- So I just got done doing some five day trainings
all about doing number talks to help kids
develop strategies around addition facts,
and also multiplication facts.
And I got a question kind of repeatedly,
and I thought I'd talk to you guys about it today.
The question was, what order should
we teach the math facts in?
I'm Christina Tondevold, the Recovering Traditionalist,
that's what we're gonna talk about today.
Is what order should we teach those math facts in?
Now, if you know me, you've seen any of my trainings,
you know my number one thing is,
we don't actually teach them, right?
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.
So, as research, 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.
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 ones,
your plus twos, your plus three,
and the same thing for multiplication.
Times one, times two, times three,
times zero would come after we'd have
a little bit of understanding, right?
But there wasn't any, like, rhyme or reason.
It was just like the order of the numbers.
Now, 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, I don't even know
how they are putting certain facts together.
Personally, I really, really love
Sue O'Connell and John Giovanni's books,
which i think are over here somewhere back behind me.
(laughs)
But they're called Mastering the Basic Math Facts.
Those two books, there's one for addition and subtraction,
and one for multiplication and division,
lay out a nice framework for us to start off with,
and it's kind of what I'm gonna talk about with you today.
Mine is a little bit different from theirs,
and you can tweak it a little bit,
but I really do love those books.
So if you've never seen those books,
and you're working on helping kids develop their fluency
with addition and subtraction,
or multiplication and division, I highly recommend them.
So, let's get started on
what order should we teach them.
Here are my thoughts, you may disagree with me.
If so, put it in the comments.
I would love to hear your thoughts.
Whether you agree or disagree, let me know.
So, my belief is that we should first off,
no matter what, start with what I call the easy facts.
And these are the facts that kids,
they just seem easier for kids.
They gravitate towards them, they resonate more with them
for whatever reason, and there are specific reasons why,
but these ones kids gravitate towards.
So, for addition, here's the chart of the addition facts.
And I'm speaking just for addition and multiplication.
It's really about then, as you're focusing on
these types of facts, that you're also talking about
the relationship of those facts with subtraction facts.
So the addition fact chart is right there,
and as you can see, it's color coded.
So the colors really 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 two plus two, three plus three,
four plus four, and so on.
The dark green are the ones that make 10.
Kids will gravitate towards those.
The blue ones, the dark blue, are basically
kind of the teen numbers, right?
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 one, 10 plus two, 10 plus three,
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,
and 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.
Now, whether you want to start with the ones that make 10,
and I start with doubles, it doesn't matter to me.
And I don't think, 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 seven
plus seven is, because they're football fans.
I've seen kids who know their make-10 facts
because they 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.
My recommendation would be not to start with plus zero.
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,
and again, these do not need to be
in any particular order, right,
but the purple ones are the properties.
Anything times zero is zero.
Anything times one is itself.
Right?
Those two ideas are really, really huge.
The blue, or the green ones, sorry,
are the times two, that anything multiplied by two
is basically you're doubling that number,
and making the connection to their addition facts.
That's usually the place I like to start,
is multiplying times two, 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 five, but I've found
that kids are really good at multiplying five
only because they can count by fives pretty quick.
They don't really have an understanding of times five.
So I like to do multiplying by 10 first,
and then showing how multiplying by 10
relates to multiplying by fives,
'cause there's some really cool connections
you can help kids see with that.
And then, again, those are those four for multiplication.
Your times ones and times zeros, which are your properties.
Your green ones are times two.
The reds are times 10, and the blue are multiplying by five.
And again, pick whatever order works for you.
But those are the ones that kids gravitate towards,
and they're, I like to call kind of 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.
So 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 three plus three,
it's all about helping them see
relationshipS to three plus four.
Right?
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 twos, multiplying by two,
that can help me with timesing by four.
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 nine before you work on multiplying by four.
It doesn't matter.
It's all about the connections.
I want kids to see how multiplying by nine
connects to multiplying by 10.
It's not about adding up a bunch of nines,
it's really about seeing how when I have 10 groups of seven,
how that's related to nine groups of seven.
It's just one group of seven less.
I don't have to count by nines to figure that out.
Or count by sevens, 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.
And then again, once you've started that development,
then you relate addition stuff to subtraction,
and multiplication to division.
Now my full free training that we did
around developing fact fluency for addition,
and the one for multiplication, is not free anymore.
It has gone into my billed Math Minds
professional development community
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 professional development community,
you'd have access to all of those free trainings,
plus a whole lot more that I do every month
in there to help you build your math minds,
so we can build the math minds of the students.
So, if you wanna join Build Math Minds,
it's only open a few times a year.
And if you click the link, and it takes you to something
that says it's a wait list now,
you can join the wait list, and when we open it
back up for a new cadre of teachers to come in,
we'll let you know.
So thanks again for joining me,
and 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 connetions can we make for the students?
And it doesn't matter what order you do that in,
as long as we're building connections.
Have a great day.
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