What do the following multiplication facts have in common? More importantly, how can knowing some of the smaller facts help you know the larger facts?

You hear a lot of talk about using strategies to learn basic facts, but I’m not sure it’s always clear what that means.

Most kids will know 2 x 3. If you ask them how, they’ll probably tell you they skip count by twos, or they know it’s 2 groups of 3 (or 3 groups of 2), or they add 3 + 3. Remember, it is really important to ask students *how* they know, because even with a very simple fact, there’s are lots of ways to see it.

Let’s move on to 4 x 3. Well, 4 is double 2, so wouldn’t 4 x 3 be double 2 x 3? Another way to look at it is that 2 x 3 is 2 groups of 3 and 4 x 3 is double that. Learning the 4s facts by doubling the 2s is a great strategy.

How about 4 x 9? Some kids might use a friendly number here, because 9 is so close to 10. So they’d do 4 x 10 and then just subtract one group of 4 to get 36. Another student might notice that 9 is 3 times as big as 3, so 4 x 9 must be 3 times as big as 4 x 3. Again, getting 36. Still another student might see 2 x 9 and 2 x 9. Still 36. 🙂

Finally, we get to a toughie–8 x 9. I was always SO bad at that one! Again, you could use a friendly number (8 x 10) – 8. Or you could double 4 x 9.

I’m sure there are lots of other ways to look at these problems, and therein lies the beauty–yes, beauty– of __number talks__. Getting the kids to talk about, and listen to, multiple fascinating strategies.

If you’re looking for a resource to learn more about strategies for multiplication and division, check out __Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students Beyond Memorization__. Long title, but a really easy to use book!

Any resources for subitizing ? Kids talking about math is really important to figure out where they make mistakes. Thanks for sharing.

Oh, LOTS of resources for subitizing! Just to the right of this post, where you see Labels, look down until you see the label subitizing. I have 13 posts on subitizing! Several have free sets of dot cards for subitizing.

We are using Investigations and that has kifs talk about what they know!

We are using Investigations and that has kifs talk about what they know!

We are using Investigations and that has kifs talk about what they know!

We are using Investigations and that has kifs talk about what they know!

It is so awesome to hear kids talk about their thinking! Love, love, LOVE it!

Ok Donna, I need to buy a few books to beef up my professional shelf for math. I already have had someone ask about Number Talks. What about What’s Your Math Problem? Getting to the Heart of Teaching Problem Solving, Teaching Student-Centered Mathematics: Grades 3-5,

It Makes Sense!: Using Ten-frames to Build Number Sense, Grades K-2 or Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3? What do you suggest? These would be for me, as well as a K-5 staff.

Thanks!

Robin

It’s All Elementary!

http://www.teacherszone.blogspot.com

The Van de Walle book (Teaching Student Centered Mathematics) is a must! EVERY math teacher should have and use this book (there is a K-3 edition as well as the 3-5). It’s really hard to narrow the others down, because they are all great for different things! Number Talks is excellent for professional development on mental math strategies for computation, although I don’t think each teacher needs one. The It Makes Sense books (one for 10-frames and one for the 100 chart) are excellent teacher resources for using those tools for whole and small group instruction. Number Sense Routines is great for developing a terrific math warm-up. And What’s Your Problem ties in problem solving. How on Earth do you narrow it down? After Van de Walle, I think it really depends on what your focus and priority is this year. I’m not sure that helped much. 🙁

OK…I am not a teacher, just a grandmother who is helping to teach my grandchildren. I think all your ideas are great. I remember when I was in school (in the last century), I hated math. It never made sense to me AT ALL. Now that I am teaching my g’kids I find the methods used today make great sense. Now with that said when I was in grade school (again last century) I had much trouble with multiplying 9’s. So a brainy kid (not the teacher) taught me a trick, i.e. 9 x 7 one less than 7 is 6, then 6 + ? = 9, that would be 3, so the answer is 63. I have never forgotten that trick. I use it to this very day. Now is this a BAD thing to teach kids? Does it do more harm than good? Just wondering, we aren’t quite to multiplication yet.

Jackie, it’s great that that “trick” helped you remember a really hard fact. But how’s this for a trick? 9 x 7 is one group of 7 less than 10 x 7, so it’s 63. It’s not that tricks harm kids, it’s just that when we teach for understanding kids don’t need tricks. I think we have a lot more knowledge about learning facts now…I sure wish that I had learned strategies when I was trying to memorize my facts! And kudos to you for working with your grand-kids on math! 🙂

Sounds good. Thanks for the info and all your great ideas.

Donna,

I came across your blog from Pinterest, and started looking up multiplication strategies. I see that a lot of the methods you mention are what is being employed at my children’s school. I’m 37, and when I was in school, we were taught differently, and when I help my kids, its usually the way I know how. At first this got the kids confused, but they have come to realize that knowing how to determine the answer in different ways can be helpful. My issue right now is multiplication. My husband and I remember the group reciting multiplication tables so it became rote. I understand when you say that the kids need to understand HOW or WHY the answer is right, but is it bad to also just memorize the table (up to 10 or 12). I find it so frustrating when my 5th grader doesn’t know basic multiplication answers off the top of his head, and I’ve considered creating my own table sets and having the kids practice with me each day. Is this bad?

Thanks for your question, Nichole! The goal of teaching with strategies is automaticity. The word automaticity seems to be preferred to memorization, I think because it implies understanding. There is practice involved, however there’s a reasoning behind what facts the students are practicing. For example, 2s, 5s, and 10s are often learned and practiced first. 4s are taught through their relationship with 2s. The 4s facts are double the 2s. In other words, 2 x 3 is 6 and 4 x 3 is double that, or 12. A book I really recommend is

Mastering the Basic Math Facts in Multiplication and Division.It contains a chapter for each strategy with easy to make games and even flash cards. I totally understand your frustration, and I hope this helps.I like how you touched upon the fact that memorizing is not the same as understanding.

Absolutely!

This very topic has been the focus of my year so far as a Math Coach K-5. I learned about running records for math from Dr. Nicki Newton and have been doing hundreds of them for addition and multiplication. It helps measure the three parts of fluency- speed, accuracy, and flexibility of thought. Some students have been automatic in their multiplication math facts but don’t have any strategies underlying their thinking. When teaching strategically, rather than learning what 4×7 is, they can multiply any number times four including decimals and fractions down the road. Magical! Once we figure out where each student needs to begin, we are having them play games and activities to focus on what they need. I think it has the promise of changing everything!

As far as building fluency with the facts, is there an order that is suggested. I teach primary but my son is working on multiplication now. He seems to get the gist of it and can determine answers using various strategies, but there is no speed or automaticity. Was thinking 0s and 1s are easy. Then maybe 2s (builds on doubles from addition) and 10s. The perhaps 5s (half the ten??). Would love some tips from those who teach this!!

Your sequence is spot on, Brittany! I would do 2s after 5s and 10s, then after the 2s you can do 4s and 8s, because they are connected. The same with 3s and 6s.

Donna, I am going to be working with a fourth grade class of students who have not mastered addition or subtraction fact fluency.They are currently working on addition, subtraction, multiplication and division facts concurrently, but I don’t think this is effective. I am considering implementing multiplication fluency…. instruction, talks, practice and a class incentive for achievement! Do you agree that its OK to put addition and subtraction fluency on the back burner?

I think I agree that they can’t work on all four at once. I do think you can work on multiplication and division concurrently by stressing the relationship between the two operations.