Author Notes

Replies to reviewers' comments to 04_01_13_1 How Big Is Earth are indicated with >>>.

M4.4.8 Understands that scale drawings can help one measure distances and angles that are inconvenient to measure directly.

>>> One reviewer is not sure this is appropriate. I believe a teacher would certainly encourage students to make a sketch, with measurements of the height of the gnomon and the ground-length of the shadow to assist in their understanding of the geometry and to determine the angle ψ. I think it should remain on the Benchmarks list.

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Apparatus: In suggesting how to ensure that the gnomon is truly vertical, there might also be value in mentioning use of a plumb bob.

>>> This is impractical for setting up a truly vertical gnomon. The radius of the solid plumb bob will interfere with placing its thread close to the gnomon. An offset hook to avoid contact between the plumb bob and the gnomon requires a good eye to make the thread and the side of the gnomon parallel, and then it must still be rotated 90 deg and aligned the same way to ensure the gnomon is vertical, as the bob pendulums about. A carpenter's level is much more efficient and simpler to use.

Procedure:
Please address the apparent inconsistency between needing to make measurements over a couple hours to determine local noon and then to use that local noon to measure the gnomon shadow at both locations.

>>> It was addressed but an additional comment has been added.

The problem arises that local noon will change daily, even if only slightly.

>>> This is true, as mentioned in the text, but a day or two difference when measuring a soft-edged shadow is not going to make a measurable difference.,

It should also be noted that the local noon at the two schools may be slightly different, depending on how close the longitudes are and the range of latitude.

>>> It is noted and repeated that both schools have to make all preparations for themselves.

Underlying Principles:
Eratosthenes: There should be some discussion about what/where the Tropic of Cancer is and its relation to the locations of Aswan and Alexandria. Possibly a map of Egypt or Africa showing the relative locations would be helpful.

>>> I'm all for mixing science and math with other subjects like geography but I think this suggestion is beyond the scope of a PUMAS activity and will take even more space. A teacher should be able to find a map and do this if it fits into their teaching style. The information necessary is present in the text or footnotes.

Overall, this section should probably be expanded.

>>> Short of following the reviewer's suggestions, I don't know what more to add.

Determining Local Solar Time without a sun dial: This procedure should be described much earlier in the document, especially in light of the concerns mentioned above about determination of solar noon.

>>> My goal is to energize this activity by showing what can be done without modern technology. A teacher only needs to read through the activity to find instructions.

"Standard time zones are defined every 15° of longitude": This is only true on average!

>>> Well, no. The definition is as stated. Geography and politics have "gerrymandered" the zones around the world. I noted this in footnote 5.

. "¦ The effect of Daylight Saving Time (or other non-standard time zones) should be explained before the example case.

>>> I disagree. The two examples were chosen, and the month of observation was specified, to demonstrate among other differences the need to correct for Daylight Saving Time.

There seems to be over-reliance on footnotes for important details that should not be overlooked.

>>> I agree there are lots of footnotes but the details in them are not critical to the activity. They are informational.

General comments:
1) What happens if the sun is not visible at both sites during local solar noon due to clouds or other obstructions?

>>> I think the collaborating teachers will figure out that they should contact each other by phone, skype, or email to confirm all's well. They don't need to be told that.

The pathological case of arctic/antarctic winter could also be mentioned where the sun may not even visible at local "solar" noon.

>>> This activity is about measuring Earth. It is not about seasons, midnight suns, six-month nights, and all the rest that I suppose could include schools in Nunavuk and somewhere in Antarctica.

2) Overall, this is a good set of activities for PUMAS. However, the manuscript should be reorganized for more even pedagogical treatment.

>>> This is too ambiguous to address. I will accept your guidance on dealing with the many issues this reviewer still wants addressed.

>>> My sense is that this reviewer didn't read this activity carefully and assumes teachers know less than I assume they do. I'm not sure who is right about that but I try and write these activities as clearly and completely as I can, while staying on topic. Changes due to both reviewers have already added two pages to the activity.

SJE

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