Student Page 1.5.4 Flexibility with Numbers: Four Numbers Problem
Use the same number exactly four times to write expressions equivalent to the numbers 0 through 20. You may use any of the mathematical symbols below. A few examples for the number 4 are provided. Choose the number you will use and tell your instructor. You may choose one of the numbers: 1, 2, 3, 5, 6, 7, 8, 9. (Note that you may not use the number 4.)
Arithmetic operations: \(+, -, \times, \div\)
Parentheses: ( )
Decimal points or percents: e.g. \(4.4\text{,}\) \(.44\text{,}\) 44%
Exponentiation: ^ (to the power of), e.g. \((4 + 4)^4\)
Square root: e.g. \(\sqrt{4}\)
Factorial: ! (\(4! = (4)(3)(2)(1) = 24\)
Concatenation: e.g. 44, 444
Repeating decimal: \(. \overline{4} = \frac{4}{9}\)
1.
Complete the table writing solutions as expressions. Use the Order of Operations; include grouping symbols as needed. Check your responses using a calculator. Some examples for the number 4 are provided. Your group's number is .
| Number | Four Fours Equation | Number | Four Fours Equation |
|---|---|---|---|
| 0 | 12 | ||
| 1 | \(1 = \left(\frac{4}{4} \right) ^{44}\) | 13 | |
| 2 | 14 | ||
| 3 | 15 | \(15 = \frac{44}{4} + 4\) | |
| 4 | 16 | ||
| 5 | 17 | ||
| 6 | 18 | ||
| 7 | \(7 = 4 + 4 - \frac{4}{4}\) | 19 | |
| 8 | 20 | ||
| 9 | 24 | \(24 = 4! \cdot \left(\frac{\sqrt{4} \times \sqrt{4}}{4} \right)\) | |
| 10 | 30 | ||
| 11 | 100 |
2.
What strategies did you use to find solutions?
3.
Find more than one solution for at least 3 of the numbers.
4.
Which of your solutions are not dependent on the number you chose? Highlight these solutions in your table.