Bedtime math extensions

Who: J1 and J2
Where: all around the house
When: 6 am

It is summer vacation for J2 and J3, so we have been doing a lot of activities. Unfortunately, there is almost no free time to blog about it.  For now, let me share some of the conversations J1 and I have had about recent Bedtime Math posts.

Doubling Volcanoes

Today, we talked about this post: Instant Island. In particular, we focused on the last part, the "big kids bonus" question: if an island is ¹/₂ mile wide and the width doubles every month, how wide will it be in 4 months?

Okay, forget about the answer for a moment, does the question make sense? First, we asked: if this were true, how long would it take the volcano to stretch around the circumference of the Earth? Using some familiar powers of 2, we figured out it would be slightly less than 16 months. It seemed pretty clear that this didn't make physical sense, since we clearly don't see small islands cover the Earth like that.

We talked about this doubling growth process for a while. What things do we know that work like this? J1 listed:

• bacteria
• people
• computer viruses
• plants

We talked about what is happening: basically, the new "material" is able to reproduce itself, so the more you have, the more productive potential you have.

Does the growth keep going forever? No, otherwise everything would be covered, actually become, the thing that is doubling. At some point, these all run into a limiting factor, food, water, space, etc.

Back to the island: J1 realized that the growing island would hit other landmasses before it went around the Earth. If you consider connecting with Asia to count as "growth" for the island, then there could be moments of extremely fast growth. At the same time, we know that the Eurasian landmass isn't growing with an exponential process, so this connection won't contribute to the further growth of the volcanic island.

Stuffed with lead?

We were scratching our heads about the weights in this Stuffed Animal post. The average weight per stuffed animal assumed in this post is 7 pounds. We had two conversations about this: how much is that in grams and how much do our stuffed animals actually weigh?

First attempt, a scant 27 grams

Hefty Panda is only 281 grams

Massive Diplodocus is about 100 grams lighter

One of our heavy-weights: still under 400 grams

Not a stuffed animal. This is the trickier we had to use to break 1 kg

Suffice it to say, we had no stuffed animals that exceeded 1 kg.

Heavy Pencils

After having an experience with unreasonable weight measurements, Pointy Gorilla helped launch a similar conversation. Actually, it came from misreading! We connected the following comments:

1. Gorilla weighs 300 pounds (we read this as the pencil gorilla)
2. The big kids question implies a certain number of pencils used (under 600)

So, how heavy are those pencils? Given what we know of real pencils, how much would that gorilla actually weigh?