Ray's New Higher Arithmetic · Arts. 1–8 · Unit 1: Introduction
1. What arithmetic is about
Goal: Your student can explain in their own words what quantity, science, art and mathematics mean, and where arithmetic fits.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The opening definitions: definition, quantity, science, principles, art, mathematics, its three elementary branches, and arithmetic as both a science and an art.
The lesson, step by step
Warm-up
Ask: Name three things you could measure, and three things you could count. Is a feeling a quantity? Why or why not?
There is no wrong answer yet; the book will give a test in a minute.
The idea
Ray starts a serious book with careful definitions. Read the first two together:
A definition is a concise description of any object of thought
Quantity is any thing which can be increased or diminished; it embraces number and magnitude.
SayNumber answers "how many?" and magnitude answers "how much?"
Science and art
Read:
Science is knowledge properly classified.
The primary truths of a science are called Principles.
Art is the practical application of a principle or the principles of science.
Ask your student to give a science-and-art pair from daily life (for example, knowing why bread rises, and actually baking bread).
Where arithmetic fits
Read:
Mathematics is the science of quantity.
The elementary branches of mathematics are Arithmetic, Algebra, and Geometry.
Arithmetic is the introductory branch of the science of numbers.
The book adds that arithmetic is also an art: it shows how to use numbers for practical purposes.
Check understanding
Sort these as number or magnitude: the pupils in a room, the length of a road, the eggs in a basket, the weight of a sack of flour, the coins in a purse, the time of a train trip.
Notebook
Start a definitions page. Your student copies the definitions of quantity, science, art and mathematics in their own words, with one example each.
Wrap-up
Ask: Why does a math book begin with definitions? (So every later rule means exactly the same thing to everyone.)
Tip
These pages are short but dense. Read slowly, and let your student argue about the examples; that is the point of a definition.