Multiplication approaches

When I started volunteering in my fifth grade class, we had an exercise that says "Solve this equation in two different ways." I panicked because I had ever only learned one way - the standard algorithm for multiplication.


Luckily, I've been working on enough multiplication tables now that I have a variety of ways to solve multiplication problems! It's great, my students have taught me a thing or two. I'll go over some different ways of multiplying that don't require a good knowledge of DDR.

1) Adding
Yes, it's not the preferred method of multiplication at the 5th grade level, but every once in a while, it may work. I would suggest you convince your students that it's not the most efficient way to do multiplication, especially if you're doing anything higher than one digit multiplication.

2) Partial sums
I've touched on this in my Greg Tang posts, but we can work through this method here. I actually really like this method and I think it works well for smaller two digit multiplication.

To do partial sums, you use several "easy" products and sum them all up to get to the answer. In the case of 83 x 24:

83 x 10 = 830
83 x 10 = 830
83 x 4 = 332

830 + 830 + 332 = 1992

Easy, no?

3) The array
I actually really enjoy this method as well. It's a more involved method of partial sums, but the visual aspect of it helps some students more than others.


You set up by making a box and separating the tens and ones. Multiply through and put your answers in the boxes. Then add everything up.


Make sure you get your students to check their zeros when multiplying the tens. Ask them how many zeros you start with and how many are in the answer. It will help with their self checking later on.

So there you have it, four methods to solving a multiplication problem!

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On a side note: leave it to the fifth graders to call me out on my doofy haircut. And I got the most adorable chorus of "Hi Ms. Minh" again when I came into the 3rd grade class. They. are. so. cute. I don't think it'll wear off anytime soon. I hope it doesn't.


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24 can arrays

Yesterday I worked in two of my classrooms. My other two classrooms I didn't make it to because of some miscommunications, but I went after school and talked to the teachers about what had happened. Although I couldn't make it to the volunteering session, I think it was important for me to contact them personally and let them know what's up. I also asked about next Wednesday. BPS is on half day schedule for the Wednesday before Thanksgiving, so I checked and made sure if I was going in to class.


My last class was extremely productive and continues to be the exemplar of what Math Rules! should be. I'm going to start calling this class the Horseshoe class because we have our separate space to work during math. My four kids were working on fractions, percents, and decimals. We played a number line game that puts fraction cards in order next to each other. I think the kids enjoyed a hands on game, getting to review what they had learned the previous day, and taking turns in different roles in the game. We rotated who got to go first, who got to shuffle the cards (the kids were very impressed I could riffle shuffle and do the card bridge), who got to deal, and who got to tally up points at the end. Having my students take ownership and responsibility was good, and the kids realized it and pointed out who hadn't gotten a chance to do different roles.


My other class unfortunately had a substitute because our teacher was out. Although this blog is supposed to be positive and student focused, I felt so bad for the kids for having this substitute. He really upset some of the children and I was helpless in the situation. Despite this, the students broke apart and worked on math in several different groups. This made working with my four kids very difficult. I got to touch base with two of them and worked with them on part of their work. One of my students was absent, and the last student I still don't recognize his face. This is really unfortunate but I'll talk to my teacher about this the next time I see her. I did work with one student very briefly on his arrays and thinking about different ways to arrange 24 cans. After I finished helping him, I circulated the room a bit, and when I came back to him, he said "Thank you for helping me with the arrays." It was awesome to hear this from a student. It was the smallest amount of effort on my part, I guided him through what he already knew, but knowing that he appreciated my time and 2 minutes of attention was amazing.


After talking to Wendy on this topic, I think it's difficult to work with the same four students on a regular basis depending on the lesson of the day and also the format of the classroom. Getting your teacher to understand the program makes everything easier on the volunteer. It's also tough to assert yourself, as a volunteer, in the classroom and say no to whatever your teacher asks. Getting this perspective of how the program works (or doesn't quite work) is important for personal reasons, but also for improvements and suggestions for the program's future.