Section 3.2
Ways of Thinking about Addition and Subtraction
Addition can describe situations that involve an additive combination of quantities, either
literally or conceptually. Numbers added together are called addends. The number that is
the result of an addition is called the sum.
A problem situation that can be represented as a + ? = b is called a missing-addend
problem. Although the action suggests addition, the missing value is b – a. It is therefore
classified as a subtraction problem.
A situation in which one quantity is removed or separated from a larger quantity is called
a take-away subtraction situation. What is left of the larger quantity is called the
remainder.
A problem situation involving an additive comparison is referred to as a comparison
subtraction situation.
When one number is subtracted from another, the result is called the difference or
remainder of the two numbers. The number from which the other is subtracted is called
the minuend and the number being subtracted is called the subtrahend.
Quantities being considered are called discrete if they are separate, non-touching objects
that can be counted. Quantities are continuous when they can be measured only by
length, area, and so on. Continuous quantities are measured, not counted.
Activity:
Pair up with someone in the class and…
a) Classify each of the problem situations below (e.g., comparison subtraction):
b) Write problem situations that illustrate four of the different views presented for
addition or subtraction.
Section 3.3
Activity: Consider the work of nine second-graders as displayed on the following slide,
all of whom were asked to solve 364 – 79 in written form without calculators or base-ten
blocks.
1. Which students clearly understand what they are doing?
2. Which ones might understand, and which do not understand?
3. Describe in writing the steps the students followed to complete their work.
Take-away message: Children do not think about math the same way adults do. Adults
have a wider range of experience with numbers. But consider that part of the reason is
that we had limited opportunities to explore numbers and the meanings of operations.
We became “set in our ways” so to speak. Young children are often inquisitive and this
can be used to their advantage. Coming up with novel ways to solve problems often
brings with it a deeper, more conceptually based understanding. The use of traditional
algorithms can still be taught to children, but only after children have the opportunity to
explore meanings for themselves.