Models of Addition

Learning the three models of addition enables children to fully understand addition used in problem solving, various operations, and in everyday life.

Putting Together: two separate sets meet in one location.

Adding On: one set moves to join another set.

Separating: adding together 2 stationary sets.

If sets are not clearly understood, group/s can be substituted for set/s. After explaining the three models, examples should be presented. It takes a while for children to realize that the numerical answer is not the answer – you want to hear which model it is. The following are some examples, first for a mother with a child or two and then for a teacher with a class:

Mother, for putting together: Sam is in his bedroom and Julia is in the living room. Their mother calls both of them to meet her in the kitchen. When they arrive in the kitchen, how many people are there now?

Mother, for adding on: Lizzy is by herself in her house. Jane and Tom are playing outside. Lizzy asks them to come inside to play with her.  How many children now are playing inside?

Mother, for separating: There are two green cars parked on the side of the street.   Two red cars are parked in a parking lot.  How many cars are parked?

Teacher, for putting together: There is a program in the assembly.  Mrs. B’s class leaves their room and Mr. F’s class leaves their room and both go to sit in the assembly. How many children are in the assembly?

Teacher, for adding on:  Our class is in our room and we invited Ms. Green’s class to come and see our play.  How many are in our class now?

Teacher, for separating: Five children in Mrs. T’s class are wearing red today. Seven children in Ms. Smith’s class are also wearing red. How many children are wearing red?

Again, it takes practice for children to answer which model it is. But when children are easily able to give the correct model, they will fully understand the use and purpose for addition.

Read more about teaching Math in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success, beginning on page 113. Also, see 7 reviews on

   Teaching Young Children © Peggy Broadbent 2011 - All Rights Reserved