The Math Education Shift Teachers Need

Unknown: Research on the what's
going on out there, and then

bringing that to you as well as,
of course, my opinion, every

month. So that is a big purpose,
just to be able to the to

gather, network, collaborate, be
with like minded people. And so

here we are, right here, feel
free to use the chat to talk to

each other, which is really one
of the benefits of being here

today. You can, in a moment,
we'll see where people are from

and what grade levels you teach.
But the other main purpose of

Saturday math, and this has
always been the case in the

eight years that we've done
Saturday math is the bottom

line. If students have number
sense, we can take off with

whatever initiative and
resources are thrown at us. So

the overall goal that has always
been on Saturday, math is

improving. Number Sense, that is
our foundation. So I'm going to

put number sense here. There's a
secondary goal. And over the

last couple of months, we've
launched an initiative called

math testing secrets that we
have an entire course for now

that we're very, very proud of,
but in that testing secrets, we

say that there are two barriers
to increasing test scores. And

the barriers are students having
a lack of number sense, but also

a lack of notation. And there
are some of my favorite

notations that have scaled
student achievement that we use,

that are not explicitly stated
in the standards, but are very

much related to the standards.
Some of you can probably guess

one of my favorite notations.
Should I have you? Guess I

should have you. Guess what's
one of my favorite notations

that relates to a task that is
the utmost of importance for

understanding numbers and having
number sense and improving

number sense? Natalie, of course
you have you are always

transplanted here to give us the
exact answer notation of square

root. We have no idea how
essential notation of square

root is. That's the one I'm
going to land on today. There

are other notations that are
absolutely essential, because

part of what is the difference
between a student passing an end

of year math test and almost
passing an end of year math

test, most often, is the
notation that is used and the

lack of understanding of that
notation. Now I'm coming out of

the gate talking a lot about
testing as if like testing is

the be all, end all. Well, no,
it's not. If you all know me,

you know it's not. But we want
our cake, and we want to be able

to eat it too. So I want kids to
have great, rich, complex,

accessible math experiences in
the classroom on a daily basis.

That's what I advocate for. I
empower teachers to create these

experiences for students,
because I cannot personally

create these experiences for
every student out there in

United States, but with your
help, I can do that. So my main

goal and mission and vision is
to empower and inspire teachers

and teach teachers how to create
these rich, complex, accessible

math experiences that target all
students, and especially

students that struggle and
students with disabilities.

Having said that, if we're going
to do that in an effective way,

the test scores should show it
so and I mean, that's what we're

judged on. We're judged on the
test scores. So why not have a

goal of these kids can, and I
know these kids can, because if

any of you know me, you know
that we have taken cohorts of

students from 27% passing one
year to the next year 65%

passing. We've taken cohorts
from 65% passing to 86% passing.

We've taken cohorts of students
from exhibiting bell curve

results, meaning bell curve,
this is 50th percentile. So

average is 50th really from 40th
to 60th percentile on bell curve

on a true standardized test. Now
I have to get on my soapbox for

just a minute.

So. We have for years, even from
the time that I was in school,

we've used very high rated,
credible standardized testing

companies that this is all they
do. And I'm going to give two

examples of those, the Iowa
battery and the Terra Nova.

Okay, I don't know if you have
heard of those, or know those,

or whatever. Those are true
standardized tests. They're

they're competitive companies.
They're two different companies.

But the Iowa and Terra Nova, I
have an immense amount of

respect for an immense amount of
respect, the same amount of

respect I have for the A C T and
S A T, again, a c t and s a t2,

totally different companies, two
totally different platforms,

competing interests, whatever.
But it's always good to have

both. And I don't have, you
know, a preference one way or

another. I think we can use both
of them to our advantage. But

the Iowa and Terra Nova used to
be the be all, end all, a

district would pick one of them,
and either every year or every

three years or every other year,
students would take this

standardized test. And the
reason that I loved how

standardized it was is it is
national, like it didn't matter

if you were in Pennsylvania or
Arizona or whatever it was,

usually one of those two
options. And what the Iowa and

Terra Nova did was, yes, it gave
you an achievement percentile,

not a percent, not a passing.
There's no passing. It gave you,

it gave students a score based
on percentile for achievement.

So there were subject
achievement, pieces of it, and

if students scored anywhere
between the 40th and 60th

percentile, spot on average,
spot on average, fantastic,

which is why. And I'll just give
you an example from the state of

Ohio, which is why in reading.
Now we have what are called

rimps in reading, their
individual plans for reading,

even if kids that are not
special ed, not on IEP, but

school districts were able to
pick and choose what what

percentile ranking was the
maximum for students that have

deficits. Too many school
districts picked 40/40

percentile. The problem is 40 is
right at the bottom of average.

So we're doing a lot of extra
work for these kids. And what

was happening in schools? What
is happening in schools is some

of those kids that are like 32nd
to 40th percentile, we're

creating these plans for them,
but they have been passing their

reading on the state test. So
there's this disconnect. The

reason is, I believe we've gone
down a very, very skewed road

for data. So I just want to
enlighten us this morning on

what data we're using and how
we're using data, and how the

data has shifted to become much
more ineffective in recent

years. So Iowa, TerraNova, I the
results of these things used to

be outstanding, spot on for
kids. Okay, now the reason I

bring this up is I'm trying to
show you in cohorts that have

used the model that we present
in all of our sessions, is we've

been able to scale exponentially
the achievement of students, not

just their achievement, but
their test score results. So

when we look at percentile
rankings, when we were using

Iowa TerraNova, we had a cohort
of students that no one in this

certain cohort scored below the
70th percentile. I mean, we

literally broke the bell curve
with one of our cohorts.

Absolutely crazy. The other
thing I want to say about Iowa

and Terra Nova is a really
important piece of them was the

cognitive ability test. So you
would get a cognitive ability

students would get a cognitive
ability score, which was like,

IQ score, okay, and on that
cognitive ability score, 100

spot on average, but really
average went from 90 to 110

and this cognitive ability score
scoring high enough. Staff would

accurately determine gifted
brains and accurately determine

students, you know, our 70s kids
that had severe brain

disconnects, and this is what
we've used forever and ever and

ever now. Okay, so let me make
two points on this. One point on

this is we have scaled math
achievement using part of what

I'm going to tell you today,
because going back, I'm talking

about the big overarching
purpose of Saturday, math is

improving number sense. We know
that with testing, we want to

improve notation sense, and I
just want to show you some of

the things that we've been able
to do, because a big purpose of

Saturday math is to empower and
inspire us to go back and when

we know better, we do better, so
that we can all be equipped to

scale math achievement in these
same ways. So I wanted to share

some of that data with you. So
that's one piece. Is the purpose

of Saturday math, and it really
starts with number sense, but

dwindles down to these other
things. And since we're in

testing season, I want to bring
bring those things to light.

Now, here's the other point. I
wasn't even going to talk about

this today. I think I've been
really fired up about it. I was

going to jump right into our
content. Remember, I said that

we're going to, well, I mean, I
kind of did, but now I'm

derailed. I'm just totally
derailed because I don't know if

any of you have seen some of the
news media about I ready, so I'm

not going to go into that
deeply, but what I am going to

say about this is, over the
years, we have states not we

states have disapproved some of
our testing entities and

disapproved some of our textbook
companies and disapproved and

disapproved and disapproved, and
for some of us, things that were

working very well for us, and
then re approved, created a re

approval list of some things
that I think are just pure

trash. Now I say that and you're
like, Okay, where's your data?

Let me go back to sort of this
is not necessarily Saturday

math, but one of the biggest
overarching leads for scaling

math achievement, and that is
shifting, shifting. And we

started to make this shift in
about the I'm going to say 20,

2015 2016 2017 then I think we
were moving in the right

direction. Covid came, and then
everything went out the window.

I don't even know what happened
with decision makers like I

don't know if, if they're
desperate or if I don't even

know, but what we have been
moving toward ever since minds

on math started this mission in
2011 what we have been moving

toward is shifting math
instruction to exactly how the

brain learns and decision makers
and states are saying they're

doing this through the science
of reading, which there's a lot

of merit to the science of
reading. I I'm not a literacy

expert. I'm not an expert there,
but here's where our downfall is

going to happen, and this is,
this is my prediction, and this

is what's going to and this is
why I want you all to be

educated on this before it comes
in and and takes over and swoops

in. The science of math.
Learning is not parallel to the

science of reading learning.
Reading is a skill that must be

explicitly taught it is not
innate, intuitive inborn, but

number sense is the exact
opposite, that we are born with

a certain level of understanding
of number. Number Sense is

intuitive, ingrained inborn. It
is a natural sense of the

magnitude of numbers, magnitude
meaning how large and small

numbers are.

And so number sense cannot be
explicitly taught, but number

sense can be. Dramatically
improved through experiences. So

I want to catch us and educate
us before some of these shifts

come into place, so we as
educators can be knowledgeable

enough to ask the right
questions based on the correct

current research of how the
brain learns and how the brain

learns certain things. So
notation, notation must be

explicitly taught. Kids aren't
just going to discover what a

square root is. So there,
notation is explicit, very much

parallel to science of reading
number sense is not so when I

share with you on Saturday
sessions How to Improve number

sense, this all falls into a
bigger picture of how the brain

actually learns mathematics, and
there are two different types of

instruction and learning
outcomes. One we call

conceptual, which is the number
sense piece, which students must

experience and figure out on
their own. But we must have

powerful instructional delivery
methods to be able to make that

happen. That's what we focus on,
on Saturday, math. And then

there are procedural,
algorithmic math ability,

notation, instructional delivery
methods that are very

traditional, okay, so we need
both, but these are competing

interests, because the more
procedure and algorithm based we

are in our classrooms, the less
this conceptual can improve. But

the more and more and more we
work to improve the conceptual,

the notation declines. So what
we do in all of our programs is

find that right teeter totter
balance of being able to improve

both because they are competing
interests and they do require a

different instructional
delivery. Wasn't going to go

into all that today, but I'm
glad that I did, because now we

have it all pieced in in one
section here. My purpose of

saying all that, though, was to
talk about the purpose of

Saturday math, and it's always
been to improve number sense,

and that's exactly what we're
going to be doing today as well.

Alright, before I move on,
though, that was, that was a lot

a lot. Whoo, that was a lot, a
lot. Okay, unmute, if you have

other thoughts, questions,
comments, etc. And I'll review

the chat, because I know some of
you have been chatting in the

chatting.

Well, I had in the chat a neat
story from an experience with my

kids this week. Please. Yes, it
actually goes along with

everything, how the brain learns
number, sense and notation were

an absolute value. And so they
were working on their lesson of

the day, and they were comparing
some absolute values. And it was

absolute value of negative 24
compared to absolute value of

positive 24 greater than, less
than or equal. So I'm walking

around the room and observing,
you know what they're writing.

And so many, of course, said the
absolute value of positive 24

was greater. And I knew you know
exactly what they were thinking.

But because, you know, I've been
with Jonily for so long, I just

each kid I touch base with, I
either said something like, Tell

me about that. Or, how did you
get that answer? Or tell me how

you know that's true something
to that effect, and they know

enough that they don't assume
they're wrong when I say

something like that. I just want
to know how they got there. So

they all just launch into the
explanation, and every single

one of them goes, Oh, they're
equal every single kid, every

time. So I did this across both
of my classes that day, probably

in total, 16 to 20 kids that
had, you know, the wrong answer.

But when I stopped them and
paused them and didn't say, Oh,

you're wrong. How would you fix
that? But how did you get that?

Tell me about that, they
launched into their explanation.

They all self corrected the
answer. And it really got me

thinking about, like, state
testing in two weeks. I was

like, you guys, you all knew the
answer. You all knew it. I

didn't even I didn't say
anything. But how did you know,

tell me about that? What did you
think about that? And you all

got the right answer. So my
like, takeaway and message to

them was like, you know more
math than you think you do, we

have to slow because we've been
talking a lot about taking your

time on the test and like, it's
not taking time for the sake of

taking time. But I was like, I
want you to slow down your

brain. Have my voice in your
head if you need to prompt

yourself to say, How do I know?
Or how did I get that answer?

Like, take your gut reaction.
Like. Course, 24 is bigger, but

take that gut reaction and
really evaluate the problem, and

you'll they're they self
corrected. But I'm like, what if

they did that five times? That's
like, a whole level on a test,

five questions where your gut
answer, and then you stop and

think about it. So I'm like,
That's the brain science. I

think, like, stop and think
about it. And they know so much,

but they just have to, so I'm
trying to get my voice in their

head, which is weird, but it was
just a really neat experience.

Like 16 to 20 kids, literally.
And they all, Oh, they're equal.

I'm like, okay, so what a time,
you

know, but I have to give a good
background on our friend,

Natalie, Krista, Amy, Sarah
Neal, that's here Kirk. Where is

Kirk today? Oh, man, I really
needed Kirk here today. It's

okay. So I want to share with
all of you. And then we have, we

have Lisa, Sarah W we have
Daphne, we have Janet. We have

so the reason I'm naming these
names is this doesn't just

happen like especially by coming
to Saturday maths. So we have it

minds on math, a math teacher
mastermind group, which these

names that I've mentioned are
either currently a part of that

or have been a part of it. The
math teacher mastermind group

launches into a math
certification group. So Natalie,

Krista, Amy, Sarah, are all some
of our certified coaches that

have been implementing this for
years, like years Natalie, not

as many years as others, because
Natalie got to be a student

teacher for one of our certified
coaches. So Natalie had an

accelerated learning experience
of this type of implementation.

And the reason that I say all of
this is it doesn't happen with

one Saturday math or one math
teacher mastermind or one

implementation. It takes a good
345, solid years of interacting

with this on Saturday maths, on
math teacher masterminds on June

events, on certification
programs, on, you know, all of

these things that we offer. And
the reason I said April 24 mark

your calendars for April 24 in
the evening. April 24 in the

evening, we are having our next
webinar. And this next webinar

is going to outline a bundle
package of all of our programs

for 2026 2027 so you can get all
of our programs that we're

launching, that we launch every
year in a bundle at a very

discounted rate. I'll send you
information on that webinar. The

registration isn't out yet, but
the reason that I say that is

it's all about interactions over
time. And what I want to say

about Natalie and her group is
it's been about interactions

over time, all year. It's not
just about the February, March

testing season. If she just
started this mindset and culture

in February, there is no way her
kids would have been there. But

this was launched in August,
what we call the first 15 at the

beginning of the school year, so
that kids by this time of year

are ready. They're just ready
for this. And I also want to say

I mentioned a lot of these
names, crystal as well. We had a

big field trip, a teacher field
trip. I wasn't even going to

mention this today, but I have
to, because it was just it was

so powerful, it was so amazing,
it was so enlightening and such

a an impactful experience for me
that I want to share it today

and have a few of you share if
you were on the field trip with

US. So last month in March, we
had a teacher field trip. There

were nine teachers that traveled
to Central Ohio, to my school

district on one day and got to
see my Algebra Two and algebra

one classes. Got to watch me
teach. Then I arranged me

teaching a class at in fourth
grade and second grade at our

elementary school. So all nine
people shadowed me all day,

watched me teach the same exact
task to every class that day.

And so the people that were
there that day, and I don't want

to forget anybody. Natalie West,
Christie Ewing, Amy Garrison,

Christy Flynn, Crystal Davis,
Kirk was there that day. We had

two other people that were there
that day from another school.

They're not here this morning.
We had another Natalie and

Jessica.

I know I'm going to forget
somebody. I don't mean to forget

anybody. It let me know if I'm
forgetting anybody. Anyway, all

of us observed in the morning at
the high school, and then the

afternoon the elementary I
taught all of the classes, and

then we had some reflection time
and thought time, and it was in

March. So I have worked with a
lot of these kids and have

trained a lot of these kids. So
what you were seeing in a lot of

these kids are kids that have
had this model all year, but

came in with some severe
deficits. All of the classes I

teach are inclusion classes, so
there's IEP students in every

class that I teach. I don't have
any advanced classes. I don't

have any advanced so when you
look at these types of scores,

it's just bad. But what we saw
on field trip day is you

wouldn't be able to tell that by
March, and it's really

spectacular to see. Well, then
the next day, Kirk and I got to

go to Natalie West school and
watch Miss Natalie, and then we

got to go to Krista Ewing school
and watch Miss Krista. And I'm

telling you people right now on
record that Natalie and Krista

teach the model better than I
do. You guys, mind blowing. So I

want to give you some
background, especially maybe if

you're here today for the first
time, you don't know any of us.

You don't know any of this. I
want to give you some of those

pieces. But Would anyone like to
share your takeaways from the

field trip experience with us
now, and I'm go back and look at

comments so unmute and let us
know what your takeaways were

from that experience.

Mine was, can you hear me? Yes.
Crystal, crystal. Okay, so my

takeaway was and I shared this
with you or with the group, was

that no matter what grade A
student is in, they can use

their brains to think past just
solving a problem, and you can

take the exact same model and
apply it at every level. And I

thought that was amazing.

And I'm so glad that you all got
to see that that day. And I

think that is more powerful than
just seeing it at the high

school level, or because it's
then you know, what does this

look like in first grade? What
does this look like in seventh

grade? And same task, same
instructional delivery model.

Now I tweak the way that I
interact with kids because of

the grade level, and you you all
got to see those nuances. But

crystal, you said it
beautifully, and I don't think

you can understand it until you
actually see it or hear it. So

if you have not had a chance to
come and observe any of us, or

you all have not had a chance
for me to come and teach it in

your classroom, or the cheapest,
easiest way. If you all have not

had an opportunity to listen to
my audio files of me teaching

these things with students, you
need to make that happen,

because I can tell you all this.
I can I can say all this. I can

tell you. The people on here can
tell you, but that hits

different when you actually hear
it done to students. So it was,

it was just a beautiful
experience those two days. Any

other takeaways from your
experience being in all of those

classrooms?

Krista, yeah, the one thing that
impressed me, particularly with

the high schoolers, because I
I'm sixth grade, they allowed,

like the culture that was built
through the methods that are

being used, they allowed, like
all of these strangers to just

come up and we were asking them
questions, and It didn't throw

them off, and they responded to
us, and that's what and it was

the true of every class that we
went to. We were just kind of

all fanned out, looked at their
work, asked these kids

questions, and they didn't know
us from anybody, and they were

just engaged and willing to
share their thinking with us.

And that kind of culture is
something that you have to build

from day one. And it was just
impressive the way that they

just kind of acclimated to us as
well,

and that is really unique. And I
wasn't sure that that they were

going to be able to perform that
way. These are kids that

struggle. They have high anxiety
for math. They've come with a

lot of baggage from you. You
know, and I'm not trying to

blame but from some ineffective
instructional practices, they've

been jaded, and I don't blame
them. And I want to go back to

what crystal said. It's about
going past the solving because,

as I've said in our testing
secrets launch this year. Let me

take a picture of this so I can
erase it. But going back to

solving. Solving is not
learning. Solving is not

learning. And if my emphasis in
my classroom was solving, Krista

and everybody would not have
been able to experience the math

and hearing that was happening.
So what is the opposite of

solving? It is thinking,
reasoning and sense making. This

is the climate and culture that
is going to scale math

achievement. It's going to
decrease anxiety, it's going to

increase confidence, and it's
going to improve test scores. A

focus on thinking, reasoning and
sense making will always lead to

solving, but we don't have to
push solving. It will happen

organically and naturally. And
that's what Krista is talking

about, that she observed, and I
wasn't sure, like I see it in my

students every day I didn't in
August, September, October, it

was like pulling wisdom teeth in
these classes. Awful. I'm like,

there is no way I'm going to be
able to create this culture with

high school students that I
mean, look at how many years

they have not had these type of
experiences. How am I going to

do this by October, November,
they started to thrive and

really come out of their shell.
So for even me to see my

students very vulnerable and
taking risks in front of nine

adults, math and earring with
them, heck yeah, heck yeah. And

I keep saying math and earring.
If you don't have the making

math and ears book, go to
Amazon. Get it today. Making

math and ears, this is for
teachers and students, improving

the conceptual understanding of
mathematics for the teacher and

the student. Many different case
studies in here of students and

teachers and their journeys and
how they've transformed to

creating these types of
environments and being in these

types of environments, in math
classrooms everywhere. So yeah,

get your book. Go to Amazon, get
your book, making math and ears,

and it's really going to kind of
lay out the foundation of the

difference between this
conceptual and procedural. So

notation goes along with what we
call math ability solving, Okay,

number sense is this conceptual
thinking, reasoning and sense

making? Now, I know what you're
all wondering right now is,

well, shoot, how do we create
this in our classrooms? Saturday

math gives you pieces of that,
but what you really want to do

is go through one of our courses
or programs so that you get that

streamlined effect of what do I
do? First, second, third. But

I'm not saying don't come to
Saturday math, because you're

going to get bits and pieces of
everything Saturday, math is

much more non linear and very
like, you know, interactive,

moving around. This is the big
question that we have been

trying to move in this mission
before we talk about the how,

though, and this is part of the
content I wanted to teach today,

before we talk about the how, we
really have to talk about the

when. And this goes back to
textbook companies. Some of

these new approved, not
improved, but these new approved

textbook companies, the when and
the structure of the year and

how the content is delivered.
And when the content is

delivered is the complete
opposite of how the brain learns

mathematics. So what are some of
our common instructional fails?

Some of our common instructional
fails are teaching one thing at

a time like a textbook is set
up, focusing on solving. That's

another fail,

treating all standards equal,
that's another fail, finishing

everything. We haven't talked
about that yet today, finishing

everything so answering every
question, solving every problem

that is a fail. We've got to let
things linger. One of the

biggest ways that we can improve
math achievement is to let

things linger. Ask questions and
give problems that we don't

finalize, because what. In the
brain is the subconscious

continues to think about that.
There's this cognitive

dissonance that we've never
really tied the bow on. We

believe, we really believe, as a
country and as a culture, that

we have to finish every problem.
And I'm telling you that that is

one of the worst ways to try to
improve math achievement, we

have to let some things linger
so that the subconscious brain

activates and continues to think
reason and sense make without

the human being even knowing
it's happening. And that is

probably the greatest fail of
some of our textbook companies.

So how do we shift some of these
fails into fixes? That is to

look at the when, and I'm going
to show you this on a document

that I created. But before we
even do that, before we even

figure out how to do this, we
have to figure out, okay, when

what's the structure of the
year, and before we even do

that, uh Oh, someone's asking a
question about what curriculum.

Oh no. Oh no. Janet, you're
poking me, aren't you? You're

getting me fired up. Janet, all
right, before all of that, we

have to ask ourselves, What the
What is, what is absolutely

essential, and what is essential
has to be exposed in 15 day

cycles throughout the year. So
Janet, to answer your question,

what curriculum would you
recommend that does go with the

brain research and is approved?
None of them. Now, I'm not

saying that you can't adopt
things. Okay, I'm not saying

because every single textbook
resource, every single

curriculum resource, can be put
in this model, every one of

them, every single one of them,
but we have to be able to be

flexible and adapt how we use
our resources. So these are the

three biggest questions in our
bigger program of delivery, the

what the essentials, the when?
When do the essentials come up

throughout the year, and it's in
cycles of 15 days, and then the

how is in the instructional
delivery process that is going

to have an impact on not only
student achievement, but

confidence and and, yeah. I
mean, amplify fantastic. I love

and hate every curriculum
resource. So I will say amplify

is is very good. Is very good in
its pieces. I think the one

thing that amplify, duh. Doesn't
have, but actually it does, but

it's kind of hidden. Is the what
and the when? I think there's a

lot of great house in amplify
and, yeah, so I'll just go from

there. Okay, you all came to
learn something today, though,

but I'm really glad that I kind
of gave all that foundation,

because I think all of that's
important to continue to empower

us to think differently about
math education. Scores across

the country are dismal. They
keep declining. We've never had

major improvements as a country,
and we keep trying things that

are not only not working, but
are working worse than what

we've done before. Oh boy. Okay.
What a downer. What a downer. I

don't mean to be a downer. Let
me share my screen, because I'm

going to Okay.

So these are the notes that I
created for today that I'm going

to work off of. And when I
follow up email for you, I'm

going to send you the PDF
version of these notes so that

you have these. This is what I
basically just did on the

whiteboard that was intentional.
But when I talk about the what,

the essentials, you know, it
comes down to my F words. Love

me some F words. So many F
words, okay, but the essential

math concepts that are going to
build both of these number sense

and notation are factors,
fraction and function. What do I

mean by that? I don't mean we do
a factors unit, a fraction unit

and a function unit. So what I
mean by this is these are the

three key concepts that should
be a part of every 15 day cycle

we should always be teaching
through factors, through

fraction, through function. And
what Crystal was talking about

is. Is seeing this effect at
every grade level. So if you're

a first grade teacher, Amy
garrison is a first grade

teacher. Amy is constantly
teaching through factors,

fraction and function, even
though the word factor doesn't

necessarily come until fourth
grade in the standards, factors

are making arrays. So if I have
24 blocks and I make an array, I

could make an array that is six
tall, four long or eight tall,

three long. Those numbers are
factors. Kids don't know it, but

making rectangles is one of our
go to experiences for students

that not only improve number
sense but math achievement. So

even as a first grade teacher,
you are teaching through these

three things. So our job as
teachers is to learn what

factors, fraction and function
look like at every single grade

level, and what the progression
is from one grade level to next.

And what we do at minds on math
is, and let me go ahead and draw

this in. What we do at minds on
math is we create reference

tasks. We call them the Dirty
Dozen. There are 12 reference

tasks that associate with
factors fraction and function.

So if you're looking for lessons
in your classroom to do, to

teach through these essential
concepts, we have 12 reference

tasks. The 12 reference tasks
are exactly the same for every

single grade level, exactly the
same. There are some differences

at kindergarten and at algebra
one, depending, you know, very,

very minor differences and
variations. But the reason we

bring everything down into
reference tasks is these are

grab and go like these are not
theory. They're not they're very

practical steps to do lessons in
your classrooms. And they are

not a one and done situation, a
reference task like making

rectangles in first grade looks
like making a raise with 24

blocks and then how tall? How
long are those blocks? What that

looks like in fourth grade are,
what are all the rectangles I

can create? Well, actually go to
third grade. In third grade,

what that looks like is, what
are all the rectangles I can

create with an area of 24 but
different perimeters in fourth

grade? What are all the
rectangles I can create with

area 24 and the up level
question to that is, what are

the factors of 24 because they
are the length and what they are

the dimensions of the rectangles
I can create. See, we're using

that same task, and we're
targeting our standards, but

what we're doing is we're front
loading this progression,

because as early as first grade,
kids are learning about factors.

One of our other tasks is a
locker problem. This is an act

it out hands on, concrete,
conceptual situation that kids

experience, that even at first
grade, they start to learn the

factors of a number. But we
don't call it factors of a

number. We call it which
students touch. Locker, 24, oh,

student eight, does, three,
does, four, does, six does.

Through these reference and
these reference tasks are not

one and done. So when I talk
about these 15 day cycles, some

of these reference tasks come
back every 15 days, and then we

up level them. So kids are
getting interactions over time.

They're getting more
interactions with the same thing

at more grade levels through
these reference tasks, targeting

factors, fraction and function.

So that's sort of the framework,
and it answers the what. Now

there are other pieces in this
what, but it just comes down to

those three things, factors,
fraction and function. If you

study the College Board, College
Board is a c t or not. I totally

said that wrong, totally so I'm
ridiculous. Got a c t on the

brain. College Board is not a C
T. College Board s, a T. If you

study that, there was a
published book called math

vertical teams. Oh my gosh, way,
way back in the early 2000s I

believe in this book that the
College Board published. College

Board is the S, A, T people. In
the book math vertical teams

that the College Board
published, they said there are

three things for students to be
successful in AP Calculus, and

it is rate function and
accumulation that very much

relates to factors fraction and
function. If you study what

algebra, two teachers say that
students need to be successful.

They. Say radicals, that's
factors. They say equations,

that's function, or systems of
equations that's function. They

say graphing, which is number,
line, factors and fraction. They

so everything that we are
reading or studying or hearing

about high school to higher ed
comes down to these same things.

And if you study math tests, A,
C, T, S, A, T, end of course,

exams, grade level tests at each
state you study the national

tests, nape, look at the Tims
report, study GRE, I've been

studying as fab, so the the test
that kids have to take, going

into the army, going into the
service. So I've learned more

about asfab This year, because I
teach high school students, and

I have some students that need
to pass the math. And so I've

been creating these it's all the
same. It's all the same themes.

It all comes down to the same
things. So no matter what

textbook you adopt, no matter
what how the curriculum changes,

no matter how the standards
change, there are certain

mathematics that are ingrained
in the foundation that are

priceless and timeless, they're
never going to change, and

that's what we based all of our
programs off of. So no matter

what comes and goes, no matter
what's approved or disapproved,

these certain essentials are
always going to be there, no

matter what. If everything's
important, nothing's important.

Nothing's important, and we have
defined what is absolutely

important. Now I'm not today
going to talk about the when I

set it up, to talk about this
today, which is, how do we

structure our school year? How
do we separate it, and how do

these 15 day cycles occur? I'm
not going to teach on that today

unless we have some time at the
end. Because here's what I want

to teach on today. I want to
teach on a practical example of

everything that I've just talked
about, and that is this

equation. This equation. It I
pulled it right off of our state

test for algebra one. Pulled it
right off our state test for

algebra one. None of my students
last week, when I gave this on a

practice test, none of my
students got the correct answer.

And these are my students that
have been ingrained in this

model all year. So this is
concerning. So what do we do

about it? That's what I want to
answer right now. What do we do

about it? Well, I didn't start
these equations early enough

this year. We have another task
called Jesse and Kay. I started

Jesse and Kay much earlier in
the year. I did not do enough

fractional pieces for Jesse and
Kay. Now, if you guys don't know

what I'm talking about for Jesse
and Kay, don't worry about that.

Just ignore what I just said. If
you know Jesse and Kay, just

know that I made the mistake. I
did not do enough fractional

examples or variations of Jesse
and Kay, and I'm seeing that

now. So live and learn. So I
want us to look at this

equation, whether you know Jesse
and Kay or not, whether you know

quick dots or not, whether you
know that counting is essential

or not. It doesn't matter what
you know or don't know about

this equation. I want you in the
chat right now to do two things.

I want you to type in what grade
levels you connect with, what

grade levels you connect with,
and what you see and notice

about this equation. So you're
going to do two things right

now. In the chat, I want you to
type in what grade levels you

connect with, so what grade
levels you teach or coach or

whatever, or you know, if you're
a principal or curriculum

person, what grade levels you're
in charge of, and what you see

and notice about this equation.

What can you tell me about? Tell
me about this equation, and what

do you see and notice?

Okay, let me look at the chat
here.

Lot of fifth grade teachers.
Hey, I know why you're here.

Hey, the fifth grade test
everywhere, the hardest one I'm

telling you. You guys know this.
There's reasons why the fifth

grade test is most difficult for
students, and we have solutions

on how to fix that too. You a
good this is excellent. Oh,

okay, one half and 1/4 Yeah,
there are two x's. There's an X

on each side. We see variables,
fractions, lots of operations,

hidden symbols, notes, oh my
gosh. You see why kids struggle

with coefficients. Yeah, you've
got to have the ability to work

with fractions. I mean, kids are
going to look at this on the

test and be like, nope, skip
next question. Just because

there's a fraction, there are
constants and variables unlike

denominators. Yeah. Amy, really
good point you would, you would

cover up those x's with smiley
face emojis, yep, and just say

the these are the the numbers we
got to try to figure out, Yep,

perfect constants and
coefficients. The, yeah, the mix

number, the mix number. That was
weird for me, too. And then I

went back to previous years test
release questions, and I'm like,

there's a few of these with the
mixed number in it. There's a

lot of these in fifth grade. Lot
of these in fifth grade. Yeah,

the x being the X being a
multiplication symbol, and not a

bit having no concept that it's
an unknown. Yep, yep. I mean,

there's so much to lose with
this question. Yeah, okay, so my

Okay, let me stop for a moment.
We're going to come back to this

and I'm going to walk us through
instructionally, what we do with

this. Instructionally, what we
do with this in algebra one

knowing my test is in a week and
a half. Instructionally, what do

we do with this at third grade?
Because this is like perfect

third grade, not equation
solving, but like third grade

content. I'm going to show you
that in a moment. But go ahead

and unmute and talk to me about
instructionally, how do we deal

with how do we improve? How do
we use this example in a

conceptual way to improve number
sense and to help students think

reason and sense make and not
solve. You've probably never

thought about equations this
way, but unmute and talk to me.

How would you what are your
ideas of using this equation. It

looks very traditional, very
notation ish, how would we use

this in a conceptual, contextual
way such that kids are thinking,

reasoning and sense, making and
improving number sense at the

same time? So there's a way to
notationally, procedurally,

algorithmically, there's a way
to solve this equation. But if

that's the only thing
instructionally we ever do with

this, we're never going to make
major gains. So what would we do

instructionally, conceptually,
to teach this? Talk to me.

So the first thing I would just
ask is, and I learned this from

you, Jonily. Is, what do you
notice?

Beautiful? Notice, what can you
tell me? And then this is, this

is what's scary, because they're
going to tell us things that we

weren't expecting, and then we
have to responsive teach on

that. Do you see? So here's what
I want you to think about. When

you use the tell me about what
do you notice? What do you see?

Do not have an expectation for
yourself to teach on it. That's

why we want to let things
linger. We want to ask those

prompts. Document, even in
writing, on a poster paper, on

the board, document, what kids
are seeing and noticing respond

with that is brilliant, and that
is interesting. I love the way

your brain thinks. Ooh, I've not
thought about it that way. We're

celebrating the thinking that's
the only responsive teaching

we're doing on the day that we
give it. And then after we do

that for about seven minutes or
so, maybe 10 minutes, we. We

then put that away, we move on
to what our regular lesson is of

the day. Then we have time as a
teacher to create the responsive

lesson based on their responses.
Don't try to do it in the same

lesson or class period. That's
what freaks us out, and that's

why some of us are afraid to
implement some of these

strategies. Is we think we have
to then create the responsive

lesson on the spot. We don't let
all that linger. Don't even come

back to it the next day. Wait a
week to come back to it. Email

me and say, here's a picture of
their responses. What do I do

next? I mean, that's the
interactions I'm talking about

with with this transformation
that we're trying to make

instructionally, and then what?
Now and then, what? So what do

we do then, when we start to
teach later, how would you teach

this?

With my third graders, I would
probably ask them, Do you think

it's going to be a whole number?
Do you think it's going to be a

fraction? I would you know, do
you think it's greater than,

less than or equal to a certain
number within the equation? Just

to get their kind of general
understanding of things, yeah,

that's really a different way to
do estimation.

That's a really great, powerful
twist on estimation. Love it.

What else would you do? Yeah,
good. Krista. Krista even brings

in a good sentence starter,
question starter, how does how

does the right side relate to
the left side? Beautiful

prompting. What else would you
do? You're

probably afraid to say of what,
what you would do. Think I'm

going to judge you or something.
Don't be afraid. Don't be

afraid, guys, I use algebra
tiles,

Janet Lane: interesting stuff
like this, so I've always tried

to encourage my kids to draw it.
We we've been trying the same

problem. And thanks to you, I'm
not, like, totally losing it

because I gave a I've been given
a practice OST tip question

today, and like, my test is
Monday, and yesterday they those

one prompt. Two thirds of my
classes got it completely wrong.

And I'm like, Ah. So I took a
deep breath, and I was like, All

right, tell me how you got that
answer. And then, and I'm like,

tell me what you know. And so it
was so interesting, because once

they I said, Tell me about I got
thinking, and I'm like, gosh,

you guys knew this. So, so my
thing is, is we were doing this

like incentive that they they
take the test, and I look at

their answer papers, like with
their work, and if they do it

their way, and then do it my way
with other strategies, then they

get to go to this extra recess.
So that's kind of cool for

seventh graders. But the push is
the thinking. So we've been

doing, you know, like you said,
Stop. What do you notice? What

did you wander? Then answer. And
I've been withholding their

calculators to say, Okay, think
about this first. Yeah, now you

can have calculator, because
beautiful. Grab the calculator.

Go. I'm like, You didn't even
think about that, guys. So

that's what I'm trying to like,
you said, sit and think, but I

would have them draw a picture,
and what do they see when they

draw the picture?

Unknown: Beautiful. Janet makes
a good point. That was little

bit of a hidden message in
there. And that is all year, if,

if students experiences every
day in our classrooms is

solving, solving, solving,
solving, solving, solving, we're

training them to not think. See
if we have less emphasis on

solving all year. If our
emphasis, if our lessons are

structured every day for
thinking, reasoning and sense

making, and that's what we
prioritize, and that's what we

celebrate, then we're going to
change their habit. They're not

going to be able to help it, but
to look at a test question and

think reason and sense make
before they solve. Because

that's the culture and climate
every day. And I can tell this,

we have a brand new fourth grade
teacher in our elementary

school, and she is phenomenal.
She came to our June event last

year. She's fresh out of
college. She started teaching

fourth grade this year. I didn't
get to work with her a lot, but

she came to the June event, and
we have another like

intervention coach at the
elementary that's been

supporting her, because I
haven't been able to do that

well, I've been in her room a
few times just in the last

month, Her room was one of the
rooms we went in when we had the

teacher field trip. And I can
tell her kids have been trained

by her really beautifully,
because I see her kids doing,

thinking, reasoning and sense
making. So when I went in just

on Thursday this week, because I
went back twice this. Last week,

when I went in Thursday, I gave
them a question, and we talked

about, pretend this popped up on
your computer, on your test, and

this is fourth graders. What are
you going to do first? And

they're like, we're going to
look at that piece of it. We're

going to ask ourselves, what do
we see? What do we notice? And

what do we wonder? Okay, now
whether they do this or not is

one thing, but the fact that
they can at least articulate it

is going to train their brain to
look at mathematics in that way,

not as a solving exercise, but
as a thinking exercise. And then

one of the outcomes is we're
going to get a solution

eventually, but we've got to
make sense of it first before we

try to solve anything. And so
you talk about effective Test

Prep. That's effective test
prep, other thoughts, comments,

questions.

I've been doing that this week
with test questions where we

haven't, I haven't given them or
worked through an answer on any

of them. It's just, this is,
what comes up, what are you

going to do? How are you going
to attack it? What's important?

What kind of strategy? What does
the model look like? And then if

they decide, I'll give them
candy, if they come to me with

the answer by the end of the
day, because some of them can't

help themselves, but we haven't,
you know, solved any problems.

We've just been, like, attacking
them and like, getting to that

understanding part. So, yeah,

I know we're just crossing our
fingers at this point, Janet,

I'll be saying a little prayer
for you guys on Monday morning.

Wow, that's, that's like, in two
days. Okay, fantastic. Um, and,

yeah, fantastic. Yeah, really
great prompt. How can you start

look the same? Yeah. Okay, so
this is really good, because you

guys know me. These are some of
my favorite early grade I don't

want to draw, I want to type.
These are some of my early grade

equations that I even give to my
secondary kids. We have

something like, let me get
bigger here. We might have

something like, oh, shoot, I'm
going to this is going to be a

bad one. Okay, hold on, let me
think. Let me think. Three plus

eight equals blank plus

five. Okay, okay, so this is
something that I do specifically

at the earlier grades to promote
unknowns equivalents. This is

more of a thinking, reasoning
and sense making prompt than it

is a solving prompt. I know if
kids have been trained to solve

or reason, and those are
competing interests. I know if

kids, like in a fourth grade
classroom, have been trained to

solve or to reason by giving
this prompt. And if kids put,

I'll draw. Now, if kids put what
is that? If kids put 11 here, I

know that their instruction has
been highly solving. The

priority is solving. I know that
that they believe that the equal

sign is an answer getting
symbol. They do not understand

equivalence and representation
and balance and same as and they

don't understand that these are
two different situations, two

different situations that need
to be exactly the same. They

don't they don't have any idea.
Same as that's really what

equivalence is. So if we want to
promote thinking, reasoning and

sense making with equations, we
need to talk more equivalence

and balancing and structure than
we do solving. So this does not

create an equal. This does not
create the same thing on both

sides. So one of the things that
I do is I give this equation, do

a tell me about then I give this
one, because this is kind of a

precursor to understanding
what's happening in the other

Yeah, very good. Great. Great
comment there, yep, Amy, you

good. You good. Did I give you
good takeaway today for your

Yeah? See, see, Amy, good. When
we read that in class, we always

say. Three plus eight is the
same as blank plus five. See,

yeah, Amy and Amy teaches first
grade. Yep, Amy's always wants

us to get to those numbers. Now,
let me go back to this. Let me

non draw. Let me get okay now,
because I'm in a desperate

attempt to make sure my kids do
know how to solve here's what I

did yesterday, because I'm like
you guys, you know how to do

this. Because if I give them, if
I give my kids equations like

this, they're not putting 11
okay, if I give kids equations

just like this with variables on
both sides that don't have

fractions, they can solve and be
accurate 98% of the time. So

this is frustrating, that they
just freak, that they totally

freak. So this is what I did
yesterday. I did the traditional

This is algebra one. They're
going to take the algebra one

course. And I'm like, what would
you do? Like, if these, if there

weren't fractions, and they're
like, Oh, we would take away

three from both sides. I'm like,
Okay, well, then why can't you

do that? They're like, well, we
can. Like, well, then do it.

Like, what the freak are you
doing? I think I said that to

them. Now this is important.
When we take away three from

both sides, I always say to my
kids, what's the point? What's

the purpose of that? What did we
want to try to do? They're like,

well, we wanted to to remove
this three. We wanted to, like,

move it to the we wanted to
remove it. How do we remove a

plus three. What goal do we want
to get? To remove it? Well, for

a plus three, we want to get to
a zero. This goes back to and

I've taught on this numerous
times, the importance of zeros

and ones, the importance of
zeros and ones. So if I want to

get rid of eliminate a plus
three, I have to make a zero. I

have to make a zero. Now if I
have 3x and I want to eliminate

a times three, I have to make a
one. So there's a train. There's

many trainings that I do, that I
talk about the importance of

zeros and ones in mathematics.
So here, let's say the half

wasn't there, 13 minus 310,

and a half. Okay, so what's the
same as what's the same as now?

So we've got x over here equals
10 and a half

plus 1/4 X. Here was another
problem I gave my kids last

week. I said y equals x over
four plus seven. Okay. And I

said, What's the slope? Now my
kids know that y equals mx plus

b is a linear function degree
one. They know they know it

makes a line. They know that
when x is zero, you have a y

intercept, so it's going to
cross the y axis at seven.

That's the 07 point. But this
trips them up because of the way

this is written. The way that
this is written, they want the

slope m to be one because the
coefficient of x looks like it's

one, but it's not. So you have
to understand the different

representations that this
actually means this. So because

I had done this problem earlier
in the week, I brought this back

and connected it to this. So the
more connections we can make to

other types of problems, the
better associations they're

going to make as well. So now
we're boiled down to this, and

then my kids are like, Oh, well,
we need to get the x's, okay.

Now what they wanted to do here
with the plus 1/4 X, they wanted

to multiply by four, which is
great if I wanted to get a one.

Now I did the multiplying by
four, and I entertained them

with that. And then I said,
okay, then we get 4x and we get

this multiplied by four. And
then over here, what do we get?

And they're like, Well, that
went away. No, it didn't,

because 1/4 times four is one.
Now I have 1x over here. Now I

have 4x here and but it's okay.
We don't have to go backwards.

We can multiply everything by
four, and it's just fine. That's

legal, but we could have done
something else that is going to

put our. X's together. Okay, so
if we think of this as our

chunk, and we want to remove
this chunk, we have a plus

chunk. Again, we have how do we
get rid of a plus chunk? We

minus the chunk. Okay, now I'm
being very traditional here,

blah blah, but I want to make
this point, and then I'm going

to stop with this traditional
nonsense. Here's the point I

want to make. Now, my kids know
that this is not zero. Many

algebra one students think that
this is zero minus a fourth. And

I'm like, but how many x's
what's the coefficient? It's not

written. It's one. You actually
have 1x now this goes back to

what Janet was talking about,
because if you use algebra

tiles, these x terms are green
rectangles. A green rectangle,

Algebra tile has a height of x
and a length of one. We call the

area of this. We call the name
of this green rectangle x. So if

I want to represent 3x i would
need this x, and I would need

three of them. Now I could draw
three rectangles, but I teach my

kids to shorthand this. There
are three rectangles. That's

what 3x look like. So over here
I have 1x so I just have one of

these here, which shows that you
have the coefficient of one and

not zero, because there actually
is one. There is a green

rectangle over here. Oh, I don't
even have a whole green

rectangle. I have a fourth. I
didn't draw that very well, but

you get the idea. Okay, so this
is, this is how much I have of

that rectangle, or that paper
strip, or whatever it is that

we're using that gives that
conceptual, concrete,

situational, contextual visual
to this equation. Now I'm going

to go ahead and stop here,
because my kids also were

successful once they know that
was one minus 1/4 is three

fourths. Now I'm not going to go
any further with that

traditional, because here's what
I want to do. Let me I want I

just Oh my gosh. Okay, fine,
I'll do it this way. Okay, let's

go down here and start over.
Okay. Now what my students in

first grade, third grade, fourth
grade, sixth grade, eighth

grade, algebra, what my students
know at every grade level is

equations. Are Jesse and K
money. So this side of the

equation is Jesse's money.

And so this side of the equation
says that Jesse starts with $3

and I know that that's the
starting number for Jesse,

because that's when x is zero.
That's on day zero, when x is

zero. Jesse has $3 that is also
y intercept. The y intercept of

Jesse's linear function is
three, because a y intercept

happens when x is zero. Now I'm
not telling third graders this,

but I'm telling you this because
you can use x as this is, and

you can notate it however you
want. This can be how much money

Jesse or Kay gets or loses every
day. And that could just be

your, you know, emoji number,
whatever you want to call it,

the number that doesn't have
that variable or unknown. That's

called a constant, and that's
the starting it's plus three. So

Jesse starts with $3, a day. And
then how many of these were

there? There were one. So Jesse
gets $1 she earns $1 every day.

Now you could say that this is
the rate, and talk about rate

speed, 60 miles per hour, but
you don't have to. You can just

say that the way that this is
notated, that means, because

there's 1x that Jesse's going to
get $1 a day. So on day zero,

Jesse has $3 day one, Jesse has
$4 day two, Jesse has $5 day

three, Jesse has $6 this is the
model and mindset of instruction

in Singapore. What they do in
Singapore is they give typical

algebra one questions to
elementary students, but they

frame it in a context that
allows access for. Graders,

third graders to do an equation
like this, but in a different

way that's going to target the
standards at elementary now we

at minds on math. We add a
different level to that. We

reference task it, we
contextualize it as a Jesse and

K problem. So now, if I go over
here, let me do a different

color, and I'll save this and
I'll send you these notes. If

this is Kay's money situation,
what's K starting? Number K

starts with 13 and a half
dollars. Now what we might say

is, oh, that is $13.50 if kids
want to do it that way. Okay, so

K starts with $13.50 now what I
could do at this point is ask my

students, what math questions
can we create? And so some of

those might be, who starts with
more money? Who gets more money?

Who loses money? Who this? Who
that? Okay, how much money does

Jesse have on day 100 how much
money does Kay have on day 100

so if I line this up, when this
number is zero, when this is

zero, when this is not there,
when the 1/4 whatever, no days

have gained any money yet. This
is Day Zero. I start to line up

this relationship here. So now
this, this one is is harder. K

is harder, I admit So on day
one, we need to know how much

money K has. But how much money
is K gaining or losing every

day? Well, K is gaining money.
So k is gaining money a fourth

of $1 every day, a fourth of $1
every day. Well, how much money

is that every day? Okay, well,
that's a we can leave it in

fraction, or we could say, Kay's
getting 25 cents. Come on. I'm

trying to do this with my just
mouse pad. Come on. Jay Z, make

a two. Okay.

Okay. So k is gaining 25 cents a
quarter every day. Now, if you

teach second graders, third
graders, and you're trying to

get them to understand money,
what a better way to do money

than to embed it in a situation
that is very algebraic thinking,

very skip counting. Ish, very
rate infused that is is grounded

in unknowns and equivalents,
like look at how many birds

you're killing with one stone.
Not that I advocate for killing

birds, but I advocate for
efficiency of instruction. I

advocate for using one example,
one situation to teach lots of

different standards. And when
crystal said, I saw the impact

of the same task, the same
thing, no matter what it is

being done at every grade level,
and being effective and

powerful, this is what crystal
is talking about. So on day one,

on day zero, if Kay had $13.50
and we get 25 cents more, then

we have $13.75 and let me know
if I make a mistake

mathematically, because I do
that a lot. On day two, how much

money does K have? Well, we add
another 25 cents, $14 on day

three, how much money does K
have? $14.25 or I could write 14

and a fourth. I can go back and
forth on variations of

representation. Doesn't matter.
Okay. Now, after we're doing

this together as a class, I'm
going to then ask again, say my

favorite words, tell me about
what you see. What do you see?

What do you notice? Make sense
of it again. We're going to

stop. And we started to, kind of
like do some solving and

counting. And so every time we
start to move to solving and

answer getting we, as the
instructor, need to back up and

say, Wait a minute. How do I
bring it back to thinking,

reasoning and sense making? So I
get this started, and then I

say, tell me about what do you
see, what do you notice in the

chat right now, I want all of
you to type in, what do you see

and notice about what just
happened. So type that in the

chat. Tell me about this
structure. Tell me about these

numbers. What do you see and
what do you notice about what

just happened?

What are your thoughts? Come on
now. Chat it up.

Oh, nice, both sides are
increasing at the same rate.

Good, yep.

Another thing I ask my students
as they're thinking reasoning

and sense making is, what other
math questions could we ask?

Nice j is increasing faster than
k, even though K began greater.

So what does that mean? What
does it all mean? Basil,

a nice Yep, will Jay end up with
more at some point and when?

Crystal, yeah, this is amazing.

Oh, yeah, okay, okay. Now here's
where your default instruction

is going to kick in. If you do
this in your classroom, and you

get to this point, your default
because you have habitual,

traditional instruction, what's
going to happen now is you're

going to have you're going to
have kids keep extending, and

you're going to have them answer
these questions. What I'm

telling you is, don't, when you
get to this point in your

instruction, in your class,
you're going to be like, Okay,

that was so beautiful today. I'm
so proud of you guys. We

realized a lot of different
things. We're going to put that

away. And I want you to take out
yesterday's homework that has

nothing to do with this. Okay, I
want you to go on to your

regular lesson now that if you
leave here with nothing else

today, I want you to hear me on
this. You're going to be like,

Oh, but the kids want to finish.
Well, the kids want to keep

going. I finally got them
focused and engaged, then cut it

off.

There are brain reasons for
this. There are cognitive

reasons for this.

We are shaping the brain, and we
are shaping the mathematical

mind. So right now, as soon as
you have the kids in the palm of

your hands, as soon as you have
them right where you want them,

you're going to stop and you're
going to be like, Okay, we're

going to put this away, and
we're going to go on to our

lesson of the day. Now you're
going to have kids still working

on it and trying to hide it.
Don't call them out. Just ignore

it. You're going to have kids
still talking about it. You're

going to have kids going, Oh,
but I know where they're going

to go do math without you asking
them to do math. How amazing is

that they're going to talk about
this at lunch. They're going to

come in the next day with the
answer, and when they give you

answers, you're going to be
like, That's interesting, you

know what? Let's start adding
that to an answer list. Let's

start documenting that. We'll
come back to this next week. But

let's celebrate what they're
doing, but do not confirm or

deny their answers. There are
some responses that are going to

negate all of the work that
you've done. You want to let

this linger. See, I'm going to
let this linger. You're going to

let this Lisa, beautiful,
beautiful, because that's what

we end up doing with Jesse and
Kay, is we graph Jesse's system

of equations. That's what this
is. We graph Jesse's function,

we graph K's function, and
that's just good practice in

slope, intercept, like boom. And
then we start asking, are we

going to have parallel lines or
non parallel lines? Parallel

lines, same slope? No solution.
We don't have the same slope

here. So we are going to
probably have a solution

somewhere. What is that
solution? Is the solution going

to be in the future or in the
past or in the negatives? And

what is this so much, so much we
can do at algebra one and Lisa,

imagine if your seventh grade,
sixth grade, fifth grade, fourth

grade, third grade, second
grade, first grade. Teachers in

your building did Jesse and K
every year in lots of

variations. So by the time kids
came to you in algebra one

they've already had a lot of
this mentality. Mm. Can you

imagine what that would look
like? It's really beautiful

because the cohorts I got rid of
the data here, but the cohorts

where we've seen this extreme
data, that's what we've been

doing in schools, and we've
earned 1520, 30, 40% higher test

score rates by doing exactly
this. All right, friends, it is

almost 11. Here's what I want to
hear right now. Type it in the

chat or unmute. What were your
takeaways from today? What were

your ahas? What are you going to
take away from today? What did

you learn from today? What
solidified your learning. So

what are your takeaways? Unmute
or type them in the chat or

both. Go ahead,

I just have something about the
field trip. Yeah, I'm going to

bring in another reference
reference task, but the painted

cube, so I had my the block that
you were in with came back on

from spring break, okay? And one
of their first questions to me

was, Hey, are we ever going to
do that cube problem again? And

not only that, but then my other
block that they kind of

intermingle with was like, Hey,
I heard that you did this cute

problem, like, are we ever going
to have a chance to do that

again? So, you know, they've
been talking about it. It's just

interesting.

That's cool. That is cool.
Lingering is so powerful. Let it

linger. Other takeaways, Hannah
says, Teach based on thinking

more than salt, yeah, beautiful
other takeaways.

Yep, thinking, reasoning and
sense making is the key and only

that's not on the kids, that's
not on the kids, that is on our

instructional facilitation and
delivery. So if kids don't have

thinking, reasoning and sense
making, if they don't persevere,

if they don't initiate, that's
on us, not on them, we have not

created the environment, culture
and habits for them to default

to thinking, reasoning and sense
making. A lot of times, I hear

these kids, they just don't
start. They don't know where to

begin. They don't they're so
helpless. They're done. They

didn't do that to themselves.
Because toddlers don't have any

of that. They toddlers don't
have any of that effectiveness.

School. Has created that in our
students that's on us, guys

that's on us. Get students
brains thinking, leave them

hanging. Yeah, that's important.
Focus factors, fractions

function, and we have more
explicit, streamlined approaches

to being able to focus on those.
Yep, very good takeaways.

Balance between procedures.
Yeah, just do it like, just jump

in. Don't be like, you don't
know what's going to happen. As

a teacher, I know that's scary,
but I've given you the out. Once

you get to a point where you
don't know what to say and do

next, and you feel yourself
defaulting to telling and

teaching, then you want to stop
and be like, Hey, we're gonna

finish that another day,
insisting that my students pre

read, understand, yeah, yeah.
What is it asking think, reason

and sense, making new way to
word, make rectangles now. Okay,

good, good. Amy, yeah, and
you're going back to third

grade. Awesome. Oh, that seems
like it's going well, that's

excellent. Wonderful. Okay, you
guys, I've got a pretty hard

stop today. Usually we stay on
and I give you some more time,

and then, like all of you, end
up staying for like another

hour. I can't do that today. I
have a hard stop time today.

Although I love you, I love you
so much. Mark down, April 24

there will be the next webinar,
a webinar with upsell. Saturday

maths. I usually don't have any
upsell. I mean, this is just

real organic like Saturday math
is free. There's nothing I'm

selling to you. But on April 24
there will be an upsell, and it

will be a bundled package of
what you can jump into for the

2026 2027 school year. I really
want you to be here on April 24

but I can't give you any link
right now. Nothing is up for

registration yet. It'll be
coming up later this week. So I

will send you the information
for the April 24 webinar this

week. Once I have the link, I'll
follow up and send you the notes

from today, the PDF notes from
today. And I want to thank all

of you for being here and
spending your Saturday morning

with us. We will have another
Saturday math in May, and you

will definitely get that
information. Also love you guys.

Bye, bye. Good luck with
testing. Enjoy the final 30 some

days of school and have a great
summer, but hope to see you in

May. Bye, everybody. You.