- Hey everybody, Christina Tondevold here,
I was just checking to make sure the live stream
was working.
Been a while since I've done one of these things,
but I got a request to do a short video
about what Number Sense is,
and why it's so important,
because I have some long videos,
but this one's gonna be short.
So, first thing, is I get a lot of questions
and concerns really,
about students' lack of number sense.
And it is a huge concern,
and I'm not saying it's not,
but the hard part is,
is we have to make sure that we define Number Sense
in order to really know what they're lacking.
So in today's video, that's what this is all about,
is what is it?
And why is it so important?
So, I am going to switch over, hopefully here,
if I can figure this out,
I'm gonna switch over
to my screen, and share a few things
with you that way.
So...
Let me see here.
This is always fun doing it live.
Okay.
So, we're gonna talk about
what it is, and why it is so essential
for our students.
So this is the most quoted quote about Number Sense
from Howden, and she says,
the part that I love about this, that she says,
is that "it develops gradually
as a result of exploring numbers,
visualizing them ... and relating them."
And to me that is what Number Sense
really is all about.
I've said it a ton of times,
but if you've never heard this,
I'm gonna repeat it again.
Number Sense can't be taught, it is caught.
Our kiddos develop their Number Sense
through the experiences that they have.
That's why we,
unfortunately I guess, we have kids coming in
to kindergarten with vastly different Number Sense
because they've had vastly different experiences.
We've had some kids who've gone to preschool for
two years, and maybe have a parent like me,
who does a lot of experiences for them.
And then we've got kiddos who come in
with no experiences.
And it's not that they don't understand numbers,
they just haven't had experiences with them.
And it's nothing against parents or anything, but we,
if I didn't have the job that I have,
I wouldn't know what to do.
You can get a lot of info about what to do for reading,
but for Number Sense there's not a whole lot out there.
So what actually is Number Sense?
And in this quote, she says
that it's a good intuition about numbers,
and their relationships,
and every time that I've seen that quote,
it has bugged me.
I do not like that part of the quote,
because it doesn't tell me what to do,
how do I teach that?
And so it wasn't until I saw John Van de Walle's work,
and his colleagues,
in teaching student-centered mathematics
that I really found what I feel like is
what Number Sense truly is,
something tangible that I can take
and do with my kiddos.
So they talk about four relationships
that kids need to have
to develop their sense of numbers, so,
here's the first one.
First one is spatial relationships.
This goes along with subitizing, subitizing,
however you say it,
but it's having a visual to go with a numeral.
But it's not just having those visuals,
but talking about how they relate.
So I can have that visual of three,
and I can have that visual of four,
but really, what does that tell me
about three and about four,
what kind of relationships can be built
once we have those visual pictures?
Because if I could just have the digit three
and the digit four,
it doesn't build hardly anything for me as a kiddo
about what three and four are.
But these visuals do.
So giving kids those visuals to go with the number
is the first place to start.
Then, once you have those visuals,
you can move into the next three.
The second one that they talk about
is that kids need to know instantly
what is one and two more and less.
If I just, again, if I just give a digit six,
and ask the kids what's one more,
just knowing that seven, the digit seven is next,
doesn't really tell me much about it.
But if I have a visual like this MathRack,
the top one is showing six,
the bottom one is showing seven,
that helps me understand better
about six and seven, and how it is one less,
and one more than each other.
The third one is the benchmarks of five and 10.
So taking that visual idea,
we want to have visuals,
but the visuals matter.
So I could have a string of nine things,
and say that's a visual representation of nine, it is.
But it doesn't help me develop what nine really is
in relationship to other things.
And the benchmarks of five and 10 are really, really huge.
So taking those nine things,
putting them into the 10 frame,
helps develop how nine relates to five,
and how it relates to 10,
along with seeing that it's nine individual things,
we get to develop the relationship.
The last one is being able to understand
that a whole can be broken into parts,
and that parts come together to make a whole.
So, I know textbooks do a great job
of having us break all of these apart,
we do lots of activities with number bonds,
and whatever else you may call them,
but being able to show all the parts that make the whole.
We'll do that with the numerals,
but we also want to do them with the visuals,
to help kids have the visual aspect,
but it's also really important to spend time talking
about not just what are all the ways
you can break apart seven,
but when would you break seven
into a one and a six versus a two and a five?
What's the point of being able to break that apart?
Now, here's my spiel a little bit
about why it's important.
Because we have all of these standards
being thrown at us,
and this is just a sampling
of some of the standards that are out there, but really
it's not about focusing on that standard.
If you focus on developing sense for your students,
all of these standards become so much easier to do.
Okay, so let's look at a really quick example.
Let's say I want to do 9 plus 7,
and I can just have kids memorize 9 plus 7,
no big deal.
But, if we spend time developing relationships,
and we have visuals to go along with 9 plus 7,
and some kids are starting to develop that,
"wow, 9 plus 7 is really like having 10 plus 6,
I can take one, and give it,
and fill the 10 frame,"
like if they have that visual in their mind,
"I can fill the 10 frame,
and then I just have 6 left over."
That's awesome!
And it seems like,
like, that takes a lot of time,
I could just memorize it.
But the power of building Number Sense
is that it lasts beyond just like facts like this,
and let's say we move into problems like this,
where we have to add and subtract
and become fluent within a thousand.
Well, doing this problem,
yes, I could stack it,
do the traditional algorithm, but man!
This problem would be so much nicer
if I could just move one over,
and create 300,
and then all I've got 300 and 356.
That problem is way nicer than stacking it.
And so having that Number Sense really isn't
even just for whole numbers.
As kids start to move into decimals,
doing a problem like this
becomes so much nicer, right?
We all hate decimals and fractions.
But think about how much nicer this problem can be
when we think, "Ah!
I get that benchmark of the whole number,
the benchmark of 4,
I just gotta bring 0.01 over.
Now I have 4, and 0.16, right there in front of me."
And the dreaded fractions,
and I know, sorry about my formatting here,
it's hard to get fractions
into a PowerPoint, but,
if I have 3 1/2 plus 5 3/4,
how can I make one of those nicer?
How could I make it friendlier?
Being able to build these relationships for kids
isn't just about the strategies,
it's about developing relationships
that kids can see and notice and use
on all types of problems.
So those four Number Sense relationships
are the real key ones that I want you
to be developing.
And get the spatial relationships going in your classroom,
get one and two more and less,
which then moves into 10 more and less,
100 more and less,
then the benchmarks of five and 10,
and when you're doing fractions and decimals,
those benchmarks become the whole numbers, and the halves.
Those become benchmark numbers,
and part part whole,
being able to break numbers apart,
and know when to break them apart,
is an essential piece of that.
If we can develop those things for our kids,
it makes all of the other standards so much easier.
I know it's hard to slow down
and spend some time focusing on Number Sense,
but if you do, you could actually speed up
through a whole lot more of the standards,
and your curriculum,
because kids will get it a whole lot faster,
instead of taking a lesson,
and having to spend three or four days on it,
because it's not clicking with the kids,
if we can slow down and take the time
to develop their Number Sense,
then the standards that we need to be addressing this year
become a whole lot easier.
Now, I know this was a very quick overview,
but that's what I was asked to do,
so it's a quick overview of what Number Sense is.
But I have a free eBook that you can download
that goes a little bit more into detail
about those four Number Sense relationships,
and also has an assessment.
Now, I'll forewarn you,
this assessment is for pre-K to second grade.
I don't have it built for the fractions
and decimals piece.
But for whole numbers,
being able to assess and figure out
which of those four areas your kiddos
are not as developed in yet,
is a great piece to be able to start off the school year.
So you can find that by going to
buildmathminds.com/numbersense,
no space in between, "numbersense" is all one word.
So, I hope that this has helped you build
some, your math mind,
so that you can go build the math minds of your students.
Have a great day.
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