Ray's New Elementary Algebra · Arts. 1–17 · Unit 1: Chapter I: Fundamental rules
1. What algebra is
Goal: Your student can say what algebra is, tell a theorem from a problem, and tell known quantities from unknown ones.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
What's in the book
The first page of definitions: quantity, magnitude and multitude, the unit of measure, abstract and concrete numbers, theorems and problems, the definition of algebra, and known and unknown quantities. There are no written exercises yet.
The lesson, step by step
Warm-up
Ask three quick questions: How long is this table? How many people live in our house? How much does a gallon of milk cost?
Point out that every answer is a number of some unit: feet, people, dollars.
Quantity and its unit
Read Arts. 2 to 7 together. The key line:
The value or measure of any quantity is the number of times it contains its unit of measure.
SayA board 6 feet long contains the unit "one foot" six times. That 6 is its numerical value.
Abstract and concrete numbers
Read Art. 10.
An Abstract Number denotes how many times a unit is to be taken.
A Concrete Number denotes the units that are taken.
Ask: Is "5" abstract or concrete? Is "5 apples"? Have your student make up two of each.
Theorems and problems
Read Arts. 12 to 14.
There are two kinds of questions in Algebra, theorems and problems.
SayA theorem asks you to show something is always true. A problem asks you to find something you don't know yet.
Ask which kind each is: "Show that the sum of two even numbers is even." "Find a number which, added to 7, makes 12."
The definition of algebra
Read Art. 15 aloud, slowly, twice.
Algebra is a general method of solving problems and demonstrating theorems, by means of figures, letters, and signs.
Have your student copy it into a notebook. This notebook of rules will grow all year.
Known and unknown
Read Arts. 16 and 17.
Known quantities are generally represented by the first letters of the alphabet
SaySo a, b, c stand for things we know; x, y, z for things we are trying to find.
Practice: in "x + 3 = 10," which is known and which is unknown?
Wrap-up
Your student explains, without the book, what algebra is and why it uses letters. Two or three sentences is enough.
Afterwards
Read Arts. 1 to 17 again before the next session and add the definition of algebra to the rule notebook.
Tip
These first pages are definitions only. Don't ask for memorizing word for word; ask for the idea in your student's own words.