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Student Page 1.5.4 Flexibility 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: +,−,×,÷

  • Parentheses: ( )

  • Decimal points or percents: e.g. 4.4, .44, 44%

  • Exponentiation: ^ (to the power of), e.g. (4+4)4

  • Square root: e.g. 4

  • Factorial: ! (4!=(4)(3)(2)(1)=24

  • Concatenation: e.g. 44, 444

  • Repeating decimal: .4―=49

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=(44)44 13
2 14
3 15 15=444+4
4 16
5 17
6 18
7 7=4+4−44 19
8 20
9 24 24=4!⋅(4×44)
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.