All the World’s Water – Volume of a Sphere Project


This picture inspires a wonderful volume project, and can easily have scientific notation and proportions integrated into the project as well.
(1) Have students calculate the volume of the Earth.
(2) Research the amount of water that’s on the Earth (about 326 million trillion gallons according to science.howstuffworks.com)
(3) Have students calculate what size sphere would hold that volume of water
(4) Either with a computer drawing program or just on a piece of paper, have students use proportions to show the size of the Earth compared to the sphere that would hold the world’s water.

** The same thing can be done with air (atmosphere), though I couldn’t find a specific number as to the exact volume of air. But considering the atmosphere extends (very roughly) out to about 300 km (there’s more atmosphere, I’m sure, but the density of the molecules would be very negligible), simply take the radius of the Earth (6,378.1 km) to figure out the volume of the Earth, then draw another sphere around the Earth that has a radius of 6,678.1 (radius of Earth + 300) and calculate the volume of that sphere, and the difference would be the volume of the atmosphere … albeit a very rough estimation. Students shouldn’t be told this, of course!

Here’s a site with more information about the Amount of Water in/on/above the Earth.

Google Earth and Complex Area

Here is a project by realworldmath.org. Real World Math integrates Google Earth with various math topics, this one on Complex Area. Below is a very brief excerpt from their site, but you need to visit the site itself for the full project:

Complex Area Problems – Real World Math

 

Objectives
•Measure distances
•Find the area of complex polygons
•Solve word problems involving rates

Lesson Description
This lesson consists of two parts. The first requires students to find the area of a complex shape using … the area formulas for a parallelogram and triangle.

The second part … Students will need to be able to solve rate problems with a proportion for this section.

World’s Largest …

coffee
I’m a great fan of dy/dan’s philosophy of teaching math. But I’m also a fan of practical ideas to integrate into a lesson plan. Luckily, he provides wonderful resources in that regard.

He has “3 Act” lessons which are lessons that incorporate multimedia. This particular lesson, as the title states, is about the world’s largest coffee cup. Here’s his complete coffee cup lesson:

dy/dan’s World’s Largest Coffee Cup

I categorized this post in the “Volume and Surface Area,” “Proportions,” and “Linear equations” because I’m considering using it as a “visual word problem” for those units.

Volume and Surface Area
- It could be a simple question about volume and surface area. How much paint did they need to paint the outside of the cup? How much coffee did they need to fill up the cup?

Proportions:
- If the average person drinks x ounces of coffee, how many people will it take to drink all the coffee in the worlds largest coffee cup or
-If the average person is 69 inches tall, what size would a person have to be for this cup to be a “normal” cup for him/her. (The typical regular sized coffee mug is 3.5 to 4 inches tall, but I wouldn’t have to tell the students this. I have enough coffee mugs that I could just give them a mug and a ruler…)

Linear Equations
- Given a rate of flow (and assuming a constant rate), students could calculate and graph how long it took to fill up the cup, or given the time of how long it took to fill up the cup, students could calculate the rate of flow, etc.

For whatever reason, my laptop mini won’t play the videos from Dan’s links, but will play them directly from YouTube. Here’s two of the videos in the lesson that can be found on YouTube:

Intro to Problem
(The repetitive “music” gets annoying…)

Video with Numbers

I’d still encourage you to go to Dan’s site, maybe his video links will work for you. You’ll also need the other information, such as the picture that shows the dimensions of the cup, etc. Lastly, you’ll see the whole picture of what Dan’s lesson is really about, which is more than my currently watered down version.


burger
Following the same concept is the world’s largest burger:
I’ll list some of the stats that can be molded into questions below, but you can find them and the accompanying video here.

1,375,000 calories
Over 600 pounds of beef
30 pounds of lettuce
12 pounds of pickles
20 pounds of onions
28 inch thick, 110 pound bun.
(That’s only a total of 772 pounds so when they say over 600 pounds of beef, I’ll assume they mean 605 pounds of beef).
14 hours to cook
3 ft thick, 5 ft in diameter

Paper Models, Scales and Proportions

paperToy
These paper toy cut-outs are instant replicas of everything from stealth airplanes to famous buildings. Some are very simple one page designs like the Great Pyramid, and others are more complex, such as some of the buildings that require up to 3 pages of cut outs.

Here’s how I integrate this into the classroom. I print out a variety of different cutout patterns (for which the actual dimensions of the real life version is easily found with a quick google search). The students then select their pattern, put together the model, and research the dimensions. On one side of an index card, they write the scale and on the other side, they write the real-life dimensions. Both sides also have the dimensions of their model. (For the models that aren’t perfect replicas, they can scale only one dimension, such as height).

(1) If we’re short of time, this is all there is to it, and it is done as a “project” to do at home. It can be done as a mobile, with their model and index card on a piece of string. These are wonderful to hang up on the classroom ceiling. Or simply staple a few to a bulletin board.

(2) If we have more time, I will place the models around the room, and students walk around to various models with its corresponding index card on display. I flip the cards around so that some show the scale and others state the real life dimensions, and students can calculate the missing piece of information.

OR

For my advanced students who don’t require much time to go through the proportions unit, I simply print out some of the more complicated designs and let them work in small groups and just put them together. You know, for those kinds of days…