Could This Be the Reason Students Confuse Many Word Problems?

After years of seeing students mix up math operations in word problems, I have finally figured out how to help students understand what operation to use in word problems.  This little word is causing students much of the confusion–EACH.  Haven’t we all taken for granted that students understand what this word means.  The word ‘each’ is in nearly every multiplication and division problem, but many students don’t know what it means–every one in the group.  If we teach students to read a word problem and replace the word each with its meaning, every one in the group, students somehow have a light bulb experience.

In conjunction with teaching students to understand the word each, also asking them questions about the problem helps facilitate understanding.   For example when you ask, “Is this a joining or a separating situation,” students start to  make sense of word problems.  Students generally understand that words like altogether and in all mean that they are joining groups.  The word total may need to be taught as a word that means in all, but  total isn’t a difficult term for students to become comfortable with.

To help students further differentiate between multiplication and addition, ask questions like:  are we adding the same amount over and over or are we adding two different sized groups?  If the answer is adding the same amount over and over, then multiplication is repeated addition of equal sized groups.  If students are confusing division and subtraction, ask, “are we subtracting different amounts or are we subtracting the same sized amounts over and over.  If the answer is subtracting the same amounts over and over, then teach students that division is repeated subtraction of equal groups.