Raven writes 3n + 2 on a card and props it against the envelope. "Puzzle two has parts. Name them."
"Three, n, two," Rocket says. "Three parts."
"Look again," says Raven. "What do you notice about the 3 and the n? Are they added or multiplied?"
"Multiplied. So 3n is one piece. Then plus 2." Rocket counts on his fingers. "Two pieces."
Nova hovers over the card, her light settling on the 3. "Two terms," she says. "And the 3 has a name of its own."
"Coefficient," Raven says. "The number riding on the letter. Three envelopes, each hiding n."
Rocket draws three envelopes and two beans. "Three n plus two," he says. "Now I see the parts."
| Name | Means | Example |
|---|---|---|
| term | A part that is added or subtracted | In 3n + 2 the terms are 3n and 2. |
| coefficient | The number multiplying a letter | In 3n the coefficient is 3. |
| factor | A thing being multiplied | In 2(8 + 7) the factors are 2 and (8 + 7). |
| sum | The result of adding | 8 + 7 is a sum of two terms. |
| product | The result of multiplying | 2(8 + 7) is a product of two factors. |
| quotient | The result of dividing | n ÷ 4 is a quotient. |
One part can play two roles. In 2(8 + 7), the parentheses hold a sum of two terms, 8 and 7.
Step back and the whole (8 + 7) is one factor, multiplied by 2. Seeing a part as one single thing is a big algebra skill.
A letter alone has coefficient 1: n means 1n. A plain number with no letter, like the 2 in 3n + 2, is often called the constant term.
To evaluate, replace every letter with its value, then follow last week's order: parentheses, powers, multiply and divide, add and subtract.
If n = 4, then 3n + 2 = 3 × 4 + 2 = 14. Multiply first, then add.
If n = 4, then n² - n = 16 - 4 = 12. The power first, then the subtraction.
The parts have names now. Tomorrow is Puzzle Lab: envelope cards, beans and a table of results.