Intermath | Workshop Support

 Write-up

Title
Fortune Telling

Problem Statement
Using only the number 4 and the four basic operations (+, -, x, ÷), write all the numbers from 1 to 31.

Problem setup

Restate the problem in your own words. Discuss mathematical similarities between this problem and other problems you have solved.

Plans to Solve/Investigate the Problem

List numbers 1-31 on a sheet of paper, looking for the easiest way to produce result by using 4, +, -, x, and ÷.

Investigation/Exploration of the Problem

At first, although I understood that 4/4=1, I didn’t see how to add 4/4+4/4 to equal 2.  Then I quick noted that 4+4=8, 4+4+4=12, 4*4=16, 4*4+4=20, 4*4+4+4=24, and 4*4+4+4=28.  Whew!  Then it was just a matter of adding or subtracting the necessary amount of ones (4/4).

 1 4/4 17 4*4+4/4 2 4/4+4/4 18 4*4=4/4+4/4 3 4-4/4 19 4*4+4-4/4 4 4 20 4*4+4 5 4+4/4 21 4*4+4+4/4 6 4+4/4+4/4 22 4*4+4+4/4+4/4 7 4+4-/4 23 4*4+4+4-4/4 8 4+4 24 4*4+4+4 9 4+4+4/4 25 4*4+4+4+4/4 10 4+4+4/4+4/4 26 4*4+4+4+4/4+4/4 11 4+4+4-4/4 27 4*4+4+4+4-4/4 12 4+4+4 28 4*4+4+4+4 13 4+4+4+4/4 29 4*4+4+4+4-4/4 14 4+4+4+4/4+4/4 30 4*4+4*4-4/4-4/4 15 4*4-4/4 31 4*4+4*4-4/4 16 4*4 ☺☻♫۩۝۞

Extensions of the Problem

Re-teach the order of operations and the concept of any number divided by itself is 1.

Author & Contact
Lorri Worman, Edwards Middle School, Conyers, Georgia
lworman@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
Order of Operations
Multiplicative Inverse