The big picture
Here are the eleven ideas.
| Idea | Remember | Example |
|---|---|---|
| Hold a number | n holds a number, not yet chosen. | n + 3 |
| Rule in letters | One line answers any step. | 4n + 1 |
| Drop the times sign | 3 × n is 3n, written shorter. | 3n = 15 at n = 5 |
| Put a number in | Swap the letter, multiply first, then add. | 2n+3 at n=4 → 11 |
| Always or sometimes | Match at every value means the same. One mismatch is enough. | 5n and 2n+3 differ at n=2 |
| Same kind | Collect only matching letter parts. | 3a+5a = 8a |
| Add expressions | String every term, then collect. | 5n + 9 |
| From a situation | Per-one amount, plus a once-only amount. | 40t + 15 |
| A formula | A formula is a rule written in letters. A regular polygon has equal sides and equal angles. With n sides of length a, its perimeter is n × a. | 6a is 42 at a = 7 |
| Letters in a square | Call the top-left date a. Right of it is a + 1. Below it is a + 7. Across the diagonal is a + 8. Each diagonal adds to 2a + 8. | 16 + 24 = 17 + 23 = 40 |
| Spot the slip | To test a simplified line, put the same number into both sides. Different answers mean a mistake. One match proves nothing. | 3(x + 5) is 3x + 15 |
Now open Part I, Chapter 4, Expressions using Letter-Numbers. Read it, then try the questions in it.