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

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

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

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

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

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

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last few weeks have been a whirlwind.

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

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

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

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you to see it happen in real time.

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This is why I didn't erase it before.

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

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are this was our last session together.

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

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

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

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

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but of the type of cohort that it is.

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

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gonna get lots of Uplevel.

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

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gonna get lots of Uplevel versions of it.

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

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on the cohort group that I'm in.

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

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time from Math Teacher Mastermind.

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

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movement and sensory big deal.

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

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

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Music up here

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and keep that as our non-academic.

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Essentials.

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Essentials.

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

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

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climate and culture for your kids.

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So we don't need to belabor this.

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

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

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

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were like that before you even met me.

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

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So I'm not worried about this.

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

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

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number line and rectangles
and lingering unfinished.

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Okay?

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I am going to get rid of this piece here.

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

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

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

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

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

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rewrite and then erase the pieces again.

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So they get it in real time.

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

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Okay.

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I'm gonna erase

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now.

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I'm gonna leave this hanging for a minute.

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You know they make smart boards for that.

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Yes.

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But something else is on my smart board.

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So yeah.

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

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

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electronically for this type of event.

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Oh gosh.

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

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But yes, Sherry, yes and no.

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

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

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You have to do it this way.

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I know.

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

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No.

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Exactly.

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Exactly.

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Great connection.

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So what do we have left here?

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We have left this music movement sensory.

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I'm leaving that there.

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

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that's gonna be important here.

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

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red also is all about lockers, rectangles,

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pizzas.

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Okay.

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

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All that.

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

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

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

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

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Okay,

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so here's what we have left.

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

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

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

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

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plus five x plus six is the polynomial.

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

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start really mastering exponents.

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And by fifth grade, kids
should have seen unknowns and

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variables for a couple of years.

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

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

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

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

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

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Tell me about what do you see?

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What do you notice?

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Because this is exposure.

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

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

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

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be seeing these types of polynomials.

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But Kathy, tell us how you used this.

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I started out working with a
couple of different groups.

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

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beginning ninth grade algebra.

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

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

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

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

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

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

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

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

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talking about factors of numbers.

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

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and that's a perfect skill for them.

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They find it fun, it's
cognitively challenging.

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They're practicing their
factors and all of that.

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For my older students, my especially
my beginning algebra students

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

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lead to factoring the quadratics.

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

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

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number and it doesn't frustrate 'em.

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

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

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

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

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

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to help you so much in the future.

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And I put that.

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Expression up there.

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

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

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

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with the school that I'm working with.

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They're classified as low learners.

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They were pulling it
out and putting it in.

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And it all started with engagement.

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And we said, I said yes.

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

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

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And it was so fascinating,

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Kathy.

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Beautiful description.

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

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for a while instead of mine.

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

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

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

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

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

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to start doing diamond problems.

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

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

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

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that you can have access to them.

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

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Diamond problems.

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

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showing that you have a diamond.

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

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to write the diamond every time.

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So we just write the
X to show product sum.

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

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Multiply and add.

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And diamond problems are diamond
problems because we've got

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this quote unquote rectangle.

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

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classifying shape, whatever.

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

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just say we have this tilted rectangle.

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Maybe the degrees aren't 90, we whatever.

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Okay, just anyway.

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The point is all of our polynomial
function, quadratic function

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can be done with diamond
problems and with rectangles.

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Lockers, rectangles, pizzas.

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Oh my.

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So once a week kids
need to see rectangles.

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Where do we get this from?

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Go to state release test questions.

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

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Go to grade levels.

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Be below yours and above yours.

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

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

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

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Getting and solving.

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

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

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

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

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that promotes answer, getting and solving.

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

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

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We wanna promote thinking,
reasoning, and sense making.

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

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What do you notice?

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I'm not asking them to solve anything.

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

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

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

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

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

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I don't even have to relate them.

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

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I can do diamonds totally separate.

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

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

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For my second graders.

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I might start with this.

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

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As a matter of fact,

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

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

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

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

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

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00:14:43,329 --> 00:14:47,550
we zoom all the way into early grade
alignment—how second- and third-graders

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00:14:47,550 --> 00:14:52,129
can begin building multiplicative
reasoning, arrays, and fact fluency using

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structures you’ve already seen today.

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

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00:14:58,667 --> 00:15:01,917
And hey—if you’re loving this and
want to get the full workshop where

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00:15:01,917 --> 00:15:05,927
we go step-by-step into the Mastery
Math Method, you can sign up to

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00:15:05,927 --> 00:15:08,907
experience one workshop for just $47.

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00:15:09,507 --> 00:15:10,717
The link is waiting for you.”