As part of a activity about measurement in class, I challenged my students to estimate .35 and .7 the width of a sheet of paper on their own without and measuring. We then brought the groups together and compared their estimates.

When I measured .35 and .7, I asked them if they thought all the .7 estimates were closer to .7 than .6 or .8. Most of them were pretty good. But when I asked them if any of their .35 estimates would round to .35, few were close enough.

With this, we talked about how we can only estimate one digit further than we have marks and still be pretty consistent and set up our discussion of sig figs.

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Corey,

This estimating .7 and .35 activity is great. One question: I think I can use the same way we add tenth marks for the glug to evaluate the .7 estimate. How do you evaluate the .35 estimate?

Donghong

So I asked them what numbers round to .7 first (.65-.74) and we drew them on the paper and saw that most estimates fell in that range. Then I asked them the same for .35 and drew .345 and .354 on the paper and only one or two estimates fell in that range. I turned the focus soon to if we could feel pretty confident that if I asked most people to estimate to the tenths we would all be pretty close. Our error range was around .05 or so. While if I asked for one hundredths, our error range was still .05 which means our estimates were not good enough to communicate the value measured to someone else.

Hrmm, I really need to write this up more thoughtfully as a full blog post. Does it make sense to you?