THE TRANSITION LINE // FIELD NOTES // STOP 33
Proportions, polygons, and the end of the line
Field Book
Lessons 125 to 128
Method
Pencil and paper. Calculators never.
END OF THE LINE runs in class this stop. Four last lessons ride ahead of the big room. The final four lessons: proportions test two ratios for equality, polygons take their names and count their diagonals, the cylinder takes pi r r h, and scientific notation writes any size on one short line. Then the room falls.
What you have to be able to do
- Test and read proportions
- Name polygons and count their diagonals
- Find the volume of a cylinder
- Write numbers in scientific notation
The procedures
ProportionsField Book Lesson 125
- A proportion claims two ratios are equivalent.
- Test it by reducing both to the same fraction, or by matching the cross products.
Polygons and diagonalsField Book Lesson 126
- Name by side count, triangle through decagon. A diagonal joins two non-adjacent vertices.
- Diagonal count: N · (N - 3) ÷ 2.
Volume of a cylinderField Book Lesson 127
- V_cyl = π · r · r · h, with π taken as 3.14.
- Three lines: formula, substitution, answer. Height runs straight between the bases.
Scientific notationField Book Lesson 128
- Move the point until one digit stands left of it.
- The exponent on 10 counts the places the point moved.
Worked: cross products
- 58 and 1524: cross products 5 · 24 = 120 and 8 · 15 = 120.
- Equal products: the ratios are proportional.
Worked: decagon diagonals
- N = 10: diagonals = 10 · 7 ÷ 2
- = 35
Worked: one short line
- 380,000 = 3.8 · 105
- The point moved five places.
Terms on the record
| Term | Meaning |
|---|
| proportion | an equation claiming two ratios are equivalent |
| cross products | the diagonal products of a proportion, equal when the claim is true |
| polygon | a closed, flat shape with straight sides |
| diagonal | a line joining two non-adjacent vertices of a polygon |
| cylinder | a solid with two circular bases joined by a straight height |
| scientific notation | one digit, a point, and a power of ten carrying the size |