The big picture
Here are all ten ideas, in order.
| Idea | Remember | Example |
|---|---|---|
| General form | 10a + b. Reverse 10b + a. Sum 11(a + b). | 52 + 25 = 77 |
| Three digits | Bigger minus smaller: the middle drops out. Difference is 99 times the outer gap. | 742 − 247 = 495 |
| Eleven test | Alternate + and − from the ones digit. | 209 → 11 |
| Nine-check | Marks disagree: wrong. Marks agree: might be right. | 372 passes, but is wrong |
| Letters for digits | A letter is one digit. A B means 10A + B, never A × B. | 63 + 28 = 91 |
| Hundred grid | Right adds 1, down adds 10 — that is the step. | 11s go down and right |
| Saying why | Write both numbers, do the sum, take out the common factor. | factor 99 |
| End digits | For 2, 5 or 10, look at the last digit. For 4, look at the last two digits. For 8, look at the last three. | 3,624 ÷ 8: look at 624 |
| Digit sums | A number divides by 3 when its digit sum does. A number divides by 6 when 2 and 3 both divide it. | 4,581 → 18, so by 3 |
| Two tests for 40 | To test 40, check 5 and 8. Checking 4 and 10 is not enough, because 20 passes both. | 7,240 = 40 × 181 |
Part I, Chapter 5, Number Play, is in your book. It asks questions on these ten ideas.