Ray's New Elementary Algebra · Arts. 60–64 · Unit 1: Chapter I: Fundamental rules
6. What plus and minus really mean
Goal: Your student can explain how a "sum" can be smaller than the numbers added, and why −10 is less than −2.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
What's in the book
A short reading section with no exercises: what algebraic addition and subtraction really mean, how negative quantities are ordered, and examples with money in a drawer and a ship's latitude.
The lesson, step by step
Warm-up
Ask: You have 5 dollars and owe 3. How much are you really worth? (2 dollars.)
Adding can make smaller
Read Arts. 60 and 61.
algebraic addition is the process of collecting two or more quantities into one.
SayThe sum of 5 and −3 is 2. Adding a minus quantity is like adding a debt.
Which is less?
Read Art. 62.
those which are numerically the greatest are really the least.
Draw a number line from −10 to 10. Ask: Which is less, −2 or −8? Mark them. A debt of 8 is worse than a debt of 2.
Money and latitude
Read Art. 63. Act out the money example with coins: put money in, take money out, and keep score with + and −. For the ship, north latitude is + and south is −; ask what sailing from 5° north to 3° south does to the number.
Subtraction in arithmetic and in algebra
Read Art. 64.
Subtraction, in arithmetic, shows the method of finding the excess of one quantity over another of the same kind.
SayIn algebra, subtracting finds the difference even when the second number is bigger, or negative.
Wrap-up
Your student makes up one example of their own (temperature, a bank balance, floors above and below ground) and explains it with + and −.
Afterwards
A quick review of five subtraction exercises from the last session, chosen from the ones that went wrong.
Tip
This is a good session for a slower day. The ideas here make the rule of signs in multiplication much easier.