Idea 12of 21Builds onGrowing by adding a core
Extend it backwards
What came before the first term you were shown?
Today you'll discover
- how to run a rule backwards
- what position 0 looks like
- where it sits on a graph
Think firstToothpicks for 1, 2, 3, 4 squares in a row
The rows need 4, 7, 10, then 13 toothpicks. What would position 0 need?
Decide first, then press Next. Find the jump, then go the other way.
A row of boxes labelled position 0 to 7: a blank at position 0, then 4, 7, 10, 13, and three blanks. Jumps of plus 3 appear under the boxes; position 0 fills with 1; then the terms are drawn as dots climbing to the right from 1.
See the whole ideathe big idea and the key word, in one place
The big idea
Run the rule backwards to find what came before; position 0 is the starting amount.
Where it goes nextIn Suzie's savings, position 0 was week 0: the $15 she had before any chores.
Easy to get wrongPosition 0 is not always 0. It is whatever the pattern holds before the first change.
Key word
- position 0
- the term before the first change: the starting amount
Ready to use it?
- Extend a pattern backwards.
- Find what position 0 looks like.