MA201JANUARY 31, 2010

Subtraction

Missing Addends

Problem

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

Missing Addends

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)

Your Answer: 6

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

Problem 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.”

So when doing our problem,

The kids were seeing it like this:18 + __ =24,

then when calculating the problem, they would

think of it like:18 + 24 = 42

So when we teach this

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:

Practice

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

Answers

3 + 3 = 6 1 + 4 = 5 4 + 2 = 6 7 + 1 = 8 2 + 3 = 5 2 + 2 = 4

Also in this article, they mentioned games to play to help kids to think this way.

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.

References

Kamii, Constance. “Instead of Teaching Missing Addends” Teaching ChildrenMathmatics. April 1998.

Morgan-Worsham, Dode. “The Dilemma for Principles.” In Achievement Testing in

the Early Grades: The Games Gown – Ups Play, edited by Constanace Kamii, 61-69. Washington, D.C.: National Association for the Education of Young Children, 1990.

Any Questions?