Measure 28 — MATH 3

Number Sense: Comparison of Quantity

Child compares and orders simple quantities

Another dimension of young children’s developing number sense is the ability to compare quantities and determine the order of the relationships (for example, if they are equal, more than, or less than). This ability is highly interrelated with the developing knowledge children have about counting and their understanding of addition and subtraction operations. Children are first able to compare and order amounts of things that are obviously the same or different. Even very young children can determine whether two groups of objects are equal or unequal in number and which group has more, as long as the number of objects in the groups are very small (two versus three) or are very different (four versus eight). During the preschool period, children begin to use strategies, like matching or one-to-one correspondence and counting, to compare and order quantities whose relationship cannot be determined by physical appearance. They also learn and begin to use relational terms, such as “same number,” “more than,” and “less” or “fewer than.”

Infants begin to learn about quantity as they interact with objects, attending to objects in their environment and manipulating objects in their play. They put objects together into groups and change the groups to make them larger or smaller. They also notice larger versus smaller amounts; for example, a child who loves grapes might be excited to see that he has a large bunch of grapes in his snack bowl.

Toddlers construct matching sets by putting things together in one-to-one correspondence. For example, they might give each friend a cup or put one block in each cup of a muffin tin. They pair objects based on similarity, function, or some other association, but not with the specific aim of comparing number. Older toddlers can, however, determine which of two groups of objects has more, as long as the groups look very different in number. They may do this non-verbally, for example by picking the container with many markers over the one with few. Toddlers also begin to use words that describe dimensions of quantity, such as “a lot” and “many” to refer to large collections. Older toddlers begin to understand and more frequently use relational terms, by saying, for example, “I have more.”

Although their ability to compare and order quantities still depends very much on whether groups appear equal or different in number, young preschoolers begin to develop a more quantitative understanding of number relationships and order. They can perceive small differences when comparing groups of one to four objects and can identify which of two small groups has more, when those groups differ by only one. They generally do this without counting. Young preschoolers also begin to use one-to-one correspondence/matching to compare the numbers of objects in two groups. They may do this in everyday situations, like setting the table, by saying, “We have four plates, but only three spoons,” for example. Additionally, preschoolers begin to use number words when they are comparing quantities, noticing, for example, that “You have three and I have three. We have the same.”

Older preschoolers learn and use relational terms such as “same number,” “more than,” and “less” or “fewer than” to compare and order quantities. They also increasingly use number words to compare quantities. They may still use one-to-one correspondence, but they also begin to use counting to compare groups, counting one group of objects and then the other to determine if each group has the same number or which has more or fewer. When older preschoolers count to compare, their efforts are usually not as reliable at first as their use of direct correspondence. Preschoolers may make mistakes when they count, and many are still misled by perceptual cues, for example, thinking that a longer row of objects has more than a shorter row. Therefore, they may not trust their counting, even when it is accurate, if groups look physically different. As their counting becomes more accurate, children are more likely to use it as a reliable strategy to compare numbers. Eventually, as their knowledge of number relationships develops, children become able to compare and order numbers in the counting sequence. For example, if told that Matt’s birthday is in five days and Juana’s birthday is in four days, the child knows that Juana’s birthday is sooner.