THE TRANSITION LINE // FIELD NOTES // STOP 24
The F-D-P triangle and units that multiply
Field Book
Lessons 89 to 92
Method
Pencil and paper. Calculators never.
Room 6 opens this stop. Every remainder means something on a manifest. Fraction, decimal, and percent trade around one triangle, signed addition gets its value rules, the four remainder types decide what a leftover means, and units themselves obey the rules of arithmetic.
What you have to be able to do
- Complete fraction-decimal-percent triples
- Add signed numbers by the value rules
- Interpret remainders four ways
- Multiply and divide units, and build composite units
The procedures
The F-D-P triangleField Book Lesson 89
- Any one of fraction, decimal, or percent converts to the other two.
- Keep the triangle handy and cross it in whichever direction the problem asks.
Signed addition by valuesField Book Lesson 90
- The value of a signed number is its distance from zero.
- Same signs: add the values, keep the shared sign. Different signs: subtract the values, keep the sign of the larger value.
Four remainder typesField Book Lesson 91
- Money divides on into cents. Field trips round up.
- Purchases round down. Assignments split the difference across the group.
Units under arithmeticField Book Lesson 92
- ft · ft = ft2, and units divide out like factors.
- A division of different units builds a composite unit, read as per.
Worked: the bus count
- 130 students, 40 to a bus: 130 ÷ 40 = 3 remainder 10.
- Field trips round up: 4 buses.
Worked: same signs
- -14 + -23: same signs, add the values: 14 + 23 = 37.
- Keep the shared sign: -37.
Terms on the record
| Term | Meaning |
|---|
| value | the distance of a signed number from zero |
| remainder | what is left over when a division does not come out even |
| composite unit | a unit built from two units by division, read as per |