THE TRANSITION LINE // FIELD NOTES // STOP 14
Decimals on the line and the five angles
Field Book
Lessons 53 to 56
Method
Pencil and paper. Calculators never.
A term walk posts this stop. Sight the angles before you name them. Between any two whole numbers the line always carries ten spaces, a fraction divided by a fraction flips the second and multiplies, regrouping carries ones out of top-heavy sums and into short differences, and angles arrive with their five names.
What you have to be able to do
- Read decimal points off a number line
- Divide a fraction by a fraction
- Regroup in sums and differences of mixed numbers
- Name and classify the five angle types
The procedures
Decimals on the number lineField Book Lesson 53
- Between whole numbers there are always ten spaces, so the bottom is always 10.
- Whole number to the left, count tenths over to the mark.
Fraction over fractionField Book Lesson 54
- Multiply the top fraction by the reciprocal of the bottom fraction.
- Reduce before multiplying when the numbers allow it.
Regrouping both directionsField Book Lesson 55
- A top-heavy fraction in a sum: carry a 1 out to the whole numbers.
- A short fraction in a difference: borrow a 1 in as a fraction worth 1.
AnglesField Book Lesson 56
- An angle is two rays with a common endpoint, measured in degrees. Rays crossing at square angles are perpendicular.
- Acute is under 90°, right is exactly 90°, obtuse runs between 90° and 180°, straight is exactly 180°, reflex runs beyond it.
Worked: carry the one out
- 6 58 + 2 78: fraction parts make 128.
- 8 128 = 9 48 = 9 12
Worked: flip the bottom
- 49 ÷ 23 = 49 · 32
- = 1218 = 23
Terms on the record
| Term | Meaning |
|---|
| angle | two rays sharing a common endpoint |
| perpendicular | crossing at square angles |
| acute angle | an angle measuring less than 90° |
| obtuse angle | an angle measuring between 90° and 180° |