## Modeling and Recording Subtraction: Overview

Subtraction is taking away or separating items from a group and finding how many are left. Children have already had various informal experiences with breaking apart and comparing groups. They are now ready to begin exploring subtraction concepts more formally, initially through the use of manipulatives and later through pictures.

Modeling subtraction involves using manipulatives such as counters, beans, and cubes, as well as pictures, to represent subtraction facts and subtraction problems.

Children at this age are not ready to understand subtraction at the purely symbolic level. They need to work with actual objects so that they can form a concrete understanding that subtraction involves breaking apart groups. At this point, children cannot be expected to memorize subtraction facts and will rely on being able to count the objects remaining in a group to find the difference.

Once children have had a wide array of experiences breaking groups of actual objects into two parts, you can use drawings and other pictorial representations to model subtraction. Children learn to circle the part of the group being subtracted and put one large *X* over this part, as shown below.

Drawing sketches and viewing pictures help prepare children for the transition to a more symbolic understanding of subtraction. These visual models make the connection between the actual items being broken into smaller groups and the numbers and operational symbols used to represent them in a subtraction sentence.

After children have had ample opportunity to model subtraction with a variety of materials, the minus and equals symbols can be introduced, but again, only in the context of grouping real objects.

The strategy of modeling subtraction can be used to teach a variety of concepts such as subtracting 1 or 2 from a number and the relationship between addition and subtraction.

As they progress in math, children will continue to use manipulatives and pictures to model concepts such as addition and subtraction of greater numbers and the relationship between addition and subtraction.