Subtraction Missing Addends

 Doreen planted 24 tomato plants in her garden and Justin planted 18 tomato plants in his garden. How many more plants did Doreen plant?  18 + =24

Recently, a principle wrote, “While visiting a first grade classroom one morning, I observed a lesson on missing addends. …Children were struggling with what that they were being asked to do and the teacher was visibly frustrated. Afterwards, when I discussed the lesson with the teacher, … she replied without hesitation, ‘Most first graders can’t do missing addends, but it’s on the test’ ” (Morgan Worsham 1990, 64)

Some kids in a first grade class would have given an answer of 42. How did they get that?

 I found this problem described in a journal article, “Instead of Teaching Missing Addends” by Constance Kamii, Barbara Lewis, and Bobbye Brooker.  The difficulty of missing addends for these children was in understanding the written form of the problem.  “… reading “3 + __ = 5” with understanding requires thinking about a part (3), the whole (5), and the missing part, simultaneously. The ability to think in two opposite direction simultaneously is called reversibility. Children who have developed reversibility can interpret “3 + __ = 5”. … Those children who have not comprehended reversibility write “8” as the answer, by adding the 3 and the 5.”

The kids were seeing it like this: 18 + __ =24, then when calculating the problem, they would think of it like: = 42

 We need to explain the different parts of the equation.  When we have “3 + __ = 5”  We can show them with the 2 Models we learned the Measurement Model and the set model.  The Set model that looks like this:  The Measurement model that looks like this:

 3 + __ = 6  1 + __ = 5  4 + __ = 6  __ + 1 = 8  __ + 3 = 5  __ + 2 = 4

 = 6  = 5  = 6  = 8  = 5  = 4

 They had “go ten”, which was “go fish” but instead it was “go ten”. You would have to make a match by asking for a card that would make you equal 10.  So I would have a 2, and I would have to ask another person for an 8 to make 10 and get my match.  The kids would slowly start to learn how to come up with the sum by having one of the numbers and finding the other number.

Kamii, Constance. “ Instead of Teaching Missing Addends ” Teaching ChildrenMathmatics. April Morgan-Worsham, Dode. “The Dilemma for Principles.” In Achievement Testing in the Early Grades: The Games Gown – Ups Play, edited by Constanace Kamii, Washington, D.C.: National Association for the Education of Young Children, 1990.