Ray's New Higher Arithmetic · Arts. 59–62 · Unit 5: Multiplication
11. Multiplication: terms and the short multiplier
Goal: Your student names the parts of a multiplication, states its principles, and multiplies by numbers up to 12 in one line.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Multiplication defined two ways, the terms (multiplicand, multiplier, product, factors), six principles, the two cases, and Case I (multiplier not over 12) with a rule and 14 examples with answers.
The lesson, step by step
Warm-up
Quick tables: 7 × 8, 9 × 12, 11 × 11, 6 × 7.
The idea
Read:
Multiplication is taking one number as many times as there are units in another.
The book adds that it is a short way of adding equal numbers. Work the book's example: How many trees in 3 rows of 42? 42 + 42 + 42 = 126, or 3 × 42 = 126.
The principles
Read these three and talk about each:
The multiplier must always be an abstract number.
The product is the same in kind as the multiplicand.
The product is the same, whichever factor is taken as the multiplier.
Ask: Can you multiply 5 dollars by 3 dollars? (No: you take 5 dollars 3 times, and the 3 is just a number.)
Case I
Read the rule:
Write the multiplicand, and place the multiplier under it, so that units of the same order shall stand in the same column
Work the book's example: At the rate of 53 miles an hour, how far will a railroad car run in four hours? (212 miles.)
Guided practice
Together:
1. 195 X 3.
10. If 4 men can perform a certain piece of work in 15 days, how long will it require 1 man?
(585; 60 days.)
Independent practice
Your student works the 14 examples under Case I. The book prints all the answers.
Wrap-up
Ask: Why does 1 man need longer than 4 men? (He does all the work alone, so 4 times as many days.)