Negative numbers have a bad reputation, but they follow the same rule as every other number in a pyramid. Every brick is the sum of the two below it. The only new thing is that some bricks are less than zero.
A picture to keep in mind
Think of a number line. Adding a positive number moves right. Adding a negative number moves left. Starting at 6 and adding −4 means four steps to the left, and you land on 2.
A pyramid with negatives
The top is −1. The left brick of the middle row is 2. The bottom row is 6, a missing brick and 1.
What we know
Top −1, middle-left 2, bottom row 6, ? and 1.
Subtract to find the gap
The middle-left brick is 6 + ? = 2. So ? = 2 − 6 = −4. On the number line: from 6 to 2 you go 4 to the left.
Add up the other side
−4 + 1 = −3. From −4 you go one step to the right, and land on −3.
Check the top
2 + (−3) = −1. That is the top we were given. The wall holds.
Three habits
- Subtracting a negative is adding. 5 − (−3) = 8. Taking away a debt makes you richer.
- Same signs add up, different signs fight. −3 + −4 = −7. But −3 + 4 = 1: the bigger one wins, and you keep its sign.
- Write the minus sign big. Most mistakes with negatives are a lost sign, not a lost number.
Books mentioned
Integer Pyramids
100 positive and negative number puzzles, a pre-algebra practice workbook. Every puzzle uses negative numbers, so it is all practice for this post's topic.
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Escape the Pyramid, Level 3
The hardest of the three Level books: 45 locked chambers with number pyramids as one of several puzzle kinds, so it is not all negatives.
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Creouts Publishing
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