THE TRANSITION LINE // FIELD NOTES // STOP 29
Variables at work and the triangle types
Field Book
Lessons 109 to 112
Method
Pencil and paper. Calculators never.
The roster board fills in: one letter, one value, one honest count. A variable takes its value and the order of operations does the rest, small equations solve by inspection, long signed sums split into two totals, and triangles classify twice: by their sides and by their largest angle.
What you have to be able to do
- Evaluate expressions with one variable
- Solve simple equations by inspection
- Add several signed numbers
- Classify triangles by sides and by angles
The procedures
Evaluating with a variableField Book Lesson 109
- Replace the variable with its value.
- Then run the order of operations, one line per move.
Solving by inspectionField Book Lesson 110
- Ask what the multiplied term must equal for the statement to hold.
- Then ask what the variable must be to make that term.
Several signed numbersField Book Lesson 111
- Add all the positives into one total and all the negatives into another.
- Combine the two totals by the value rules.
Triangle classificationField Book Lesson 112
- By sides: equilateral all equal, isosceles two equal, scalene none equal.
- By largest angle: acute, right, or obtuse. An obtuse equilateral is impossible.
Worked: evaluate
- 4R - 9 at R = 7
- = 4(7) - 9 = 28 - 9 = 19
Worked: two totals
- -18 + 25 + -7 + 12: positives total 37, negatives total -25.
- 37 - 25 = 12, positive since the larger total is positive.
Terms on the record
| Term | Meaning |
|---|
| variable | a letter standing in for a number |
| equilateral | a triangle with all three sides equal |
| isosceles | a triangle with exactly two sides equal |
| scalene | a triangle with no equal sides |