Although Rory is only in Grade One, he has shown an interest in multiplication and has even recognized situations where multiplication would apply; but before I teach him more, I need to see if he is ready. Here’s a little check:
- Is he interested? YES!
- Can he skip count? YES!
- Can he add? YES!
- Does he understand equality and equal groups? YES!
So does that mean I should pull out the flash-cards and make him memorize multiplication facts? Absolutely not! I want him to enjoy the process, and begin to understand what multiplication is (conceptualize), by teaching him through real-life context; I don’t want him to hate the process, and end up with no understanding, by solely memorizing facts (symbolize).
With that goal in mind, here is the progression I use to make multiplication meaningful.
The first thing to do is link multiplication with equal groups. Rory was playing a game and had four piles of chips. He noticed that all four piles were equal. This was a teachable moment and a great one to introduce multiplication! We counted one pile, recognized that he had 4 groups of them and added repeatedly to get our total…in other words, we were multiplying!
Now link equal groups with arrays. An array is any arrangement of objects in rows or columns. To do this, we decided to go on a scavenger hunt. We started in the house, took it outside and now we keep our eyes open for arrays everywhere! Sometimes we solve them (find the total), sometimes we don’t. The important point is for Rory to recognize situations where multiplication would apply: equal groups in arrays.
Next, link the arrays to repeated addition (finding the total). Explain that multiplication is a faster way to add. Students progress through different levels of strategies when learning to multiply. First they solve problems by direct modeling, then by skip-counting or counting, and lastly by derived facts. I am not rushing Rory to derive facts, I am connecting multiplication to addition, equal groups, and arrays, and thus building a conceptual understanding which will help him to develop a strong sense of number. When you are introducing arrays in primary, start with small quantities that are relatively easy to subitize. To do this, I kept the totals under 20 and tried to use his knowledge of skip-counting by 2’s, 5’s, and 10’s.
The last thing to do is to replace ‘groups of’ with the symbol for multiplication. But notice, I stayed away from that as much as possible. I want Rory to conceptualize, not symbolize; so we always wrote the problem using the words: ‘groups of’.
How can I nurture his understanding of multiplication even more? With real-life context!
Van de Walle says, “Use story problems as a means to an end…not as the end itself”.
Here is a video of Rory and I doing exactly that. You may notice that some of the tasks look like division instead of multiplication. That’s on purpose! Another connection to multiplication you can build on, while still focusing on equal groups!
So, the way to make multiplication meaningful? Concentrate on the connections between equal groups, arrays, and repeated addition; but most importantly, embed instruction in real-life context!
Stay tuned for more ideas on how to introduce multiplication!