THE TRANSITION LINE // FIELD NOTES // STOP 01
Place value, vertical work, and missing numbers
Method
Pencil and paper. Calculators never.
First shift on the Line. The dispatcher logs every column you carry. Four lessons to open the year: reading big numbers by their groups, keeping addition and subtraction in straight columns, running longhand division all the way to a mixed-number answer, and the first missing-number rule.
What you have to be able to do
- Read and write whole numbers by place and by group
- Add and subtract vertically with carrying and borrowing
- Run longhand division and write the remainder as a fraction
- Find a missing number in an addition or subtraction statement
The procedures
Reading by groupsField Book Lesson 1
- Commas cut a whole number into groups of three: units, thousands, millions, billions.
- Name the digit by its place, then read the number one group at a time.
Vertical arithmeticField Book Lesson 2
- Line the digits up in columns and right-justify before any math happens.
- Work from the ones column leftward, carrying or borrowing one column at a time.
Longhand divisionField Book Lesson 3
- Divide, multiply, subtract, bring down one digit. Repeat until the digits run out.
- Write any remainder over the divisor to finish as a mixed number.
Missing numbers: add and subtractField Book Lesson 4
- Decide whether the missing number sits in the largest position of the statement.
- Missing the largest number: add the two given numbers. Otherwise: subtract.
Worked: the missing addend
- N + 38 = 92. The largest number, 92, is known, so subtract.
- 92 - 38 = 54, so N = 54.
- Check the line: 54 + 38 = 92.
Worked: remainder to mixed
- 173 รท 8: the division gives 21 with remainder 5.
- Write the answer 21 58.
Terms on the record
| Term | Meaning |
|---|
| place value | the worth a digit carries from the position it sits in |
| group | a block of three places sharing one family name, cut off by commas |
| carrying | trading ten of one place for one of the next place up |
| borrowing | trading one of a place for ten of the next place down |
| fact family | four statements built from the same three numbers and two opposite operations |