THE TRANSITION LINE // FIELD NOTES // STOP 03
Comparing, sequences, and the order of operations
Field Book
Lessons 9 to 12
Method
Pencil and paper. Calculators never.
Tests start riding home this stop. Parents grade; misses get reworked. Comparing any two numbers on the line, extending sequences by their rule, reducing an expression to a single number in the right order, and the multiply-divide version of the story rule.
What you have to be able to do
- Compare two numbers with the correct symbol
- Find the rule of a sequence and extend it
- Evaluate an expression by the order of operations
- Solve multiply-divide missing-number stories
The procedures
Comparing numbersField Book Lesson 9
- Left on the number line is less. Right on the number line is greater.
- Write the symbol with its small end pointing at the smaller number.
SequencesField Book Lesson 10
- Find the rule that carries each term to the next.
- Apply the rule to write the next terms.
EvaluateField Book Lesson 11
- Grouping symbols first, then exponents and roots.
- Then multiply and divide left to right, then add and subtract left to right.
Missing numbers: multiply-divide storiesField Book Lesson 12
- Missing the total or largest amount: multiply the two given numbers.
- Given the total: divide it by the known number.
Worked: one clean sweep
- 30 - 18 ÷ 3 + 4 · 5
- = 30 - 6 + 20
- = 44
Worked: extend the run
- 7, 13, 19, 25, ... adds 6 each step.
- Next come 31 and 37.
Terms on the record
| Term | Meaning |
|---|
| sequence | a string of numbers that follows one steady rule |
| evaluate | to reduce an expression to a single number |
| greater than | further right on the number line |
| less than | further left on the number line |