THE COMPOUND // FIELD NOTES // WEEK 06
Radicals, scientific notation, and equal-distance motion
Field Book
Lessons 20 to 23
Due
Test 4 due ยท Supplement 6
Method
Paper first, every step
Vocab 1 runs in the Yard this week. The radical rules land here and never leave.
What you have to be able to do
- Combine like radicals and simplify radical expressions
- Write and compute in scientific notation
- Set up equal-distance uniform motion and solve systems by graphing
The procedures
Like radicalsField Book Lesson 20
- Like radicals carry the same radicand under the same root.
- Simplify each radical first, then combine coefficients of like radicals only.
Scientific notationField Book Lesson 21
- One nonzero digit, then the point, then the power of ten.
- Two statements equal to the same thing are equal to each other. Use it to chain equations.
Uniform motion, equal distancesField Book Lesson 22
- When two travelers cover the same distance, set R1T1 = R2T2.
- Express both times or both rates in one variable before solving.
Systems by graphingField Book Lesson 23
- Graph both lines carefully on one grid.
- The crossing point is the solution. Check it in both equations.
Worked: equal distances
- A walker at 4 mph starts one hour before a cyclist at 6 mph on the same path. When do they meet?
- Distances match: 4t = 6(t - 1).
- 4t = 6t - 6, so t = 3 hours after the walker starts.
Terms on the record
| Term | Meaning |
|---|
| radicand | the quantity under a radical sign |
| scientific notation | a number written as a single digit value times a power of ten |
| uniform motion | travel at a constant rate, so distance equals rate times time |