Math Background

Modeling Subtraction: Overview

Subtraction involves three different types of situations. The first, and the easiest for children to learn, is separation, or taking away, in which one quantity is taken away from another to find out what is left. The second is comparison, in which two quantities are compared to find the difference. The third is part-whole, in which the quantity in the whole set and one part are known, and may be used to find out how many are in the unknown part. Early instruction should provide many opportunities for children to explore the three types of subtraction situations. Children learn the meaning of subtraction through concrete experiences and then learn to record subtraction in horizontal and vertical forms.

7 − 3 = 4   7
− 3

Children were introduced to subtraction in Kindergarten and have experience with separating and comparing groups. Many children are now ready to learn the formal structures and rules of subtraction.

Subtraction is the inverse of addition, and although it is a different concept, it may be taught by using similar materials, models, and methods.

As for modeling addition, have children use manipulatives, such as counters, connecting cubes, and beans, to model subtraction, as well as pictures to depict subtraction facts and to illustrate subtraction problems.

7 cannisters - 3 cannisters = 4 cannisters
7 − 3 = 4

Using manipulatives to model subtraction is extremely important for children. By manipulating objects, they can actually see what it means to “take away” from a group. Children need time to gain an understanding of this concept before they begin to represent subtraction symbolically in number sentences or memorize basic facts and perform mental calculations.

Modeling subtraction can also be used to give children experience subtracting zero. Help them recognize that the difference between any number and zero is the original number and that the difference between any number and itself is zero.

7 cannisters - 0 cannisters = 7 cannisters
7 − 0 = 7 7 cannisters - 7 cannisters = 0 cannisters
7 − 7 = 0

Once children have had experience “taking away” objects from a group, have them use drawings and other pictorial representations to model subtraction.

7 birds - 3 birds = 4 birds
7 − 3 = 4

By drawing pictures and using illustrations, children can make the transition to a more symbolic understanding of subtraction. These visual models help children make the connection between the actual items and the numbers and operational symbols used to represent them in a subtraction sentence.

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

Houghton Mifflin Math Grade 1