THE TRANSITION LINE // FIELD NOTES // STOP 31
Rates, the quadrilateral family, and paired angles
Field Book
Lessons 117 to 120
Method
Pencil and paper. Calculators never.
The timetable is a rate: miles over hours, read as per. A rate divides two amounts with two different units into one composite unit, evaluation runs with several variables at once, the quadrilaterals sort by their parallel pairs down to the square, and paired angles total 90 or 180 degrees.
What you have to be able to do
- Compute and name rates
- Evaluate expressions with several variables
- Classify the quadrilateral family
- Find complements and supplements
The procedures
RatesField Book Lesson 117
- Divide the two amounts and keep both units.
- Read the composite unit as per: miles per gallon, feet per second.
Several variablesField Book Lesson 118
- Replace every variable with its value.
- Then the order of operations, one line per move.
The quadrilateral familyField Book Lesson 119
- Sort by parallel pairs: none for the trapezium and kite, one for the trapezoid, two for the parallelogram.
- Inside the parallelogram: rhombus with four equal sides, rectangle with four equal angles, square with both.
Complements and supplementsField Book Lesson 120
- Complementary angles total 90°.
- Supplementary angles total 180°. Past 90°, an angle has no complement.
Worked: read it as per
- 328 miles in 8 hours: 328 ÷ 8 = 41.
- The rate is 41 miles per hour.
Worked: the supplement
- The supplement of 74° totals to 180°.
- 180 - 74 = 106, so 106°.
Terms on the record
| Term | Meaning |
|---|
| rate | a comparison of two amounts with two different units, building a composite unit |
| trapezoid | a quadrilateral with exactly one pair of parallel sides |
| rhombus | a parallelogram with four equal sides |
| complementary angles | two angles that total 90° |
| supplementary angles | two angles that total 180° |