Once students understand that multiplication is repeated addition of same-size groups, they can assess what their story problem asks and decide whether they need to multiply. Asking, "Am I combining several groups with the same number of members?" affirmatively indicates a multiplication problem. For example, in the problem, "Sam has four packages of cupcakes. Each package contains six cupcakes. How many cupcakes does Sam have in all?" the students should see that they are combining like groups by repeated addition -- multiplication is the shortcut to adding 6 + 6 + 6 + 6. Arrays in which students line up the sets can help with a visual prompt for multiplying. In this example, students could draw four rows of cupcakes, six in each row, to see the problem clearly.
Relying only on the key words in the story problem won't always give students the correct answer, but they do give the learners a clue to get started. For multiplication problems, students should look for "in all," with equal groups, "total," "of," "times" and "product."
In "partitioning" or "fair sharing" division problems, the problem gives the total number of items and the number of sets and the students determine how many items will be in each set by separating the whole into parts. For example, faced with the problem, "Suzy has 24 cupcakes and she wants to share them with three friends. How many cupcakes will Suzy and her friends each receive?" students need to understand that they are splitting -- or dividing -- the whole group of cupcakes into four smaller groups. Students may also think of division as repeated subtraction when they are looking for the number of possible groups they can make from the whole. If Jim has those same 24 cupcakes and wants to know to how many people he can give six cupcakes, he can subtract 24-6 and make a tally mark for one group, continuing to subtract six and mark the group until there are no cupcakes left. Counting the tally marks tells him how many groups he has made, and using his division facts lets him take the short road to the answer.
Clue words for division include "each," "every," "out of," "equal groups or pieces," "into," "in each" and "shared." Other key words include "split" and "cut," along with "how much."