Ray's New Higher Arithmetic · Arts. 72–78 · Unit 6: Division
16. Division: terms and principles
Goal: Your student defines division three ways, uses the words dividend, divisor, quotient and remainder, and knows the principles connecting them.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Division defined, its terms, how it relates to multiplication, three ways of writing it, four principles, the two classes of division problems, and long and short division introduced with 820 ÷ 5.
The lesson, step by step
Warm-up
Mental: 72 ÷ 8; 100 ÷ 4; how many 25s in 175?
The idea
Read:
Division is the process of finding how many times one number is contained in another
Division is a short method of making several subtractions of the same number.
Work the book's example by subtracting: How many times is 24 cents contained in 73 cents? 73 − 24 − 24 − 24 leaves 1. So 3 times, remainder 1 cent.
The terms
Read:
The Remainder is the number which is sometimes left after dividing.
Quotient is derived from the Latin word quoties, which signifies how often.
Dividend, divisor and quotient match the product and its two factors in multiplication.
Principles
Read:
The dividend is equal to the product of the quotient by the divisor, plus the remainder.
The remainder is like the dividend.
Check it with 73 = 3 × 24 + 1.
Two kinds of problems
Read the two classes:
To find the number of equal parts of a number.
To divide a number into equal parts.
Ask for an example of each: How many 5-cent stamps for 60 cents? Share 60 cents among 5 children.
Practice
Divide 820 by 5 both ways shown in the book: written out in full, then short division with the work done mentally. (164.)
Wrap-up
Ask: If you divide dollars by dollars, what kind of answer do you get? (An abstract number: how many times.)