The Vocabulary of Subtraction

Near the beginning of this month, there was a blog entry (“Vocabulary of Addition”) in which I defined the math terms for an equation using the operation of addition. Today, I will show you the English math words associated with the fundamental skill of subtraction and its associated numerical expressions {language model}.

A minuend is the number from which another is to be subtracted.

The minus sign is the symbol that represents the operation of subtraction in this equation.

The subtrahend is the number to be subtracted from the minuend.

The difference is the result of subtracting the subtrahend from the minuend.

As you can see, the terms associated with subtraction are a little more obscure and less commonly used in math conversations than the ones for addition. These terms emphasize the fact that the order of terms in subtracting two numbers does matter.  We need to recognize this difference when we use language to describe mathematics.

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The Standard Algorithm of Addition: Part 3

In the blog “Standard Algorithm of Addition: Part 1,” we learned how to set up addition problems in a vertical format so that we can manually calculate their sum. We also learned the mathematical terms for the components of arithmetic expressions of additions. In the blog “Standard Algorithm of Addition: Part 2,” I used a {visual model} to explain the concept behind this fundamental algorithm using green square blocks and blue rods to represent the addends. In this blog, I will show you how the standard algorithm works {number model}.

First we set up the arithmetic expression in a vertical format (A). Now we will first focus on the ones column and work our way from right to left (B). We mentally add the digits in the ones (9+7=16). Note the sum is greater than 9. This sum is equivalent to 1 unit of ten (blue rod) and 6 units of ones (green squares) (C). I write the digit for the 6 units of one in the ones column under the underline (D). I place the 1 digit of ten at the top of the tens column (E).

Working our way from right to left, we move to the tens column (F). We add the digits in this column noting that we are actually adding multiples of ten (G). Since the sum is not greater than 99, we simply write the sum of the digits in the tens column underneath the underline (H). Therefore, the sum of the addends, 29 and 47, is 76 (I).  It is the most common technique of addition taught to math students, but it is not the only one.  We’ll look at some other addition algorithms in future blogs.

Can Alice do Addition?

John Tenniel (1820-1914) was a British illustrator, graphic humorist and political cartoonist. He achieved considerable fame as the illustrator of Alice. Tenniel drew ninety-two drawings for Lewis Carroll’s “Alice’s Adventures in Wonderland” (London: Macmillan, 1865) and “Through the Looking Glass” (London: Macmillan, 1871). There is an illustration to the ninth chapter of Through the Looking Glass and excerpt that touches upon the topic of recent blogs.

Illustration to the ninth chapter of “Through the Looking Glass” by John Tenniel. Wood-engraving by the Dalziels.

“Manners are not taught in lessons,” said Alice. “Lessons teach you to do sums, and things of that sort.”
“Can you do Addition?” the White Queen asked. “What’s one and one and one and one and one and one and one and one and one and one?”

“I don’t know,” said Alice. “I lost count.”
“She can’t do Addition,” the Red Queen interrupted..

The .pdf copy of this book was made available to the public by Lenny de Rooy at her website, Lenny’s Alice in Wonderland Site.