Equation: written left to right and states what is known and what is not known. Usually includes a variable representing the number or quantity that is unknown. A diagram is a good way to show you how to set up the equation, but it is not the equation itself.
Commutative Property of Addition: you can change the order addends (numbers you are adding) are put in and the sum (the answer for an addition problem) will stay the same.
Associative Property of Addition: you can regroup the addends (numbers you are adding) in different groups and the sum (the answer for an addition problem) will stay the same.
Word Problems: words like both, and, together indicate that you will need to add.
Words like more and left tell you to subtract. Some problems have more than one step. There may be two or more things not said in the problem that you have to find the answer for before you can find the answer the question is asking for. You may have to add more than once, subtract more than once or add and subtract to find the solution to a word problem.
Regrouping: when we add large numbers, we sometimes need to regroup (carry) when we have more than one place value can hold.