[Another page in need of overhaul. The basic idea is order of magnitude calculation and perspective seems potentially accessible quite young.]
Counting by tens
... on your fingers.
David M. Schwartz and Steven Kellog's children's picture
book "How Much is a Million?" tries this...
"If one million kids climbed onto one another's shoulders, they would be...
taller than the tallest buildings,
higher than the highest mountains,
and further up than airplanes can fly.
If you wanted to count from one to one million...
it would take you about 23 days.
If a goldfish bowl were big enough for a million goldfish...
it would be large enough to hold a whale."
(Though I wonder whether one can really count on, and build up from, mental images of airplane hight, stadium and harbor volume, etc...)
"A child asks an adult. "What is that?" The adult says, "I don't know, but it is good you asked. Asking questions is very important. It is how you learn things.". Later the child asks "What does that do?". "I don't know." says the adult. "How does that work?" "I have no idea, but it is good you are asking questions." "How big is that?" "I don't know." the response. How long was it before the child stopped asking questions?"
One advantage of the back of the envelope is that it makes many things accessible. One can often estimate things to an order of magnitude just by thinking about them. Things where obtaining the "real" values might take days or months of research.
The Fermi Off-The-Wall Math League includes grades 1-6.
Comparisons of distance, size, area, volume, mass,
weight, density, energy, temperature, time, speed
(see Resources page)
Beyond Facts & Flashcards: Exploring math with
Mokros, Jan; and TERC
"... offers parents a rich collection of games and activities that help children become successful math learners. The activities are engaging, easy to understand, and designed so that parents can incorporate them into the busy schedules of their daily lives."[back cover]
[One learns learn reading by "being read to every day and from having grown-ups listen to [your] reading." And one learns math the same way...]
(Not on the Resources page)
Comments encouraged. - Mitchell N Charity <email@example.com>
History: 2003-Feb-03 Added link to Fermi League. 2003-Feb-03 Repaired links - 1 fixed, 1 flagged. 1998.Jun.01 Added link to Rutherfoord's Atlas project. 1997.Aug.27 Added `A presentation sequence'. 1997.May/Jun Previous significant revision.