The Order Math Facts Should Be Taught

I just recently finished doing some five day trainings all about doing number talks to help kids develop strategies around addition facts, and also multiplication facts. I repeatedly received a particular question, and I thought I’d talk about it today. The question was, “What order should we teach the math facts in?”

**The free trainings mentioned in this video are no longer available for free.  They are available to the members of the Build Math Minds PD site.

There Is No One Way That Everyone Agrees Upon

If you know me and seen any of my trainings, you know my number one belief is we don’t actually teach them. If we try to teach them to kids, it doesn’t resonate and they end up either having to just memorize, or they’re counting on their fingers. The whole idea is to develop some strategies and relationships that help kids get into what’s known as the derived fact stage, and then into the fact stage.

If you go and Google any kind of research about the addition math facts, or multiplication math facts, you will see lots of different ideas about the order that we should present them to children and the way that we should help them develop their understanding. There does not seem to be a consistent way. I know when I was in school, it was just your plus 1s, your plus 2s, your plus 3s. The same thing applied to multiplication, times 1, times 2, times 3, and times zero would come after we’d have a little bit of understanding. However, there wasn’t any rhyme or reason. It was just the order of the numbers.

There are some programs out there that seem to have a rhyme and reason. There are other programs that I’ve seen that have no rhyme or reason and I don’t even know how they are putting certain facts together. Personally, really love Sue O’Connell and John Giovanni’s books.

These two books, one for addition and subtraction, and one for multiplication and division lay out a nice framework for us to start off with. Mine is a little bit different from theirs, and you can tweak it a little bit, but I really do love these books. If you’ve never seen these, and you’re working on helping kids develop their fluency with addition and subtraction, or multiplication and division, I highly recommend them.

Start With The “Easy” Facts (Dark Colored In The Charts)

These are the facts that just seem easier for kids. They gravitate towards them, they resonate more with them for whatever reason, and there are specific reasons why. For addition, here’s the chart of the addition facts.

I’m speaking just for addition and multiplication. It’s really about them. As you’re focusing on these types of facts, you’re also talking about the relationship of those facts with subtraction facts.

The addition fact chart is color coded. The colors go like this…The dark shaded ones of whatever color, are the ones that kids gravitate towards. So, the dark orange are the doubles. Like 2 plus 2, 3 plus 3, 4 plus 4, and so on. The dark green are the ones that make 10. Kids will gravitate towards those. The dark blue, are basically the teen numbers. As we kind of group them all into that terminology. But it’s really when you have 10 and then you add some more to it 10 plus 1, 10 plus 2, 10 plus 3, that’s a type of fact that kids gravitate towards and that they should be learning before others. The purple ones are the ones that are plus zero. So, those four, the doubles, the make 10, the 10 plus something, and the plus zero, for me, are the first things that I want to help build for students.

Whether you want to start with the ones that make 10, or start with doubles, it doesn’t matter to me. And as far as I have seen, it doesn’t matter to kids. What I’ve seen that matters to kids is from their own experiences. What have they had around experiences with number that they hook to.

I have seen pre-K kids know what 7 plus is, because they’re football fans. I’ve seen kids who know their make-10 facts because they can see it right there with their fingers. So it just depends upon the experiences they’ve had as to which ones they will gravitate towards, so for me, there’s not a particular order of those four. However, my recommendation would be not to start with plus zero. This is because adding nothing is a little weird for students, and you first want to help them to understand what it’s like to add something, before you start adding nothing.

When it comes to multiplication, the four types of facts, these do not need to be in any particular order.

On this chat the purple ones are the properties. Anything times 0 is 0. Anything times 1 is itself. Those two ideas are really, really huge. The green ones are the times 2. Anything multiplied by 2 is basically a doubling of that number, and making the connection to their addition doubles facts. That’s usually the place I like to start, is multiplying times 2, because its got a nice connection to their addition doubles. I then like to go to the times 10, which is the red. Some people go to times 5, but I’ve found that kids are really good at multiplying five only because they can count by 5s pretty quick. They don’t really have an understanding of times 5. So I like to do multiplying by 10 first, and then showing how multiplying by 10 relates to multiplying by 5s, because there are some really cool connections you can help kids see with that.

Those are the 4 types for multiplication facts. The times 1s and times 0s (which are your properties),green ones are times 2, reds are times 10, and the blue are multiplying by 5. And again, pick whatever order works for you. But those are the ones that kids gravitate towards, and they’re what I like to call the Power Facts. They’re the ones, that if they learn those, they can derive all the other facts. That’s why all the other colors are just shades of those colors.

Focus On Relationships

If we go back to the addition one, the next piece is really once they’ve learned these four types, it’s all about connections, and helping kids see relationships between the ones they know, and the ones they don’t know. So the shading from the chart here on out, is the lighter colored ones connect to a darker colored one. So, if kids know 3 plus 3, it’s all about helping them see relationships to 3 plus 4. We want them to see how those connect together. It makes learning, and being able to recall their facts a whole lot easier. So, that’s what the rest of that chart on both of these are, is the lighter shaded ones connect to the darker shaded ones.

So, on the multiplication chart, the dark green helps us with the light green. If I know my times 2s, multiplying by 2, can help me with timesing by 4. Because all I have to do is just double it. So it’s all about getting those four types solid with kids, and then the last piece is really helping them make connections. So again, to me it doesn’t matter if you want to work on multiplying by 9 before you work on multiplying by 4. It doesn’t matter. It’s all about the connections. I want kids to see how multiplying by 9 connects to multiplying by 10. It’s not about adding up a bunch of 9s, it’s really about seeing how when I have 10 groups of 7, how that’s related to 9 groups of 7. It’s just one group of 7 less. I don’t have to count by 9s to figure that out or count by 7s, however they want to do it, right? It’s helping kids develop relationships between the types of facts. And that holds true whether you’re helping kids with addition facts or multiplication facts. Once you’ve started that development, then you relate addition to subtraction, and multiplication to division.

My full free trainings that we did around developing fact fluency for addition and multiplication are no longer free. They have gone into my Build Math Minds professional development site for members to be able to have access to it any time. So, below this video, and at the bottom of this post is a link, that if you’re interested in joining the PD site, you’d have access to all of those free trainings, plus a whole lot more to help you build your math minds, so we can build the math minds of the students. Build Math Minds, only opens a few times a year. So, if you click the link, and it takes you to the “waitlist”. Just signup, and when we open it back up for a new cadre of teachers to come in, we’ll let you know.

I hope that this has given you some insight into how to help your students with developing their fact fluency because remember, the order doesn’t matter. That’s really the big thing I hope you take away from this. The order doesn’t matter. It’s about connections. What kinds of connections can we make for the students? And it doesn’t matter what order you do that in, as long as we’re building connections.