The big picture
Ten moves, one habit. Check every rewrite with a number.
| Idea | Remember | Example |
|---|---|---|
| Parts | A coefficient, and a letter part if there are letters. | 5a²: coefficient 5 |
| Joining | Add or subtract coefficients. Letters do not change. | four dates: 4a + 16 |
| Term × term | Multiply coefficients, write letters side by side. | 3x × 4x = 12x² |
| Into a bracket | The term reaches every term inside. | 2(3a + 5) = 6a + 10 |
| Two brackets | Every term meets every term, then join. | (x + 3)(x + 5) = x² + 8x + 15 |
| Square in four | a² + 2ab + b², drawn as four pieces. | 85² = 6,400 + 800 + 25 |
| Easy way round | A pattern that is true at every value. | 98 × 98 = 9,604 |
| Factor out | Divide by the shared part. Write it outside. | 6x + 9 = 3(2x + 3) |
| Put a number in | One mismatch proves a rewrite wrong. | x² ≠ 2x at x = 3 |
| A trick as a line | Name it, write each step, join. | x + 4 − x = 4 |
Part II, Chapter 6 is Algebra Play. Your book uses them on number tricks, number pyramids and calendar squares. A number pyramid stacks numbers in rows.