Ray's New Higher Arithmetic · Art. 63 · Unit 5: Multiplication
12. Long multiplication and practical problems
Goal: Your student multiplies by numbers of several figures, placing each partial product correctly, and solves the book's practical problems.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case II (multiplier more than 12): the rule, the worked example 246 × 235, 14 examples for practice, and 8 practical problems (inches in the earth's circumference, the distance of the sun, and others). Answers are printed.
The lesson, step by step
Warm-up
Mental: 25 × 4, 25 × 40, 12 × 15.
The rule
Read:
Multiply each figure of the multiplicand by each figure of the multiplier successively
Each partial product starts under the figure of the multiplier that made it.
Work the book's example
Multiply 246 by 235. 246 × 5 = 1230; 246 × 3 tens = 738 tens (write 738 one place left); 246 × 2 hundreds = 492 hundreds (two places left). Add: 57810.
Guided practice
Together:
1. 7198 X 216.
2. 8862 X 189.
(1554768 and 1674918.)
Independent practice
Your student works the rest of the 14 examples, then as many of the 8 practical problems as time allows. One begins:
In a mile are 63360 inches: how many inches are there in the circumference of the earth
Check
All answers are printed. Check one problem a second way: swap the factors and multiply again.
Wrap-up
Ask: Why does each partial product move one place left? (Each figure of the multiplier is worth ten times the one to its right.)
Afterwards
Finish the practical problems on a second day if needed.