- Well, as I gear up for
my number sense courses
to open up for registration,
I always like to provide some free content
around number sense so that you
can implement number
sense into your classroom,
whether you take the full course or not.
I'm Christina Tondevold, the
Recovering Traditionalist,
and I hope that you will
stick around as we look
at building number sense in
the early elementary grades,
my top tips, as we work
to build our math minds
so that we can build the
math minds of our students.
My first top tip is something
that I'm fairly well known
for saying is that number
sense can't be taught.
It's caught.
And what I mean by that is that we need
to provide experiences for our students.
If we really want them
to attach to numbers,
to mathematics, it needs to be
connected to their real life.
So often we have kids who see school math
as separated from real math
and that just should not
be the case, number one.
And number two, when we
connect it to their real lives,
they get to see the mathematics in action
and it isn't just this
abstract concept to them.
When we can take a concept
we're trying to work on
and put it in something
real life for them,
they can see the
mathematics in all new ways,
ways that we cannot
directly teach to them.
They need to experience it and see
how numbers work together.
Let's say we're working
with kids and we want
to talk about how numbers
compare to each other,
like four compared to five and really,
we're wanting to talk about
how five is one more than four,
that five is greater than four,
all of those kinds of
concepts that we want kids
to understand when they're
looking at two numbers
and trying to compare them.
Well, if we just give them
four and five as digits
on a piece of paper, it doesn't
connect as well for them.
If we put it into a story format
and we say something like,
Sierra has four cookies.
Her brother has five cookies.
Who has more?
How many more?
That image that that portrays,
so many kids can bring that
image up in their mind,
that they aren't even seeing
four and five as digits,
they're seeing amounts.
Like this, you'll see kids
who will model that problem
by counting out four things,
counting out five things,
and maybe they do need to count because
that's the stage they're in,
but you'll also see kids
who can just visualize
those amounts, but I wanted
to bring the visual up here
so we could talk about even the kids who
are visualizing something
and who don't need
to physically count out the amounts,
the image that they are
conjuring up when we put
it into some kind of a context for them,
creates an image like
this, similar to this.
And when they have that image,
they can do so much more,
and they can talk about
how those numbers relate
to each other in various
different ways and in ways
that may be different than
the way we were seeing it.
Let's say I was really
hoping that kids might
be able to understand that
five is more than four
and it's one more than four.
You definitely will get
those kids who will see
that extra one sticking
out there and can talk
about and verbalize that extra
one that's sitting out there.
And then you can help
formalize that thinking
and talk about, so five,
is one more than four,
or four is one less than five.
You can attach the more proper verbiage
that you want kids to talk about,
but when they can physically
see it with their eyes, say,
oh, that's what they
mean when we're saying
one more than or one less than.
If we just have the digits,
they don't see those things.
And the other cool piece
that I talked about
is they may see something
completely different.
You may have some kids who see it as
I see that both sets
really have four in it.
And that is a huge mathematical idea
that a lot of kids really struggle with
is that within five, you
still have four things.
Even though you have
five, you have the amounts
that are smaller than it as well.
And you don't see that
unless you're putting it
into some kind of a context
that kids can create visuals
to go along with those contexts.
My first advice for building
number sense with your kids
is provide experiences,
help them catch number sense,
because you cannot directly teach it.
My second one is something that
you've kind of already seen
in what we've been talking about so far,
but it's using lots of
visuals and manipulatives
with your students.
Kids need to be able to have those visuals
and if they don't personally have
those experiences that
they can conjure up,
we need to provide
manipulatives so that they
can create and model the
problem we're talking about
and create those visuals for themselves.
Often this is known as the CRA model.
So, it stands for Concrete
to Representational,
to Abstract.
So let's say, for example, we're
trying to work on addition.
And we're doing eighth plus seven.
You don't just start with eight plus seven
on a piece of paper.
They don't have any
visuals or manipulatives,
anything to connect eight plus seven to.
So any time we're starting
with something new,
we wanna start with concrete,
give them physical things to move, touch,
and model the problem with.
And then we attach a
representation which is often times
a model or a drawing and then
we attach the abstract symbols.
Let's take a look at
what that would look like
with eight plus seven.
I don't wanna jump straight
to just eight plus seven,
so instead, I ask them to
show it on a math rack,
and I might even give it to
them in a story problem format.
I might say something
like a popular context
to use for the math rack is a bunk bed.
It could be something like
Sierra is having a slumber party.
She has, all the girls are
sitting on her bunk bed.
There are seven girls on
the top bunk and there
are eight girls on the bottom bunk.
How many girls are on the bunk bed?
Now the cool part is
that they can model this
with the math rack and
I am actually showing it
with an app just so I
could write on it and kind
of show you the strategies
that kids talk about,
but you could have them actually
have physical math racks.
Those are also known as Rekenreks.
Having them model it
and then the whole idea
is how do you actually figure
out how many are there.
Because even thought we
have eight and seven,
you might have some kiddos
who are sitting there counting
one by one by one by one,
but you might have other
kids who are grouping.
And they would never see this grouping
except because it's in a math rack.
If I just had seven things
in a line and eight things
in a line or in like little piles,
nothing's begging me to
group that information
or those numbers together.
But when we can model it with a math rack,
that really brings out some
groupings and some relationships
that kids can see.
One of the most popular ones that kids see
is the groupings of fives.
They will find the fives.
And so they'll see five and five
and they know five and five make ten,
and then they'll grab
the two and the three.
Now, of course, on a real math rack,
they're not writing the numbers on there.
So it's very concrete.
They're just moving it with their hands,
they're seeing it visually
and grouping things
with the concrete manipulative.
However, we don't want kids to always stay
in that concrete phase.
We really do need to move
them through to the abstract
so that when they see eight plus seven,
they just know what eight plus seven is
or they have a strategy
even when it doesn't
have a visual attached to it.
But in order to get kids
to that strategy point,
we have to create the visuals
that help manifest those strategies.
This whole strategy of
finding five and making a 10
from those fives is an awesome strategy,
but again, it can't be taught.
Kids have to catch that
strategy and they're gonna catch
it if we provide manipulatives and visuals
that help them see those groupings.
Once they see those groupings,
then we can help them attach
a representation to it
and that representation,
one of my favorite ways
to do a representation
is using a number path
because kids don't have
to draw all the little rectangles.
The rectangles are already there for them
and they just circle he
amounts that they're seeing.
They're modeling it on the number path.
So that's the representational
phase and then
when we attach the
symbols, the digits to it,
then it's becoming more abstract.
We're typing that concrete
and the visual representation
to the abstract symbols.
Man, when you can do all
three of those things
with your students, it just
makes some awesome connections
for your kiddos that they can't see
if we just jump straight to the abstract.
So any time your kiddos are
needing to learn something
that's new to them or that
they're struggling with,
I highly encourage that you drop back down
and get some concrete
manipulatives for them to work with
and attach it to a representation
and then attach that to the abstract.
All three of those
together will help build
their understanding.
All right, now our last one
is I really want to encourage you
to make building number
sense a daily routine.
If you don't set aside
time every single day,
it's gonna go by the way side.
It will, because the
pressures of what you need
to be teaching, all of those standards,
the next lesson in your textbook,
whatever it is that you're
using as your guide,
that's gonna get in the way
because you're always gonna
be behind and be behind.
It's just the fact of teaching.
But number sense is so
important, you guys.
When we look at our standards and we say
this is the end standard
I need to get kids to,
our standards don't talk about
how we actually get them there.
With all the information and
knowledge kids need to know
in order to do that
standard and number sense
is usually the root of a lot of it.
But it's not built into our textbooks
because it's kind of
assumed that kids know this.
Our textbooks are jumping kids
straight to the final product
and they're not giving
kids enough time to play
and to make connections around numbers.
So if you don't make a concerted effort
to build that into your day,
it's not going to happen.
So whether it's you decide
I'm gonna do story problems,
I'm gonna put things in
context every single day,
or maybe, we're gonna
do some manipulatives
and working with concrete
stuff every single day.
Just make a time where that's gonna be it.
And you guys, it does not have
to be during your math time.
The cool part of developing
some kind of routine
is that you want it to be
a short thing that you do,
five, 10 minutes.
Whatever the concept is
that you wanna work on,
make it be short and it can
be part of your math time
or it could be, as you're
looking at your schedule
and you're okay, we finished
math here or we finished,
even reading, and now
we have to go to lunch.
But I've got five minutes.
That's the time where I'm always gonna
do our number sense routine.
It can be the things that I mentioned here
or I'm also going to
highly recommend the book,
Number Sense Routines by Jessica Shumway.
There is one that's for the early grades
and then there is one
for third through fifth.
You guys want the early grades,
so I will link to that below this video,
but it is one of my favorites.
It talks about some of the
stuff I talk about here
but gives you other specific routines
like counting circles and dot patterns
and things like that that you can do.
So it is definitely worth
the cost of the book.
Highly recommend it.
Now, no matter what time of year
you are watching this video,
whether it's the start
of the year, mid-year,
or towards the end of the year,
it is never too late to get started
on building number sense.
You know the old saying of the best time
to plant a tree was 10 years ago,
but the next best time is right now.
Yes, it's wonderful if
you can start your year
off building number sense
but if you're coming
to this video part way through,
the next best time is right now.
Start building your kids number sense.
If you want help with that,
I've got some upcoming webinars,
we've got a full course all
on developing number sense
from pre-K to second
grade that I would love
to have you join in as well.
So if you like that, if
you're interested in that,
be watching for emails from me.
If you're not on my email list,
look up above if you're on the vlog.
Come over to the blog,
there's a spot where you can sign up
to be notified about stuff,
so join my email list.
Another way you can join
my email list is grab
the little freebie that's
down below this video.
I've compiled all of my recommendations
that I just gave you here in this video
in one nice little cheat
sheet that you can print off
and have posted right next to your desk
as you're planning lessons,
wherever you wanna put it as a reminder
of the things that you can be doing
to build number sense so it
doesn't go by the way side.
Number sense is such an
important piece guys.
I really, really hope
that this video has helped
you build your math mind,
especially around number sense,
so you can go build the
math minds of your students.
Have a great day!
