This lesson absolutely drips with potential, but the worksheet here is life-sucking. How would you fix it? What media would you use? What activities would you use?

[Original source.]

1. A journalist is asked to cover a major event in a large ballroom. She wants to include a note about how many people attended the event. How could she estimate the number of people without actually counting everyone?

2. Describe several different methods that could be used to estimate the size of a crowd at an outdoor political event. How might the estimate of the crowd size supplied by organizers of the event differ from estimates made by other groups? Why?

3. Find a location where you can make a rectangle that measures 5 feet by 5 feet. Have your classmates stand close to each otherÂ inside this rectangle (as if you are in a small area watching a music concert). Count the number of people you can fit in this rectangle and find the ratio of this number to the area of the rectangle. Then use a proportion to estimate the number of people who could fit into a rectangle that measures 6 feet by 9 feet.

4. Can the perimeter of a rectangle be used to provide an accurate estimate of the number of people standing inside it? Why?

5. Suppose that a crowd has gathered in a rectangular ballroom with an area of 5,000 square feet and that the room is filled to capacity. If each side of the ballroom were enlarged by 25%, determine if it is true that 25% more people could stand inside this larger ballroom.

Just to kick things off, here’s a potential bit of media.

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Filed under: Education, Mathematics

mathspig, on November 16, 2009 at 4:13 pm said:HI Jason,

Love to see you linking maths to the media. I’m always looking for maths links to media in all forms. You might be interested in my last post.

10 Movie Cliches Debunked with Maths.

Thanks for the link to the Carnival of Mathematics. It certainly linked my mathspig blog to the greater, um, universe. That’s what it felt like.

Keep up the good work.

Kerry Cue

aka Mathspig

Tyler, on November 16, 2009 at 4:24 pm said:My first thought is that the 5 questions are not related. Each of the 5 relates to the general problem of estimating the size of a large group of people. But they don’t relate to each other. It couldn’t hurt to try and chain them together better.

This is very much off the top of my head, and I’m not suggesting at all that this is the best possible improvement. I hope it’s a start though.

1. A journalist is asked to cover a major event in a large ballroom. She wants to include a note about how many people attended the event. How could she estimate the number of people without actually counting everyone?

2. Find a location where you can make a rectangle that measures 5 feet by 5 feet. Have your classmates stand close to each other inside this rectangle (as if you are in a small area watching a music concert). Count the number of people you can fit in this rectangle and find the ratio of this number to the area of the rectangle. How could the journalist use this information to her advantage? [You might need to be a little more explicit here — more hints maybe]

3. Suppose there are two areas in the ballroom: A dance floor, where people are pretty tightly packed, and a separate area where there is much more space between them. How would this change the way the journalist uses the information from the previous question?

So there is (hopefully) some kind of flow from one question to the next, each building off the one before it, rather than just a bunch of questions that all fit into the same category.

Crowd Stuffing Revisited (Introduction to Area) « The Number Warrior, on January 20, 2010 at 9:54 am said:[…] Fix this Lesson: Crowd Stuffing […]