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from NCTM:

How many knots will form if you pull the ends of the string in opposite directions?

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Find four distinct integers
a, b, c, and d such that

ab = c + d and
cd = a + b.

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New learning updates old learning. A "rule" that was very useful in first grade becomes incorrect when you learn later that you can, indeed, take the square root of a negative number. Can you come up with an example for which each rule is broken?

When do these Rules expire?

1. When you multiply a number by ten, just add a zero to the end of the number.

2. Use keywords to solve word problems.

3. You cannot take a bigger number from a smaller number.

4. Addition and multiplication make numbers bigger.

5. Subtraction and division make numbers smaller.

6. You always larger number divide by the smaller number.

7. Two negatives make a positive.

8. Multiply everything inside the parentheses by the number outside the parentheses.

9. Improper fractions should always be written as a mixed number.

10. The number you say first in counting is always less than the number that comes next.

11. The longer the number, the larger the number.

12. Please Excuse My Dear Aunt Sally.

13. The equal sign means "Find the answer" or "Write the answer."

https://www.nctm.org/Publications/Teaching-Children-Mathematics/2014/Vol21/Issue1/13-Rules-That-Expire/