We live in Boston, Massachusetts. My 14-

Answer

**Tonight's micro-goal (10–15 minutes):** Sit at the kitchen table with the table below. By the end he should be able to walk you through the table and tell you, in his own words, why the answer to (-2) × (-5) can't be -10 — using either the pattern method or the money/debt method. If he can do that without reading from a screen, the goal is met.

---

### The full demo (using (-2) × (-5), not the teacher's (-3) × (-4))

**Step 1 — See what multiplying by a negative *does* to the answer.**

Hold the second number steady at -5. Lower the first number by 1 each step. Write the answers in a column:

```
5 × (-5) = -25
4 × (-5) = -20
3 × (-5) = -15
2 × (-5) = -10
1 × (-5) = -5
0 × (-5) = 0
```

Each row, the first number drops by 1, and the answer goes **up by 5**. Tell him: "Math is built so this pattern keeps going. What has to come next?"

**Step 2 — Keep the pattern going past zero.**

If the rule holds — first number drops by 1, answer goes up by 5 — then continuing down gives:

```
(-1) × (-5) = +5
(-2) × (-5) = +10
(-3) × (-5) = +15
```

The minus signs don't get to "fight." Once the first number crosses zero, the answer has crossed zero too. So (-2) × (-5) = +10, not -10.

He might say, "But couldn't the rule just stop at zero?" That's a fair question — the answer is that if the rule could stop anywhere, you couldn't trust math. Two plus two couldn't equal four on a Wednesday. We build numbers so the pattern holds all the way down. That's the whole point.

**Step 3 — Same idea, different lens: money / debt.**

This one clicks for some kids. Have him imagine his allowance:

- `3 × (-$5)` means: borrow $5 from me **three times**. You owe $15. We write that as **-$15**.
- `(-3) × (-$5)` means: do the *opposite* of borrowing, **three times**. The opposite of "borrowing $5" is "paying back $5." So you pay back $5 three times = +$15.

Two negatives mean two flips: the first flip turns "borrow" into "pay back"; the second flip (multiplying by -3) does the paying-back **three times** instead of borrowing three times. Two flips land you back on positive ground.

---

### 5-minute micro-task

Give him a blank piece of paper and ask him to do **both** of these:

1. **Extend the table yourself.** Make the column `? × (-6)` going from `5` down to `(-3)`. Write all nine answers in order, then circle the row `(-2) × (-6)`.
2. **Explain it back to me in your own words.** Pick **one** of the two methods (pattern O money) and tell me, without looking at the screen, why the answer has to be positive. One sentence is fine.

When he explains it back, don't correct the wording — just check that the *reason* is in there (pattern keeps going past zero, O two flips cancel out).

---

### If he gets stuck

- **"Why can't the pattern just stop?"** → Tell him that's exactly the right thing to ask. The answer: if patterns could stop, no math would work anywhere. We chose numbers so the pattern holds.
- **"But my teacher said memorize it."** → Tell him his teacher wasn't wrong — the rule is faster on a test. Tonight he gets to see *why* the rule exists. Tomorrow he can use the rule, and now he'll know it's not arbitrary.

### What "got it" looks like tonight

He can point at the row `(-2) × (-5) = +10` and say either:

- "The pattern says it has to be +10, because the row before it is +5 and each step adds 5." **O**
- "Borrowing -$5 three times is paying back $5 three times, which is +$15 — same idea."

Either one is enough. **Don't** ask him to do (-3) × (-4) tonight — that's the teacher's example, and he's heard "just memorize it" about it. Let his own table do the talking.

### Next step (tomorrow or whenever)

If tonight goes well, the natural next move is `(-2) × 5 = -10` and `2 × (-5) = -10` — the cases where the signs are different, and the "flip" only happens once. Same pattern logic, simpler answer. Save that for the next kitchen-table session.

No saved file, no PDF — this is a kitchen-table talk. If he wants to keep the table on paper, that's his to keep.