THE TRANSITION LINE // FIELD NOTES // STOP 08
Formulas on three lines and the three notations
Field Book
Lessons 29 to 32
Method
Pencil and paper. Calculators never.
Room 2 opens this stop. Formula work travels on three lines or it does not travel. Formula problems run on three lines: the formula, the substitution, the answer. Tenth-power fractions read straight into decimal places, and every number can wear three notations: expanded, product, and value.
What you have to be able to do
- Work any formula on three lines
- Change tenth-power fractions to decimals
- Write whole numbers and decimals in expanded, product, and value notation
The procedures
The three-line protocolField Book Lesson 29
- Line one: write the formula, starting with what it describes.
- Line two: replace the variables with the given values. Line three: calculate. A_rect = L · W.
Tenth-power fractions to decimalsField Book Lesson 30
- A bottom of 10, 100, or 1000 reads the top straight into tenths, hundredths, or thousandths.
Notation for whole numbersField Book Lesson 31
- Expanded names the digits by place. Product multiplies each digit by its place value.
- Value adds up those products to rebuild the number.
Notation for decimalsField Book Lesson 32
- The same three forms continue right of the point, riding 110 and 1100.
Worked: area on three lines
- A_rect = L · W
- = 14 · 6
- = 84 cm2
Worked: straight into place
- 23100 reads into the hundredths place.
- 23100 = 0.23
Terms on the record
| Term | Meaning |
|---|
| formula | a rule written in symbols, worked on three lines |
| expanded notation | a number named as digits in their places |
| product notation | a number named as digits multiplied by their place values |
| value notation | a number named as the sum of those products |