One To Ten: An Arithmetic Game

The purpose of this game is to help students think through different ways of combining numbers using addition, subtraction, multiplication, division, exponents and parentheses, and to evaluate the resulting expressions using proper Order Of Operations.

Object of the Game

To create all the numbers from one to ten using the arithmetic operations and the four numbers specified by the computer.

Game Instructions

The computer selects four numbers from one to ten. You must combine these integers, using each one once, to form each of the integers from one to ten. For example, if the computer selects 1, 2, 3, and 4, you could create the following expressions:

(2-1)*(4-3)	12/4+3
(2*1)*(4-3)	13-4-2
4-3/(2+1)	12/3+4
1+2+4-3	14-3-2
12-3-4	14/2+3

Enter an expression in the space provided, and click 'Calculate' when you are ready for the computer to check your expression.

Game Tips

You can combine your numbers to make two or three digit numbers.
You can use parentheses, and you can even have nested parentheses.
Use '^' for an exponent. (2^3 means 2 cubed)
Each problem is solvable without parantheses or exponents.

Order Of Operations

Hopefully you have learned PEMDAS, PODMAS, or some other similar mnemonic for order of operations.

I usually remember PEMDAS as "Please Excuse My Dear Aunt Sally", and the letters stand for: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the proper order for evaluating an expression. For example, if an expression has both parentheses and exponents, you do parentheses first, and then do the exponents.

HOWEVER... many people are unaware that Multiplication and Division are at the same "priority level", as are Addition and Subtraction.

In other words, if your expression contains both multiplication and division, you do not necessarily do all the multiplication first, and then all the division; you do them in order from left to right. The same is true for Addition and Subtraction.

You can read more about this here: Order Of Operations Explanation at The Puzzler Blog.

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