Math grid games are similar to manipulative games, but they provide a
bingo type of board with designated spaces to set the counters. This sup-
ports one-to-one correspondence concepts, because children must typi-
cally place one object on each space to win the game. The grid spaces
allow children to visualize how many more objects they need to cover the
total number of spaces, which provides an addition or subtraction prob-
lem like they will encounter in other forms later in school.

Path games also encourage children to create and compare sets, but
instead of forming sets with concrete objects, children move a specific
number of spaces along a path equivalent to the set of dots they roll on a
die. This is more abstract than simply taking objects that match a number
of dots. As the child moves his or her mover, the spaces that have been
counted are not represented with a concrete material, such as a cover-up
piece. Path games are important because they introduce the concept of
a number line, with each step along the path one more than the previous
space. The easiest path games are called short path games because they
have approximately 10 spaces, which is many fewer than their counter-
parts, long path games. There are two other differences between these
two types of path games. To make them less confusing for children who
are transitioning from grid to path games, the short path games provide
a separate path for each player and the path is straight. In contrast, the
long path games have one curved path for all players. While the short path
games are more difficult than grid games, they are considerably less dif-
ficult than long path games.

How does assessment guide planning?
Teachers who carefully record observations of children can use these infor-
mal assessments to guide their planning for the class as well as for an
individual child. For example, if a teacher has a group of children who are
largely at the global stage of quantification, she may include more oppor-
tunities throughout the classroom for children to explore one-to-one cor-
respondence, such as asking a child to get one cup for each person at the
snack table or one paintbrush for each paint container. This may encour-
age children to move forward to a new level in their thinking, perhaps at a
faster pace than if they had fewer opportunities to think about one-to-one
relationships. Likewise, the teacher might create additional opportunities
in the classroom to model counting as a quantification strategy if she feels
children are ready for more of this type of experience.

chapter 2