Math Background

Number Concepts: Overview

Before children begin kindergarten, many of them will be familiar with rote counting and the recitation of numbers. However, careful development of the concept of number gives meaning to counting. This understanding comes gradually and can be reflected in the following stages.

  • Children begin by matching members of one set with the members of another set. If the sets have the same number, they are equal. If the sets do not match one-to-one, children learn to determine which set has more and which has less.
  • Children will see a set of a specific quantity and will learn that the set contains a specific number of items. In time, children will understand that the number associated with the set has nothing to do with the size, shape, color, or position of the items in the set. The number reflects only how many objects are in the set.
  • Finally, children will learn that every number has a word name and a symbol.

Although rote counting may come easily to many children, it is important for teachers to remember that the concept of number is very complex. However, the opportunities to reinforce number concepts during the school day are numerous! As you read a story, look for ways to explore numbers. Look for opportunities to ask comparison questions during your daily routine, such as Are more children having hot lunch or cold lunch? Did more children ride the bus or ride in a car to school today? Did we have more sunny days or rainy days this week? Did more children wear sweaters or jackets to school today?

Using numbers during the school day also gives children the motivation to count and write numbers. Providing a purpose for counting and writing helps children recognize the everyday importance of their new knowledge. Point this out during the day, and praise their efforts to recognize and write numbers.

Some children will be having more difficulty with the ordinal number words than with the concept. Again, provide opportunities during the day to practice by asking questions such as: Who is third in line? Will the third person in line please clap his or her hands? Is Alex fourth or fifth?

Children need to be able to understand the following concepts as they begin to learn about numbers greater than ten and place value:

  • The digits 1-9 are used to count up to nine objects.
  • Numbers greater than 9 have a group of ten.
  • The digits 0-9 are used for counting ten and more.

One way to help children prepare to understand greater numbers is to emphasize the concept of ten and some more as often as possible. Have children make their own bean sticks by gluing 10 beans on a craft stick. Have them keep their bean sticks and single beans in a small plastic bag for modeling numbers. Children will also benefit from using number lines from 0-30 as they learn about greater numbers.

Number Line 10 to 19

When estimation is introduced to children, it is important to remember that you are asking them to think in a different way. Emphasize that sometimes a reasonable guess is acceptable and that an exact answer is not always required. At this level, focus on reasonable visual estimates, and praise children's attempts. Once children get past their fears of a "wrong answer" they will usually enjoy estimating activities. You may wish to introduce activities such as the following as estimating games:

  • Use small fish-shaped crackers and a small glass fishbowl. Place 5 crackers in the bowl and ask if there are more than 10 or less than 10. Count and check. Continue with other numbers. Then reverse roles, having volunteers place the crackers in the bowl and ask an estimation question.
  • Place 30 crackers in a see-through bowl. Ask if children think there are enough crackers for each child in your class to have one. Record the estimates and then count and check. Discuss the estimates and enjoy the snack!
five starfish and five fish

Houghton Mifflin Math Grade K