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.
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.
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.”