Do you have students in your 4th-6th grade class that just can’t seem to master multiplication? No matter what you try (flashcards, incentives, computer based programs), they just can’t get past their 5s? I have had several students in my classrooms over the years. It can be very frustrating, to say the least. Last year, I researched a few new strategies and finally found one that I knew would help my students.
I will tell you that it is not a “quick fix” strategy. This is a “I have got to be able to figure out what 7 x 8 is to solve this multi-digit problem, and I don’t have time to draw a picture of 7 circles with 8 dots inside each circle.” Yes, I literally have students in 5th grade who resort to this each year.
This particular strategy has the students using the distributive property of multiplication, with a bit of scaffolding and support.When I taught it to my struggling multiplication students, I immediately saw light bulbs go off. It worked wonders for them!
Basically, the students use what they know (their 1s, 2s, and 5s) to determine the answer, using the distributive property of multiplication. Here is an example:
The student in the above example knows that 5 x 8 = 40, and 2 x 8 = 16, so the two products added together give you 56, which is the answer to 7 x 8.
When I first introduced this strategy to my students, I did a lot of conceptual talking about the numbers and even manipulatives to ensure they understood the concept. When talking about the equation, I would say 7 groups of 8 (versus 7 times 8). Then when I refer them to their “known facts: 1s, 2s, and 5s,” I would say something like: “You need 7 groups of 8. Which of your known facts will give you the largest amount of groups, without going over?”
After the student picks 5 x 8 (or 5 groups of 8) we talk about how many more groups are needed to make 7 groups, etc. Then we talk about why adding the products works. I really try to get them to conceptually understand why this strategy works. It keeps them from making mistakes, and eventually leads to quicker thinking and using those benchmark fractions that students with strong number sense can do. (i.e. I know that 6 x 8 = 48, so I just need another group of 8)
Here is an example of one of my student’s work when he used this strategy for 9 x 6. He marked out the 5 x 6 after he used it because it was too big, and he knew that he could not use it again. He then used the 2 x 6 twice. Eventually, the students will begin to make connections between the numbers and do 5 x 6 and 4 x 6.
As I mentioned earlier, this does take a bit of time, but the students will gain fluency with it. They will learn to do this without the need to write about the list of facts each time. Also, what better motivation to memorize multiplication facts to save from having to do this each time a student needs to multiply one-digit numbers.
Click here to grab your copy of the poster shown in this post as well as a few printables that I use when teaching this strategy.