 Estimation 180  Andrew Stadel
A new estimation challenge every day of the school year, with accompanying video answers. Join the number sense challenge online by submitting your own estimates, explaining your reasoning ("What context clues did you use?") and rating your accuracy ("How confident are you?").
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 QAMA  QAMA, LLC
"The calculator that thinks only if you think, too," QAMA requires the operator to first enter a reasonable estimate. QAMA encourages rounding and rapid backoftheenvelope reckoning, but does not tolerate errors of magnitude or sign, or of basic operations with single digits. Read user instructions, scope, and more. QAMA derives from "Quick Approximate Mental Arithmetic," but also happens to mean “How Much?" in Hebrew.
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 A View from the Back of the Envelope  Mitchell N. Charity
Pages about approximation. Counting by powers of ten includes the "what order of magnitude is ...?" game, illustrated instructions for counting to ten billion on your fingers, and lots of dots  a million dots on one page, and a dot for every second in the day, with a realtime countdown graphic. The section on scaling the universe provides ways to visualize how big things are using analogies and examples, covering nanometers (nm), micrometers (um), millimeters (mm), meters (m), kilometers (km), megameters (Mm), gigameters (Gm), terameters (Tm), and petameters (Pm). How to simplify a number by rounding, rounding to an order of magnitude, sliding the decimal point, and using a number you can remember; this section also offers some calculations comparing the volume and surface area of a sphere and a box. Exponential notation discusses sliding the decimal point, order of magnitude and rounding to it, and scientific notation and how to write and speak it. Fermi questions examine rough quantitative estimates about the world: the "What order of magnitude is ...?" game, a Pinocchio estimation game, an order of magnitude investigation into the emulsification power of raw eggs in the making of mayonnaise, reflections on Why be approximate? and On Being Approximate, and a few notes on landmarks, bounding, and honesty. The scale of some things: people, peopleseconds, volume, area, length, time, mass, energy, area, the ratio surface volumetodensity, speed, volume rate (how fast volume flows, shifts, accumulates, or drains), and power. The section on developing "deep" understanding addresses brevity as a measure of comprehension, and getting a feel for big numbers, with examples on picturing altitude above maps, teleportation, probing near space with a flashlight, and atomic bonding. Body ruler measuring covers length with your body: measuring angle and distance with your thumb. Additional resources include the 1957 book Cosmic View: The Universe in 40 Jumps laid out on web pages.
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