We're Teaching MATH Backwards

Hey everybody and welcome to Tier One
Interventions podcast, where we look

at your core classroom and we try to
maximize your gifts and help you reach

every student with their math, with their
writing, and with their reading skills.

But we concentrate mostly on math here
at Tier One Interventions podcast.

And our math leader, miss Jonily, is
ready to share some gold nuggets today.

Welcome to the podcast Jonily, and
they are gold nuggets because these

last few weeks have been a whirlwind.

I'm gonna kinda take us back a little
bit, and there's another community that

I teach called a Math teacher Mastermind,
and I'm going to launch our session today.

now I want you to watch, while I
erase some of this stuff, I want

you to see it happen in real time.

This is why I didn't erase it before.

So if you are a part of Math Teacher
Mastermind, which I think a lot of you

are this was our last session together.

And so what I'm, I wanna make some
connections and then we're gonna extend

beyond Math Teacher Mastermind because
math Teacher Mastermind is we are not

gonna do in Math Teacher Mastermind, some
of these things that we do in level two.

Every group that I teach at the level
of that cohort, not of the people,

but of the type of cohort that it is.

So Saturday maths, on Saturday
maths, you're never really

gonna get lots of Uplevel.

You're gonna get, you're gonna hear
things differently, but you're never

gonna get lots of Uplevel versions of it.

I'm very deliberate and intentional about
the content that I release, depending

on the cohort group that I'm in.

So what I'm gonna do is you're gonna
watch me erase some of this in real

time from Math Teacher Mastermind.

What's really cool is I wasn't
even gonna connect this, but

movement and sensory big deal.

But I'm gonna add to that here on our
chart, and I'm not gonna erase movement

and sensory, but I'm gonna add to that.

Music up here

and keep that as our non-academic.

Essentials.

Essentials.

Now, I'm gonna erase all the
climate culture stuff because I

believe that this group that is
here, your experts in creating this

climate and culture for your kids.

So we don't need to belabor this.

If I walked into any of your math
classrooms right now, there would be

a feel and a buzz and a Jay-Z Nest.

That would be really beautiful because
that's who, because you, many of you

were like that before you even met me.

And so now we just add those extra
flares and we're growing together.

So I'm not worried about this.

I'm gonna erase this for our tier one
interventions, level two math teacher dah.

I am gonna erase the movement from
there, but I am going to keep the

number line and rectangles
and lingering unfinished.

Okay?

I am going to get rid of this piece here.

See, this wouldn't have been,
this wouldn't have been as

powerful if I would've erased
these parts without you watching.

And I will do this in my classroom also,
I will have the custodian know, don't

erase those boards, because what I'm
gonna do tomorrow is I'm just gonna erase

pieces of them in front of my students
and then for my next class I have to

rewrite and then erase the pieces again.

So they get it in real time.

But anyway, I'm not complaining
about the extra work.

Okay.

I'm gonna erase

now.

I'm gonna leave this hanging for a minute.

You know they make smart boards for that.

Yes.

But something else is on my smart board.

So yeah.

So I actually have seven full-sized
dry erase boards in my room.

And I'd rather have that than doing it on
smart board and customizing it per class

electronically for this type of event.

Oh gosh.

That's a, that, that's
a whole nother podcast.

But yes, Sherry, yes and no.

Okay, so I'm also gonna erase this 'cause
I'm gonna give myself some board space.

It's just like you saying that
you can't do a PowerPoint anymore.

You have to do it this way.

I know.

It's where I am all about
the PowerPoint I Exactly.

No.

Exactly.

Exactly.

Great connection.

So what do we have left here?

We have left this music movement sensory.

I'm leaving that there.

I was gonna erase all that, but
because of our conversation, I think

that's gonna be important here.

This is absolutely essential because today
is all about, and I'm gonna write this in

red also is all about lockers, rectangles,

pizzas.

Okay.

I also, I'm leaving this, which is
funny, I wasn't gonna teach on that.

All that.

All the linear and then the
interleaving and the out of, I've

used a lot of examples of this and
I forgot this was even written here.

Like in all honesty, I totally forgot
and I wasn't even gonna teach on that.

So I'm gonna leave that here 'cause
I'm proud of myself is what I'm saying.

Okay,

so here's what we have left.

And Kathy, I remember you saying you
just used this when I wrote that.

Not to put you on the spot, and if you
don't have anything to say, that's fine.

But could you tell us about
that and how you used it?

And for those that are listening and
maybe don't have the visual x squared

plus five x plus six is the polynomial.

And let me just remind you that
in fifth grade, kids need to

start really mastering exponents.

And by fifth grade, kids
should have seen unknowns and

variables for a couple of years.

So the first time in the standards,
it says to represent unknowns using

a different, using different symbols
In first grade is the first time in

the content standards it says that,
see, we're missing all this stuff.

So if you're a third, fourth grade
teacher, you can show x squared plus

five x plus six to your students,
and then use our famous prompts.

Tell me about what do you see?

What do you notice?

Because this is exposure.

It's random acts of math, it's
interleaving, it's exposure over mastery.

So this is perfectly, actually,
not even perfectly, okay.

It's necessary for third, fourth grade,
but definitely in fifth grade, kids should

be seeing these types of polynomials.

But Kathy, tell us how you used this.

I started out working with a
couple of different groups.

One group is a low sixth grade
group and another group is

beginning ninth grade algebra.

So I started both groups working with
diamond numbers and where the vision in

your mind, an X and in the top most part
of the X is what numbers you, you put a

number in there for a product of a number,
and in the bottom portion of the X, you

put in what the same two numbers are
gonna add to, which leads to, obviously

for those who are teaching secondary
math, it leads to what two numbers add

to a certain number and the same two
numbers multiplied to a certain number.

Now for my younger students, my fifth
and sixth graders that I'm working with.

For them, it's practicing their
multiplication facts where we're

talking about factors of numbers.

So they, because at that age they're
getting factors in multiples mixed up

and that's a perfect skill for them.

They find it fun, it's
cognitively challenging.

They're practicing their
factors and all of that.

For my older students, my especially
my beginning algebra students

that I'm working with, it's really
good for them because it's gonna

lead to factoring the quadratics.

And so I do show them I was working
with usually when I start out I

start with lower numbers because
it's easier to start with a lower

number and it doesn't frustrate 'em.

And they experience success and feel
really confident about their math ability.

And so I did that one where,
what two numbers add to five.

So five would've been in the bottom
of the diamond and multiply to six.

And it was interesting because they
started coming up with different ones

and all of a sudden two and three came
through and I said, and this is going

to help you so much in the future.

And I put that.

Expression up there.

And then all of a sudden the everything
started like falling out of their mouths.

Like saying, oh, if we take one of those
numbers and we put it in for X and then we

square it and this, these were my fi fifth
and sixth graders and they're classified

with the school that I'm working with.

They're classified as low learners.

They were pulling it
out and putting it in.

And it all started with engagement.

And we said, I said yes.

And I said, do you know
that this is algebra one?

You guys are, and they're
like, lighting up.

And it was so fascinating,

Kathy.

Beautiful description.

It was so much better for some,
for all of us to hear your voice

for a while instead of mine.

'cause that's exactly you said
exactly what I was gonna say.

So if you are not doing diamond
problems in your classroom, Amy,

this would, you'd probably be
the only exception to the rule.

Amy is a first grade teacher, but if
you are not doing diamond problems

in your classroom and you teach
third grade and beyond, you need

to start doing diamond problems.

And this is deliberately, intentionally
what I was gonna share today.

And I actually have a resource,
I have two resources for you PDFs

that I'm gonna share, and then we'll
get them where they need to be so

that you can have access to them.

I'm gonna show you when I share
my screen in just a moment.

Diamond problems.

The reason you write an X is because
it's just a shorthand version for

showing that you have a diamond.

And I did the outline of the diamond,
but it's just a lot more work

to write the diamond every time.

So we just write the
X to show product sum.

And the two numbers on the
sides are the two numbers.

Multiply and add.

And diamond problems are diamond
problems because we've got

this quote unquote rectangle.

I know when we talk about diamonds
and parallelograms and now we're

classifying shape, whatever.

Don't worry about the classification
when we say diamond problems, let's

just say we have this tilted rectangle.

Maybe the degrees aren't 90, we whatever.

Okay, just anyway.

The point is all of our polynomial
function, quadratic function

can be done with diamond
problems and with rectangles.

Lockers, rectangles, pizzas.

Oh my.

So once a week kids
need to see rectangles.

Where do we get this from?

Go to state release test questions.

Go to state release test questions for
your grade level and other grade levels.

Go to grade levels.

Be below yours and above yours.

Best place to find good rectangles is
go to state release test questions.

Take a picture of whatever the
rectangle is, remove the noise, what

that means, not the noise we hear,
but the noise that prompts answer.

Getting and solving.

We don't want to force answer getting
and solving on the release test question.

We wanna get rid of the promotion of
answer, getting and solving, and we

just wanna show the rectangle piece
with the numbers or the whatever in any

information that the students need, but
get rid of the question and the prompt

that promotes answer, getting and solving.

Because when we want kids to swim
in the mathematics, especially at

higher grade levels, we don't wanna
promote answer, getting and solving.

We wanna promote thinking,
reasoning, and sense making.

So when I give this polynomial
and I'm like, what do you see?

What do you notice?

I'm not asking them to solve anything.

So we're just exposing this notation in
math and asking them what they think.

Then if we're doing diamond
problems out of context, and I'm

gonna show you some, I'm gonna, I'm
gonna share my screen in a minute.

If we're doing this separately out of
context, there will be times where we

can relate these, but I don't even have
to relate them as a non-algebra teacher.

I don't even have to relate them.

I should, and I can, but
I don't even have to.

I can do diamonds totally separate.

Now, there are different levels of
diamond problems and I'm gonna give

you a resource in a moment, but for
kids in my, for my second graders.

For my second graders.

I might start with this.

Now, this is totally
related to what I just said.

As a matter of fact,

I am planning this out loud
right now in real time.

When I go to second grade next week,
I'm going to do this because for

my second graders, I would start
with the numbers on the sides.

“Okay teacher friends, that concludes
today’s look at rectangles, x-models,

early variable exposure, and the
power of diamond problems. Next week,

we zoom all the way into early grade
alignment—how second- and third-graders

can begin building multiplicative
reasoning, arrays, and fact fluency using

structures you’ve already seen today.

This next episode will blow your
mind with how simple it can be.

And hey—if you’re loving this and
want to get the full workshop where

we go step-by-step into the Mastery
Math Method, you can sign up to

experience one workshop for just $47.

The link is waiting for you.”