THE TRANSITION LINE // FIELD NOTES // STOP 25
The coordinate plane and part-to-whole
Field Book
Lessons 93 to 96
Method
Pencil and paper. Calculators never.
The map room opens: every car on the plane has an address. Points take their places on the coordinate plane, subtraction of signed numbers becomes addition with one flipped sign, mixed numbers and decimals trade their fraction parts, and a known part rebuilds the unknown whole.
What you have to be able to do
- Plot points in all four quadrants
- Subtract signed numbers
- Trade mixed numbers and decimal numbers both ways
- Find the whole from a known part
The procedures
Plotting pointsField Book Lesson 93
- An ordered pair reads (x, y): x runs right or left, y runs up or down.
- The sign chooses the direction from the origin.
Subtracting signed numbersField Book Lesson 94
- Change the subtraction to addition and flip the sign of the second number.
- Never change the first number.
Mixed numbers and decimals tradeField Book Lesson 95
- Swap only the fraction part for its decimal form, or the decimal part for its fraction form.
- The whole number rides along unchanged.
The whole from a partField Book Lesson 96
- Divide the known amount by the top to find one share.
- Multiply one share by the bottom to rebuild the whole. A percent changes to a fraction first.
Worked: whole from three fifths
- 35 of the cars is 45 cars.
- One share: 45 ÷ 3 = 15. The whole: 15 · 5 = 75 cars.
Worked: flip the second sign
- -8 - (-15) = -8 + 15
- = 7
Terms on the record
| Term | Meaning |
|---|
| coordinate plane | the flat grid where ordered pairs live |
| ordered pair | an address (x, y) locating one point on the plane |