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Models of quantitative relationships also require hands-on approaches to build awareness and understanding of values. Ask young children a question such as "How many eyes in a group of four people?" and you may witness a variety of problem-solving approaches. Some children may gather together in a group of four and count the number of eyes. Some may draw pictures of people with eyes. Still others may use four paper plates with two counters on each plate. Some may be ready to write 2 + 2 + 2 + 2 = 8. As educators, we encourage children’s thinking by asking questions such as "How do you know there are eight eyes?" "What other ways can you show this situation?" "What kind of pattern do you see?" "What if there were only three people?" These questions open the doors for dialogue that prompts further thinking about models of quantitative relationships.

Teachers can use models to represent and teach quantitative relationships during everyday classroom experiences. For example, in Mr. Carson's prekinder-garten classroom, children model and discuss quantitative relationships during snack time. Mr. Carson invites four children to each choose three snacks from a plate of crackers and pretzels. Elena chooses three crackers, Tyrone picks one pretzel and two crackers, Martin selects two pretzels and one cracker, and Rosa decides to have three pretzels. The teacher encourages the children to compare and contrast their snack choices. He asks them if they have the same amount. Martin answers, "Mine is more pretzels, but I know I have 3." Rosa replies, "I have all pretzels—my 3 is easy." Tyrone adds, "Threes can be different." In this exchange the children represent and verbalize an understanding of the different ways to compose the quantity of three. In so doing, they explore models of quantitative relationships in a real-life context.