Session 4, Part A:
Meanings and Relationships of the Operations (40 minutes)

In This Part: Addition | Subtraction | Multiplication | Division

We will begin our look at the various meanings for each of the operations and the laws that govern the operations by examining addition.

Addition is the simplest of the four operations. The operation, however, may look quite different depending on whether a problem has an unknown result, starting point, or change. We can describe addition as a merger or joining of two or more things; we can also describe it as combining parts of a whole, with the whole or one of the parts unknown.

The following table gives an example of each kind of addition problem:

Problem Type

Starting Point Unknown

Change Unknown

Result Unknown

Merger

 Sam had some blocks. Billy gave Sam 7 more blocks. Sam now has 23 blocks. How many blocks did he have before?? + 7 = 23
 Sam had 16 blocks. Billy gave him some more blocks. Sam now has 23 blocks. How many blocks did Billy give him?16 + ? = 23
 Sam had 16 blocks. Billy gave him 7 more blocks. How many blocks does Sam have now?16 + 7 = ?

Parts of a Whole

 Jennie has some green marbles and 9 yellow marbles. She has 24 marbles in all. How many green marbles does Jennie have? ? + 9 = 24
 Jennie has 15 green marbles and some yellow marbles. She has 24 marbles in all. How many yellow marbles does she have? 15 + ? = 24
 Jennie has 15 green marbles and 9 yellow marbles. How many marbles does Jennie have? 15 + 9 = ?

The merger or joining concept always requires some sort of combining action, whereas the parts-of-a-whole concept is static. Note 2

One of the most important facts about addition is that no two quantities can be added unless they are measured or reported in the same units. For example, you cannot add 2 tens and 3 ones, or 2 halves and 3 fourths, and expect to get 5 of anything. These quantities can only be combined if we can somehow find a common unit with which to measure or label them. Note 3

Problem A1

Label each of the addition problems with the correct situation label, and identify the units involved:

MR: Merger, result unknown
MS: Merger, starting point unknown
MC: Merger, change unknown
PW: Parts of a whole, whole unknown
PP: Parts of a whole, one of the parts unknown

 a. Moisha has 7 cars. Three are red, and the rest are blue. How many blue cars does she have?
 Write an equation and see if you can match it with any of the above descriptions.   Close Tip Write an equation and see if you can match it with any of the above descriptions.

 b. Jake read 5 mystery books and 8 adventure books. How many books did he read? c. Bret has \$5, and Wendy has \$4. How much will they have if they pool their money? d. Natasha had 4 rabbits. One of her rabbits had babies, and now she has 7 rabbits. How many babies did the rabbit have? e. Reed's parents gave him \$5 for his birthday. He then had \$12. How much money did he have before?

 Part A: Meanings and Relationships of the Operations adapted from Chapin, Suzanne and Johnson, Arthur (1999). Math Matters: Understanding the Math You Teach (pp. 40-72). © 2000 by Math Solutions Publications.
 Session 4: Index | Notes | Solutions | Video