THE TRANSITION LINE // FIELD NOTES // STOP 12
Longer statements and decimal division
Field Book
Lessons 45 to 48
Method
Pencil and paper. Calculators never.
Room 3 opens this stop. Long manifests still close one entry at a time. Missing-number statements grow extra terms and still fall to the same rule, decimals sort place by place from the left, two-digit multipliers stack partial products, and division carries its point straight up into the answer.
What you have to be able to do
- Solve longer missing-number statements
- Order decimal numbers
- Multiply by two-digit numbers
- Divide a decimal by a whole number
The procedures
Longer statements and external zerosField Book Lesson 45
- Combine the known numbers first, then apply the add-or-subtract rule to what remains.
- Zeros may be inserted or removed only on the outside of a number, never between digits or against the point from inside.
Ordering decimalsField Book Lesson 46
- Compare place by place from the left: wholes, then tenths, then hundredths.
- The first place that differs decides the order.
Two-digit multipliersField Book Lesson 47
- Multiply by each digit of the multiplier on its own line, shifting one place per line.
- Add the partial products.
Decimal divided by wholeField Book Lesson 48
- Bring the decimal point straight up from the dividend into the answer.
- Add zeros to the right of the last digit as the division needs them.
Worked: the point rides up
- 37.8 ÷ 4: the point rises into the quotient.
- 37.8 ÷ 4 = 9.45
Worked: close the statement
- 8 + K + 15 = 41. Combine the knowns: 23 + K = 41.
- K is not the largest: 41 - 23 = 18, so K = 18.
Terms on the record
| Term | Meaning |
|---|
| partial product | one line of a multi-digit multiplication before the lines are added |
| external zeros | zeros that may come or go only at the outer edges of a number |