### 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.