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.

9 thoughts on “Multiplication Strategies

  1. I like your approach. However, how do you make sure your students commit the facts to memory? Multiplication facts are some of the very few things that have to be committed to memory. I don’t give my students timed tests, per-se. I use songs for the multiples, stories for some of the facts, rhymes, games, websites, and tricks that the students discover (we look for patterns – I don’t tell them the tricks, except for the finger trick for the 9s), and anything else my students tell me that helps them. I also test the students every day (as much as possible) individually to see which facts that they have difficulty with. Those facts, and only those facts, they have to write 5 times for homework. When they have this homework, they have to say it, look at it, hear it, and write it. I try everything possible to avoid repetitive worksheets and timed tests.

    • Thanks for the comment Chris. We also use some songs and rhymes to practice. I find that as we work through various multiplication activities and students do daily practice, that a lot of facts become “known” simply because they so frequently work on the questions. As they have worked out a variety of strategies and spent time sharing them, their confidence grows. Often students share what they have learned with the whole class in our discussions so we can explore the strategies as a group. Students also are self motivated to practice the ones they don’t know. I send their practice sheets home regularly and they work on learning the tricky facts on their own or with parent support. I think the key thing is to take the boring/stressful drill aspect out of the picture and instead instill a belief that facts can all be learned with various strategies and practice.

  2. Thank you for sharing the changes that you notice now! I love hearing about what great math learning is happening in your classroom. I’m really struggling right now as in just over a month, I’ll be administering EQAO. While I don’t want my entire teaching practice to be based on a standardized test, I also don’t want to ignore the fact that this test is coming (and it’s a big one). Since students cannot collaborate with each other during the test, and since they can’t use a calculator for multiplication and division, I feel like they need to independently feel comfortable with the math facts. This goes against so much of what I do in my room. When do you force independence and when do you encourage collaboration? What might you do in this situation? I’d love to know your thoughts on this!

    Aviva
    http://www.weinspirefutures.com

    • Aviva, some of your issues just aren’t mine – i.e. I’m not facing a standardized test and my students, at this age, don’t have to demonstrate mastery but rather understanding of the concepts and be able to utilize a variety of strategies to solve problems.

      However, I have my own children who are in Grade 5 and I know that they need to know their multiplication facts with fluency and confidence to handle more complex questions and not be held back and slowed down by figuring out the multiplication facts. And one of my children has that “math fact sticky brain” and one doesn’t. So I know that regular practice really is necessary. With my child who needed more practice, we did a variety of things – concentration games, practiced at low stress times like on a walk and let her do “flashcard” type practice on the Ipad. She directed it though – which facts she would work on, etc. And so felt less anxiety and real pride as she eventually mastered various facts. Her teacher noted at our last conference how much more confident she has been!

      I guess if I were you, I would really stress how it is totally normal that some kids are going to learn facts with much more ease than others – it is not a sign of intelligence – just how different brains work and that everyone needs to put various degrees of effort into learning facts. I would still allow practice times to be without stress and full of fun and celebration but would involve students in goal setting around their fluency with facts.

      So tricky when tests interfere with your instincts, but nonetheless I do think learning facts is an important skill – our job is to make it as fun and low stress as possible though!

      • Thank you, Carrie! I really want this review to be stress-free. All year long, I’ve encouraged the students to take risks and try new things, and know that the only person that they’re competing with is themselves. As a class, we’ve celebrated all successes, and students are really proud of what they’ve accomplished. I want the same to be true in this area. Your posts have given me lots to think about!

        Aviva
        http://www.weinspirefutures.com

  3. Such a simple change: Instead of saying 5 times 6 I start encouraging students to say 5 groups of 6 when they see the x. (or we can say 5 by 6 if we are talking area.) Why didn’t you tell me this at the beginning of the year?! 😉 I find that the language teachers sometimes take for granted, thinking kids understand it more than they actually do. 5 times 6 is not as clear as 5 groups of 6. Silver lining, it’s not too late for me to try out your wording, especially on the students that are having a tougher time understanding multiplication. Have a good weekend!

    • So true Nicole. Language can really trip kids up. And in math it really interferes especially when kids are learning new concepts and new language at the same time. I think language in math must mirror the teaching/thinking/learning. So groups of makes the most sense as it is how we learn the concept – by visually making groups of objects to match our thinking/the question asked. I even go as far as to have the kids say groups / of as they write the strokes of the x – one word for each cross. Sticks with them more.

  4. Carrie, I enjoyed reading about how you deal with timed tests and how you help your kids really focus on the concept of multiplication rather just memorizing the facts. I had commented on Aviva’s blog that I wonder if the struggle with facts is less about not knowing facts and more about not understanding number sense. The strategies you described here kind of confirmed that for me.

    I can’t tell you how much I appreciate you getting involved in my incentive discussion. I’m looking forward to learning more with you! 🙂

    • I am so pleased that this was helpful. I am learning as I go to try and be reflective and responsive to the learning my students are doing. If you really pay attention, the messages come through loud and clear! I am rooting for you in this process with what is happening at your school. Please keep me informed. And good luck!

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