I knew this would cause a bit of disequilibrium. But I also knew that the right amount of disquilibrium = a great environment for new learning. After thinking a bit, he wrote out a long problem of 10+10 until he'd written 20 tens. He then made 5 boxes and drew curved lines connecting a 10 to each box. In the middle of this he stopped and said, "I know! They cost $.40!" I asked how he knew. He said that there are 20 tens in $2. And 20 divided by 5 equals 40. (Since he seemed to be on the right track and was obviously thinking in decimals, I didn't interrupt.) Then, after a while, he grinned and said, "We should get 4 candy bars for $1.60. Then [brother] and I can each have two so it's fair."
When do you successfully use math in the moment?
, in which an inchworm measures a variety of birds (a flamingo's neck, a toucan's beak, a heron's leg...) only to be told by a nightingale, "Measure my song or I'll eat you for breakfast." The inchworm "measures," moving farther and farther away as the bird sings, eventually inching out of sight. 
next to it, and asked my son to estimate how many tiles would be needed for the total length. He guessed 25 by looking at the first group of tile and explaining it would probably take 5 of those to finish the string. I put tile along about half the string and asked if he wanted to revise his estimate. With 11 tile now along the string, he changed his estimate to 22. He measured the string with tile, finding that it took 23.
, a slightly different version of the traditional Jack tale. Both boys enjoyed hearing about how Jim helped the giant by measuring him for new glasses, new teeth (!) and a new wig. We then continued with a little giant measuring of our own.
. One side tells the story from the goose's p.o.v. (favoring the giant!) while the other side tells Jack's story in the traditional way.
while preparing for my math and literature class. (*See note at bottom of post about the related 
.)
marble roll last Christmas. It's been a hit at our house with ages 3* and up...way up. (*This assumes the 3yo does NOT put things in his/her mouth. That would NOT be true of the child I caught in my son's preschool class this morning. I asked him what the lump was in his mouth and he guiltily spit out a marble. True story.)
or the 
, but my son says "we should buy a bigger fridge so we can get them."
The creator, Theoni Pappas, is also the author of several well-known 
, including titles such as 
, 
, 
...all titles that I own and use in my math/literature class.
, also by Pappas. (I read that the children's version is suitable for grades 3-8.)
by Donna Jo Napoli, totally changed. When I read it alone, I wasn't terribly excited. When I read it to my student, his enthusiasm was catching. In the book, siblings, ages 8, 8, (twins), 4, and 2, wish on a star. Over several nights they discover that their wishes are granted in fractions, determined by their ages: 8yos get 1/8, 4yo gets 1/4, 2yo gets 1/2. My student quickly understood the concept of fractions, exclaiming after the second page (which shows four 1/4ths make 1), "then one penny is 1/5th of a nickel!" In the story, the siblings put their wishes together to make one whole wish and get the wish that all of them want. [Concept: fractions]
My current student and I have not talked much about probability. The book, 
by Virginia Kroll, some animals witness children playing a game of tug-o-war and set out to play their own game. It quickly becomes obvious, however, that they have a problem making the sides "equal" with five animals competing. But even when the sides have equal numbers, the groups still aren't fair because the weights aren't equal. They set about figuring out how the animals' weight can be evenly distributed by balancing on a park teeter-totter. But when the bear is distracted by honey, they learn that equal effort is also important. Super cute. [Concept: equality]
by Patricia Reilly Giff is part of "The Kids of Polk Street School" series, chapter books for young readers. This book has a reading level (R.L.) of 1.9 (first grade, ninth month). I read it aloud to my sick 7yo. The story captivated him and he would read ahead over my shoulder and then hide his eyes because he was nervous about the events.
