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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

 

 

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