development. The competition is at 10:30am sharp!

Friday: imagine a 'bouncy' ball being held 10 feet in the air. You drop it and each time it bounces only to 90% of the previous height. For example, it starts at 10 feet, then 90%*10=9 feet, then 90%*9 = 8.1 feet etc. Questions:

1) How many bounces until the ball doesn't reach one foot?

2) How many bounces until the ball doesn't rise up from the ground at all?

3) What is the total distance the ball bounces from the start until it stops moving?

Answer:

• H(n) = 10*(0.9)^n where H(n) is the maximum height of the ball on bounce n (21 bounces to reach less than 1 foot)
• A perfect ball will never stop bouncing - INFINITY
• This is a fun one. First question, do you think it will be a finite or infinite number? We will leave this one unanswered and have the boot camp participants discuss it over the summer...