### Student Page1.5.4Flexibility with Numbers: Four Numbers Problem A4US

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.