# Proportions

By the time kids reach Algebra II, proportions are second nature. "Cross multiply and divide!" they will scream at you. But have they ever stopped to wonder if proportions work in the first place? There are many easy ways to turn this lesson into a "leave the classroom" activity. My first year I did it by having the kids measure small objects, wander outside and measure their shadow and the objects' shadow and solve for their height. Worked well, the heights were within a percentage point or two, but you need nice weather.

Last year I did not do the activity because the weather didn't cooperate but with such a push for language and my own goals for groupwork, I found an alternative.

You need:

• rulers
• paperclips
• objects too tall to measure
• notebooks

The paperclips attach to the bottom of the ruler to give an extended edge for the bottom. At the beginning, have the kids measure their actual heights. Walk out to your objects and hand them a ruler. Tell them to pick a spot where the object "fits" on the ruler noting where they're standing and the "fake height" of the object. Without moving, have every member of the group run out next to the object and record a "fake height" for each person. In my case we used three objects so each kid wrote down three fake heights for themselves. Well, every kid wrote down the entire group's worth of data, useful on calculation day when some kid forgot a measurement or wrote it down wrong.

Back in class have every class make a guess on the real heights of the tall things. Share the guesses on a spreadsheet on the board. Walk through the math. Have the kids compute a real height based on their individual fake heights. Share with the group, determine a group average for the object's real height. Share the averages. Discuss challenges. My kids had to speak saying "One challenge we faced was..." and "One reason our results might be off is..." and that brought up the imprecision of 99ยข rulers, shaky hands, and distracting group members.

Finally, reveal the answers. I had a couple groups nail it.

My school cafeteria has a two story ceiling, offering plenty of choices. I picked the second floor railing, a large maintenance door, and columns:

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