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Four Fours Use the symbol 4 exactly four times to write number sentences equivalent to the numbers from 1 through 20 and beyond. You may use any of the mathematical symbols listed below. A few examples are provided. • Arithmetic operations: + – × ÷ • Square root: • Parentheses: ( ) • Factorial: ! [4! = (4)(3)(2)(1) = 24] • Decimal points or percents: e.g., 4.4, .44, or 44% • Concatenation: e.g., 44 or 444 • Exponentiation: ^ (to the power of) Number 1 • Repeating decimal: .4 = Four Fours Equation Number 44 11 ⎛ 4⎞ ⎜ ⎟ ⎝ 4⎠ =1 2 12 3 13 4 14 5 15 6 16 7 4+4− 4 =7 4 Four Fours Equation 44 + 4 = 15 4 17 8 18 9 19 10 20 4 9 Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing