Take any 4 consecutive numbers. For example, 3, 4, 5, and 6. Place '+' and '–' signs in between the numbers. How many different possibilities exist? Write all of them.
There are 8 different possibilities for placing '+' and '–' signs between 4 consecutive numbers.
For numbers 3, 4, 5, 6, the expressions are: 3 + 4 + 5 + 6 = 18 3 + 4 + 5 - 6 = 6 3 + 4 - 5 + 6 = 8 3 + 4 - 5 - 6 = -4 3 - 4 + 5 + 6 = 10 3 - 4 + 5 - 6 = -2 3 - 4 - 5 + 6 = 0 3 - 4 - 5 - 6 = -12
Explanation
The chapter introduces this activity to explore patterns in arithmetic expressions. With 4 numbers, there are 3 positions for signs, and each position can have either '+' or '–'. This gives 2³ = 8 possibilities. The systematic listing helps students discover that all resulting expressions have the same parity (all even or all odd). For consecutive numbers starting with an odd number, all results are even.
Solution Steps
With 4 numbers, there are 3 positions for signs between them.
Each position can have either '+' or '–'.
Total possibilities = 2³ = 8
List all 8 expressions systematically by varying the signs.