Constituative Rules of Chutes and Ladders

Players all begin with a value of zero. Players alternate turns adding a random number of 1–6 to their current value. The first player to reach a value of exactly 100 wins (if adding the random number to a player's total would make the total exceed 100, do not add the random number this turn). When a player's total exactly reaches certain numbers, the total changes. For example, if a player reaches exactly 9, her total becomes 31. If a player reaches exactly 49, her total becomes 11.(This r...

 Teaching Temperature

Outside Temperatures. Place a thermometer outside a window so students can make daily calculations and keep a chart reporting the actual temperature and the temperature change from the previous day. Students will see that the change can be a negative number without the temperature falling below 0—an often-confusing concept that is clarified by these observations. An achievable-challenge extension could include barometers, and students who need more advanced work can learn how negative—or...

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...

 All the Ways of Intuiting 1729

Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two integral cubes is inappropriate and obscures the workings of the naive mathematical mind. To be sure, a computer-mind could come up with that list at a wink. But what would induce it ...