Multiplication Strategies

This post has nothing to do with something new and brilliant I’ve discovered about helping students learn their multiplication facts. Instead, it is about my learning. About a year ago, I wrote this post: Times (x) they are a changing . . . .  It was a reflection on how and why I stopped doing timed multiplication drills. Back then, I learned from my students about what they needed. We began to work on our facts in a different way and I was excited about what I saw.

In no way did I throw the baby out with the bathwater. I still believe children benefit from knowing their multiplication facts. Especially if they know them “by heart” so the answer to 7 x 8 is as easily retrieved as a birth date. This allows them to use these facts easily and quickly as they work on more complex problems in the intermediate grades.

But one year later, what am I thinking? Watching my students approach their daily practice with multiplication facts, I remain absolutely convinced that timed drills are not the way to go. Why?

*The stress of “being timed” just completely shuts some learners down before they even begin.

*Timed drills have a “test like” vibe and everything gets quiet. The “talking through thinking” stops and often, so does the thinking.

*Timed drills highlight what you already know as a teacher. Some kids learn their facts almost instantly, some learn them with lots of memory work and some struggle no matter what. So why create a situation that highlights this? It doesn’t highlight learning.

*Creating a situation where memorization is the only route to success means not everyone has success

What do I do instead? 

*We spend a lot of time on the concept of multiplication. The symbol x is taught as “groups of” so we would read this math sentence 2 x 4 as 2 groups of 4. We draw pictures. We work with manipulatives. We play games. We build and draw arrays (with blocks, graph paper, rows and dots) We solve problems (using pictures or blocks, etc)

* We then move on to learning that there are strategies to answering multiplication questions – this comes from our observations, discussion and the patterns we notice as we go. I never teach “tricks” at this stage like “just add a 0 to the other number when you multiply by 10” I let students figure it out themselves so that the “trick” is connected to the concept. Not so it replaces it.  It sounds something like this: Student A says, “I was counting by tens to solve these problems (4 x 10 and 7 x 10) but then I noticed that all of the questions that are groups of 10 always end in a 0.” Student B concurs, “Yes! It’s kind of like because you are counting down the 100s chart at the end part where you are skip counting by 10s. So you can just put a 0 on the end of the other number.” Another child listens to this and looks confused. Student A and B get out blocks or the hundreds chart and show them with skip counting.  They try out a few more and boom, they have a strategy that now works for them. And, they all understand because they have made meaning together.

*While we continue using multiplication to solve problems and even move onto division concepts, we do a daily practice sheet that contains 16 multiplication questions. Students move through these sheets at their own pace. They can talk. They can ask for support. Some work with a partner. Some get out blocks and build arrays. Some skip count on their fingers. Some do what they know first and then add on another group i.e. “I know 5 x 6 is 30 so 6 x6 is 30 +6)

What is happening in the room that wasn’t back in the days of timed drills?

*Self talk. I often hear a child talking through the questions

*Talking together and building knowledge

*Discovering strategies and sharing them

*Recognizing patterns

*Time and space to think

*Confidence and competence develop together

*And multiplication facts begin to become known facts. For some it is many. For others,    just a few. Some children are working on learning the 6s and 7s. Others are working with 2s and 5s. Others know them all fairly well and get sheets with a variety of questions to practice. When they feel ready, they tell me they want to move on. Often it just clicks and a child ralizes that they “just know” many facts and they get very excited to learn more. The exciting thing is when they move on to a new set of facts and recognize that they already know many of them!

*Everyone is making progress and multiplication is something we feel confident about!

So fellow primary teachers, how do you deal with learning multiplication facts? Would love to hear how things work in your room.

Times (x) they are a changing . . .

Times Tables

Multiplication facts

No matter what you call them, knowing them helps as we move up the math concept ladder. I use multiplication facts frequently in the “real world” and knowing my facts helps make my problem solving faster. At the grocery store – 3 kiwis for $1.00 I have $5.00 with me So . . . I want about a dozen. If I buy 12 (3 x 4) then I’m going to have enough money (4 x $1.00) Yes, I need to understand a few things to do this mathematically but knowing 3 x 4 and the rule about multiplying things by multiples of 10 and 100 helped me solve this much more quickly.

In the primary grades we begin to explore the concept of multiplication. I often start the unit with a game of Noodles and Plates (Math to the Max Grade 3 Number Operations) I don’t tell students how to solve the equations. I just explain the rules of the game and let them get started.

P1020690The game is lots of fun. You need dice (I like the soft foam ones to cut down on the noise), pencil and paper. Player 1 rolls one die and draws that many circles for plates (if you roll a 4,  draw 4 plates) Player 2 then rolls and draws his/her plates. Then player 1 rolls again and this role determines how many noodles go on each plate (some kids drew tally marks, some drew numbers) Player 2 does the same. Then write a math sentence to represent your turn. (i.e. 2 x 6 = 12) Whoever has the higher total wins a point. Start again. We could have played all day. Everyone was on task, partners were helping each other solve the equations. Lots of math talking! Full on engagement.

To make this more complicated for higher grades, roll both die!

By the time we have played this game for a math period, many kids totally “get” groups of (which is how we read the math statement 4 x 2 is 4 groups of 2) and have started applying repeated addition and skip counting without me telling them to. We then practice more – linking repeated addition (5 x 3 is 5 + 5+ 5) , skip counting (5, 10, 15), working with arrays, understanding that 2 x 3 is the same as 3 x 2, understanding that 4 x 3 is the same as 3 x 3 + 3  etc. Building strategies and understanding through hands on activities, drawing models, looking at pictures, etc.

But how do I help them start committing these facts to memory? Next year’s teachers want them to know their facts. Knowing their facts helps make more complicated problem solving easier (well at least faster). Yes, there are calculators and computers and all but sometimes we won’t be carrying a device with us. What to do?  I had been doing drills – many kids loved them! Math drills. Yippee! These are the kids that have “number sticky” brains. They just know math facts – they stick in their brains and don’t leave. I was one of these kids. I still remember correcting my Grade 3 teacher’s math drills on the board (“You already put 5 x 6 for question 3“) She always gave me that Aren’t you a delightfully annoying child? smile and got up from her desk to fix it. (How did she ever have time to sit at a desk?) But not everyone has those sticky brains that facts just stick to . . .

The other kids tolerated them. We would answer 16 questions in 90 seconds – each child working at his/her level (once you had 3 16/16s in a row you would move on) So some kids had worked their way up to the 7s and 8s. Some were still on the 2s and that was okay. There was progress. We did math drill corrections. We trudged along.

But this year a few things changed. We started this process and it didn’t go so smoothly. I still had the celebrators and the tolerators but now I had a few rebellors (is that a word?) Some kids just wouldn’t do it with the timed aspect etc. And you know? I kind of respected them for it. Then I lost my timer (or maybe it walked away?) This was a sign. It just didn’t feel right. So we stopped for a few weeks.

But I got back to thinking about it. Do we need to memorize? Isn’t process as important as product. Don’t I need to allow students to begin developing and shaping their own learning?

The answer? Not sure. Here is what I am trying. We are going to still work on these 16 questions a day at our individual levels. But I’m removing the timed component and therefore the “drill” aspect. Instead, I pass out the sheets early in the day and students try to finish them by day’s end. Some finish in 16 seconds truthfully because they have “math fact sticky brains” Others take all day (working on the questions at various down times). They are noticing patterns, they are applying strategies, they are talking to others and asking for help (yes that’s okay and even encouraged) math peer tutors (self-appointed) are talking them through it (“Remember you can skip count” “You already did 3 x 6 so 6 x 3 is . . . “) Then I ask them to tell me when they are ready for the next level. Because, (really what was I thinking before?) they know better than me. Self directed learning. Student ownership. And what do I do? Guide, mark, respect, give feedback, smile and count up my celebrators 2, 4, 6, . . . 14, 16 🙂

P1020712Working on questions together allows for all of that fantastic “talk” time that is necessary in math. Not talking by me but talking by students. I can confirm “Ms. Gelson, if I want to answer 7 x 2 – that’s like 7 + 7 right?”

“Yep.” and move on. The child is on a roll, I am not needed.

Peer teaching is some of the most powerful teaching in the room!

P1020708So I asked the students what they think of this new system.

They were happy to share.

“When you are rushed, it confuses you. When you take your time, you learn it better.” That timer will not be coming back!

I don’t feel so much pressure. It’s better.”

“Now we have time to draw out the ones we don’t know.”

Look what happens when you ask!!



So now I am getting drill sheets handed in with little notes like the one on the right: “I’m redy to move up.”

“Can I move up?”

“I wanna move up.”

“I can do the next.”

If they are writing me these notes and still making errors, I let them know and we practice a few more times. If they are consistently getting perfect scores and don’t tell me they are ready, I offer encouragement.

The big thing here that I’ve learned – communicate with your students about their learning. Watch for the signs they are giving you. Listen . . . and you will learn.