inside the bag. Next, the teacher (or a child volunteer) takes a little walk (as if going to school) and encounters Plus Pup along the way (by picking up the Plus Pup card). As the icon on the card suggests, Plus Pup gives the cookie carrier one more cookie. The bag is opened up slightly to receive a real cookie and is then promptly closed. The challenge children confront is this: How many cookies are in the bag now? How can we figure this out?
If the teacher is patient and allows children to explore these questions as genuine problems, a range of solution strategies are often provided as children play and replay the game with different quantities of cookies. The first and most obvious solution children suggest (and implement) is to open the bag, take the cookies out, and count them. This provides opportunities for the teacher to draw children’s attention to the quantity transaction that has occurred to produce this amount. For example, the teacher may say, “We have five cookies now. How do we know how many Plus Pup gave us? How can we figure this out?” If no answers are forthcoming, the teacher can prompt the children by asking, “Does anyone remember how many cookies we had at the start?”—thus leading them to make sense of the quantity transaction that has occurred (i.e., the initial amount, the amount added, the end total) by describing the entire process in their own words.
As children replay this game, they gradually come to realize that they can use the counting numbers themselves, with or without their fingers, to solve this sort of problem, and that dumping the cookies out of the bag to count them is unnecessary. When children begin to offer this solution strategy, the teacher can shift the focus of her questions to ask, “Who can predict how many cookies are in the bag now? How do you know?” After predictions and explanations (or proofs) have been offered, the children can be allowed to examine the contents of the bag “to confirm or verify their pre-