- Bookmark this picture at 101qs.com
- Do coin estimation with your students.
- Go to the bank and withdraw a few dollars worth of pennies.
- Get some Gorilla Glue.
- Take whiffle balls from your son's collection (source of whiffle balls may vary).
Show your students the picture from Step 1. Do the estimation task from Step 2. Show them the following slide!
*If you don't know yet, we covered surface area of spheres in Geometry this week.
We just completed Nathan Kraft's Soccer Ball 3 Act lesson which was spectacular for volume of a sphere! (Nathan, post act 2 and act 3 for everyone NOW!) The Cent-ed Whiffle Ball is a simple task. You know you have a keeper when you hear the following come out of students:
"This is fun!"
"This is stressful!"Students first started this task by using a tape measure to find the circumference of their whiffle ball. Thankfully, I've finally won them over on using centimeters. Shooosh! Don't tell those people who like inches. Students then used the circumference to find the radius of the whiffle ball. Well done, kiddos! Next, students either used a tape measure or ruler to get the circumference or diameter of a penny, respectively. Ultimately, they wanted the radius of the penny. Then they got stuck.
"Mr. Stadel, what's the surface area formula for a sphere?"Sweet! They want it. They need it. They crave it. I didn't write it on the board or give it to them on a handout. Here's where I wish I had an additional hour with these kids to explore this formula. Instead, I had a demonstration ready for them. I took our Nerf basketball we use for Math Basketball Review. I told students that I measured the circumference of the ball in order to construct a circle that has the same circumference. Before class, I cut out a second congruent circle and cut it into eight congruent sectors. I then played this game with students:
Me: How many of these circles will it take to cover the entire ball?
Student 1: Three
Student 2: Four
Student 3: Three and a half
Student 4: Five
Me: Let's find out!I pinned the sectors onto the Nerf ball with thumbtacks, covering a fourth of the ball.
Student 2: I was right! It's four!
Student 5: Cool!BOOM! We had our formula: 4 areas of a circle with the same circumference as the sphere. Simply put: 4πr^2. Most groups immediately found the surface area of the whiffle ball and penny, dividing the two to get something like 88 pennies. One group of girls immediately came up to me and asked for their pennies. Before giving students their pennies, I drilled each group, asking them to explain their number and show their work.
Me: Now girls, if we've learned anything in here this year, we know that our answer on paper isn't always the actual answer. Have you accounted for everything? Look at this picture again (from the ingredients). Did you account for everything?
Devon: There's spaces between the pennies.
Me: Yup. Why don't you go back and mathematically show me a different number of pennies, now accounting for those spaces.I had this conversation with each group, or some variation of it. This is where the magic begins. Remember, students were allowed a maximum of six pennies. Here's what they came up with. I'll let the pictures do the talking:
Chris asked for a compass to draw a circle having the same circumference as the sphere.
Elle found the area of a rectangle formed by six pennies. She then subtracted the area of six pennies to get the area of the space created by six pennies.
Noelle used a parallelogram of pennies to execute the same idea as Elle.
Groups started coming back with revised numbers. They quietly told me their amount. Remember, there's a CASH PRIZE on the line! Im still not sure what that is yet. Groups came in with the following amount of pennies to cover their whiffle ball:
70 pennies
65 pennies
69 pennies
62 pennies
Good luck to them all. They are almost done gluing their pennies. Two groups are done and the other two are close. Here's a few pics!
 |
| This group used 71 pennies versus a theoretical 69. |
I highly suggest you make Cent-ed Whiffle Balls in class! If not, here are the dimensions:
Whiffle Ball circumference: 28 centimetersPenny diameter: 1.9 centimeters
Cent-ed,
1050
P.S. Help me make this task better.
AHHH, this is fantastic, Andrew!!! I love this lesson because we get to play with penises!! I love the pre-lesson estimation on 101qs and on estimation180, talk about fun and safe entries into the problem. I'm definitely stealing this in its entirety. For sequel, I'd have a larger ball (tennis?) for kids to estimate. Then I'd have kids estimate with different coins, maybe with nickels and dimes.
ReplyDeleteThank you!!
I like this lesson too, maybe not for the same reason Fawn likes it, but it's still good.
ReplyDeleteI'm curious to see how the areas of the four circles match the nerf ball surface area. Do you have a picture of this?
I hate when I read your blog, because you make me realize how boring I am (can anyone say Bueller?) My concern with this in a high school class is that students would just proportionally reason, but it would not match the objective, which of course is to find the surface area of a sphere.
ReplyDeleteI echo Nathan's thought about the surface area. I've always wondered how I could explain to the students why the SA of a sphere is what it is without calculus. I am having a little troubles visualizing it.
As for a sequel, what about a FOOTBALL?
This is so great Andrew. I will be sharing this with all of the teachers I work with. You asked for ways to make this better but honestly I am struggling to think of any. Kids were engaged, came up with a solution path, adjusted it as needed, persevered, and explained themselves. Maybe the only thing I could think of would be to try to communicate in writing as well? Great job.
ReplyDeleteBTW, the best example I have seen that connects the area of four circles to a sphere's surface area is this: http://www.youtube.com/watch?v=VvFYZLpMbR4
Fawn....you may want to double-check your spelling and edit your response. :).
ReplyDelete