THE COMPOUND // FIELD NOTES // WEEK 03
Percent, graphing lines, and the Pythagorean theorem
Field Book
Lessons 7 to 11
Due
Test 1 due ยท Supplement 3
Method
Paper first, every step
Five lessons this week, the only five stack of the year. Pace them one per day and keep the graph paper out.
What you have to be able to do
- Set up and solve percent equations, including percent word problems
- Graph a line from a table of values
- Use the Pythagorean theorem and add fractions over a common denominator
The procedures
Percent equationsField Book Lesson 7
- Translate directly: what percent of A is B becomes P100 times A equals B.
- Solve the equation like any other. The percent is just a number.
Graph a line from a tableField Book Lesson 8
- Pick three easy x values and compute each y.
- Plot the three points and draw the line through them. Three points catch mistakes that two allow.
Percent word problemsField Book Lesson 9
- Decide which quantity is the base before writing anything.
- If the problem states no agreement, take the percent of the other quantity, per the lesson's rule.
Pythagorean theoremField Book Lesson 10
- Only in right triangles: leg2 + leg2 = hyp2.
- Solve for the missing side, then take the positive square root.
Adding fractions and inscribed anglesField Book Lesson 11
- Identify the LCD first, build each fraction up to it, then add tops.
- An inscribed angle measures half its intercepted arc.
Worked: a 6 8 hypotenuse
- A right triangle has legs 6 and 8.
- hyp2 = 62 + 82 = 36 + 64 = 100.
- hyp = 10.
Terms on the record
| Term | Meaning |
|---|
| percent | a ratio out of one hundred |
| Pythagorean theorem | in a right triangle the squares of the legs sum to the square of the hypotenuse |
| least common denominator | the smallest quantity every denominator divides evenly |