All right, thanks so much, Jordan.
Um It's so nice to see you and have all of you here today.
Um As Jordan said, my name is Sarah Paul.
I'm joining you today from Austin, Texas here.
I'm a researcher and teacher at the University of Texas at
Austin. If you want any information from me today,
you can find me on my website or you can email me or you can
also find me on social media, both on Twitter and Instagram.
I only share math things.
Um So I'd love to, you know, continue to come,
uh continue these math conversations with you beyond today and
if you feel comfortable, you do not have to do this.
But in the chat,
if you'd like to say hi and kind of share some of your interest
about math in the home,
I'd love to know a little bit more about you.
We don't have time for everybody to go around and share.
But in the chat,
go ahead and say hi and share your interest in math in the home.
And as we go today, if you have questions,
go ahead and raise your hand,
I'm kind of watching uh the participant section,
but you can also drop them in the chat and I'll try to answer
them as quickly as I can. Um, as you do that,
I just want to tell you a little bit more about myself.
So I am a former kindergarten teacher.
I am also a student who at some point struggled with math in
middle school,
but I had an amazing ninth grade math teacher who really showed
me that I can learn math.
Um even when I didn't feel that my confidence in math was that
high. And so, uh since then that time,
all of my teaching and research has been in the area of math.
I right now run uh research based programs funded by the US
Department of Ed,
anywhere from preschool all the way through grade eight where we
really try to figure out best ways to support teachers in terms
of their teaching of math and best ways to support students in
terms of their learning of math.
And while a lot of the things that I'll talk about today are for
many learners,
uh my focus group of learners are students who struggle with
math and like,
what are some of the ways that we can support them?
So, um I'm really glad you're here today.
And if you do have any questions as you go,
please feel free to drop them in the chat.
So when Jordan um asked me to talk a little bit about math at
home.
I was super excited to do this and I have grabbed probably no
fewer than 20 things in my office.
That would be really fun activities for you to do in the home
with your kid or kids.
Um, but before we get started, I want to think about, well,
what's important to ahas in math.
So there are tons and tons of things that students have to learn
in math across grades K through five K through eight K through
12 where wherever you kind of are thinking about your um your
student.
Uh but there are some things that are absolutely essential.
And so we know in the earliest grade levels.
So we're thinking preschool or below kindergarten.
Um an understanding of what we call early numeracy is really
essential for many kids. This is about counting comparison,
early addition and subtraction,
early understanding of tens and ones and also early
understanding of shapes and doing measurement.
So there's a lot of things that students have to learn early on
that are going to be very important for essential and math later
on. And so as we think about students, as they progress in math,
there are a few different gates that students have to pass
through.
So when students have really strong early numeracy skill,
that kind of opens that gate up and that leads them to be
successful with whole numbers.
If students don't have a lot of strong skill with early numeracy
that gate is harder to pry open and then that's going to cause
implications for students later math. So after early numeracy,
and so now we're thinking about the early elementary grades
continuing into the late elementary grades,
students have to know a lot about whole numbers.
So whole numbers are numbers that are not fractions and decimals,
but numbers like 13, 102 4 and so on.
Um And often we think about students adding subtracting and
multiplying multiplying and dividing these whole numbers.
And what we know about whole number understanding this is also
like place value like tens and ones and also thinking about
numbers on a number line that opens up the gate to rational
numbers.
So when students have a strong understanding of whole numbers,
those students typically show later better scores on assessments
of rational numbers. And when we talk about rational numbers,
most often the conversations go to fractions decimals and
percentages.
These are all really important concepts and procedures that
students have to understand in order to open that gate up and to
be successful with, oh let's see, be successful with algebra.
And so as you're thinking about, well, what are the,
what's the math that you wanna support in the home while there's
a lot of math out there really thinking about this um like
continuum of math as students are going to be successful with
algebra,
this is where you would want to spend a lot of your time.
Now, if you're wondering what's really important across grades K
through eight, um,
this is an excellent one pager about what's essential across
grades K through eight in mathematics.
Um This comes from the achieve the core documents.
Some of you might have already seen this already. If not,
you can follow that QR code or this website and it will lead you
to this landing page here.
But the idea is that at any grade level,
there are typically 20 to almost 35 different math standards at
that grade level.
And sometimes it's difficult for us to pay attention to all of
those. And so here,
they've tried to outline what is absolutely essential for math
from one grade level to the next grade level.
And so what we can see here is that in kindergarten and probably
all of you would shake your head and say, yeah, Sarah, I agree.
But students need to know their number names and the counting
sequence.
They need to be able to count to tell you how many objects there
are. They need to be able to compare numbers,
they need to understand the earliest uh meanings of addition and
subtraction and they need to understand the teen numbers.
And if a kindergartner understands all of those things,
they are more likely to be successful with what we see in first
grade math, second grade, math, third grade math and so on.
So I like to refer to this if I'm thinking, well,
what are some of the things that I want to make sure my student
understands or my child understands?
You might wanna refer to this list there as well.
So, let's think about what we are going to do today.
So when Jordan talked about math in the home, thought, well,
there's so many things we could do here,
but really thinking about math through, I'll say, like, um,
play or through fun activities.
And so we'll just briefly talk about four things here today.
And I,
I'm going to ask you to share the things that you do in the home
as well because you all probably are doing some of this already.
And so we can have a really vibrant conversation where you can
share. Oh,
these are the games that we play or these are the books that we
read so that everyone here can benefit from all of us as we
share our different ideas. But as we go through today,
we'll just briefly talk about some different games and
activities that you might want to think about playing in the
home or having in the home.
Um we'll look at the role of books uh that you are reading with
your Children and some of the ways that they can be more
mathematical in nature.
We'll also talk about virtual tools and then we'll do a brief,
brief, brief chat about word problem solving,
especially if you are supporting a child.
Probably grade two and above in terms of their word problem
solving prog progress there.
So let's go ahead and get to games and activities.
So often when we think about math,
um we think about the four operations,
operations are defined as adding subtracting,
multiplying and dividing.
But there's so much more to math than that,
especially there's so much more to math fluency than that.
So some of you might be also working with your young Children on
counting in comparison,
maybe you're working on things with money.
So how do we count these coins or say how much money there are?
Uh there is or how do we like tell time.
Um some of you might be working with your students on fractions.
So identifying equivalent fractions or benchmark fractions,
maybe you're working to try to find common denominators.
And so you're working on well,
what are the multiples of these numbers?
And maybe some of you are working with geometry,
like identifying shapes or working with shapes or knowing
formulas. There's, there's just so much in mathematics.
But the idea here is that we want students to develop fluency in
mathematics and fluency only ever uh comes to students through
practice.
It's not just like this magical thing that some students are
fluent in math and some students aren't.
No, that's not how it is,
but fluency comes through practice and that's where games
activities, books, virtual tools.
That's where those can all become important for developing
fluency with our students. Now,
some of the conversations in fluency especially around adding
subtracting multiplying and dividing those are going to go
toward memorization and automaticity.
So those are things like the facts like the addition,
facts are like four plus four or nine plus six, subtraction.
Facts are things like 10 minus five or 14 minus eight
multiplication.
Facts are facts like three times four or nine times nine and
division facts are facts like eight,
divided by four or 81 divided by nine.
And so those we eventually not at the beginning,
but eventually we do ask that students have automaticity with
those. And there are 390 math facts and all.
And our typical expectation is that students at the end of
second grade know all of their 200 addition and subtraction
facts.
And by the end of fourth grade know all 190 multiplication and
division facts.
Now a lot of students meet that bench, some students don't.
But the important thing is is that as we're working with
students to develop that fact,
fluency we have to practice and practice doesn't have to be
worksheets and practice just doesn't have to be like drill.
But there's a lot of cool things that we can do to help students
with their practice of those facts.
But then there's a lot of things in math that students do that
we don't expect automaticity and memorization. So for example,
if I asked your child to uh do um 805 divided by 12.
We would never ask them to memorize the quotient to that,
but we would ask them to have an efficient strategy that they
were able to use easily and accurately.
And so you also want to balance that in the home.
Um You're not always memorizing,
but a lot of times you're practicing things to make things
easily and accurate for your students.
So let's go ahead and get into some of these games and
activities,
games and activities allow students to see math in a lot of
different ways.
And so as we talk about this, on the math side of things,
we often talk about this as the concrete pictorial abstract,
the concrete are hands on tools that students can use to touch,
uh touch,
um touch and move to see different math concepts and procedures.
There are hundreds of these available.
You can purchase a lot of concrete tools,
but you can also um you can also uh find some of these in your
home. So like paper clips or straws or markers or, you know,
a lot of things your kids already have.
Legos are a great concrete tool,
but you can use these to help students understand these
different concepts and procedures in math.
And so what I'd like to do is I brought in or I have nearby to
me,
um some of my favorite hands on tools that if you don't already
have some of these already.
You might want to get them and I know it's gonna be a little
noisy because I'm gonna open up some of my Ziploc bags as I show
you some of these different tools.
So if you are working with really little kids,
one of the things that you probably want to have or if you don't
have already are different types of counters.
Um, these are counters that are different motors.
So here's one that's a school bus, a train.
So many kids love trains, cars and there's a little fire truck.
And so something like that is really helpful for kids.
If you're maybe adding and subtracting or maybe you've been
working on multiplication and division or just counting here.
I have four things. Um I'm going to count those four things.
Another set of manipulatives that you might want to consider are
just something like buttons.
Probably a lot of you have extra buttons.
If your, if your closet looks anything like mine,
I have a whole drawer full of extra buttons.
These are little buttons that you can buy.
They're really good for sorting and classifying.
They're really good for making patterns like,
oh what are some of the different patterns that we can make,
you know, pattern making is a,
a mathematical task that I just made a pattern of orange, green,
orange, green, orange, green.
So that might be something that you want to consider.
And then other things you might want to consider are just little
counters like these two color counters.
Um These are really helpful for counting.
They're also really helpful for fractions.
They're also really helpful for algebra.
Uh Another manipulative that you might be interested in are
these pattern blocks.
These are really great for shape recognition and understanding
shapes. Students can do a lot with also making patterns here.
They could also make different TESS like what are the different
ways that we can make these shapes fit together.
And so there's just a lot of really cool stuff that you might
want to consider if you have students do the pattern blocks.
Now, a lot of these were just counting and,
and things like that,
but I'll show some other manipulatives that are also helpful for
things related to math that may not be just counting.
So, um, these are what they call the inch worms.
Um, if we measure these,
each of these are exactly one inch long.
And so students can, um,
put together these inch worms and that they can take them apart
and they could measure different things in the home.
And then one of my favorite manipulatives right now are the
angle legs. I've also seen these called geo sticks. Um,
let me get a set out here and then I'll show you how they are so
cool. Um, so with these sticks here, they students can, uh,
pick them apart, I'll move them up a little bit,
but I can pin them together.
So maybe you're asking your students to um think about Pentagons.
And so I could say, OK,
I'm going to make a five sided shape and I can just quickly pin
all of these things together to make a five sided shape.
And there, I've got that and it looks like that.
But if you've got some older students and maybe they're starting
to work with angle measurement,
these angle legs also have a really nice protractor.
And that protractor typically pins right on top of there.
So then I could measure the interior and exterior angles of this
shape.
I could talk about right angles, acute angles of two angles,
all kinds of different stuff.
So um I have a few other manipulatives that I'll show a little
bit later.
But those are some of the common manipulatives that you might
want to either have at home or you know,
talk about whether your students are using these manipulatives
at school.
So lots of really great resources there in terms of those
concrete manipulatives.
Now, um in terms of other games and activities,
we also want to emphasize the pictorial.
So these are two dimensional flat images that students can touch
and move to talk about different math concepts. Later on,
we'll talk about these in books and then we do the concrete in
the pictorial to help students understand mathematics in the
abstract,
that is mathematics with the numbers and symbols and words.
And often a lot of adults will say, well,
this is math right here,
but I would say math is all of those things that I just showed
you and a lot of these games that we're now going to look at.
So speaking of games,
there are so many things that we can do with students.
So I'm gonna show you about probably 10 to 15 different games
and activities and then I'd like you to share some of your
favorite. And in fact,
if you want to go ahead and drop some of your favorite in the
chat, please do so before I even get to it. So,
uh probably some of you have some beach balls or you can go to
the dollar store and buy a beach ball.
Lots of cool things that we can do on this.
Um This is an activity,
let's say your student is working on multiplication where you
can write different numbers there and you can toss the beach
ball back and forth and wherever your thumbs land,
then you can multiply those numbers together or maybe you can
subtract those numbers if you're working on subtraction.
So that's a really nice,
easy little game that students can either play with you or they
can play with their siblings or other kids in the neighborhood.
Um Every kid loves bingo and there are so many math bingo boards
that you can print out here.
I even have a bingo uh board that I was able to buy on Amazon.
Um It's just like simple math bingo.
This one's on addition and subtraction,
but you can create them for whatever you want them to be.
Um And you could just like, you know,
sit around the table and play some bingo and here,
uh what you do is you read out facts and then if you said seven
times seven a kid,
they cover 49 or if you said um six times two,
they cover 12 and then who's going to get to be the first one
that gets to bingo playing cards? Playing cards are awesome.
If you are a family that uh likes to have playing cards in the
home, um You can do a ton of stuff with adding and subtracting,
multiplying and dividing.
You could also do things with patterning and comparison of
numbers and so many times playing cards are best when you remove
all of the face cards from the deck.
Um Because if you have the aces through 10,
you've got some really good number cards there.
And another really cool thing about the playing cards is that
they help students with. Super.
So this might be something that you are familiar with.
Um But maybe if you're not, you,
you probably know what I'm talking about.
You just don't know the term.
So super is instantly knowing how many.
So if I look at that pattern and let's look at the first card of
those six hearts. I see that they're six.
I don't have to count them 123456.
And what we know about super is that when students automatically
recognize some of these patterns, it makes math easier for them.
And speaking of those patterns and I'll move over here to,
I'm gonna move back and forth to between my, um,
my camera and my presentation here today.
Sorry about that Jordan, if you're operating that.
Um So uh die, probably a lot of you have some die in the home.
Um Dye like this are just absolutely fantastic to work with,
I can roll those and add those numbers together or multiply
those numbers. Um But, and they also help with super,
I'm um looking at that and I immediately see six and I'm looking
at this dye and I immediately see four,
but there are a lot of fun dye out there.
This one has, I think that's a 12 sided die.
This one here I believe is a 20 sided die and then they even
make, they have Dy that are within Dy. So if I roll this,
you can see there's a little dye within the bigger one.
And so I can multiply those numbers together.
They also have dye that are with fractions and look at this.
I have a dye with negative numbers on it.
And you guys, my dye collection is really amazing.
Um And then this diet has placed value all the way to the
different thousands place.
I also have some dye that are printed in Japanese.
I have dye that are printed um in Hebrew and I have some diet
that are printed in.
Um I think it's Korean but I'm not sure I'll have to look at
that so you can find those on the internet.
They are all over the place.
And then the other thing that's closely related to die are
Domino's probably a lot of you have these uh where you can just
play Domino's the game. But you can also do things where I,
I take two Dominos and maybe I add all of these numbers together.
Also, Domino are helping me practice that super.
Oh, I immediately see four instead of having to count 1234.
And I can also multiply those numbers divide and put them in
order.
There's just a lot of really cool things that we can do there.
Now in the chat,
a great suggestion came up that they used to play war with the
times tables.
Yeah, those cards are just excellent for playing war.
You can also do the same games with dice and you can do the same
games with the Dominoes.
And so there's a lot of really awesome options there as we um
think about doing the doing those games.
Now, continuing with our Dominoes.
Uh we can think about uh math facts if you want to use fact
cards such as the ones you see here. That's totally fine.
I wouldn't use them all the time. All right.
Sometimes kids get a little tired of fact cards. But, uh,
we do some fact stuff in the schools and we use the fact cards
really, uh,
all pretty much a lot of the time but find fun cards.
These are triangle fact cards here.
So, um, these are actually for multiplication and division.
And so what you do is you cover up one of the angles and so 28
divided by four is seven or 28 divided by seven is four or seven
times four is 28.
And so not all flash cards have to be like the typical
rectangular flash cards that you might see or buy at the store.
Um As we also work with flash cards,
you might want to do games like a magic square.
Uh The magic squares, I can send you a template for this.
If you are interested, you can also find these on the internet.
There are a lot of resources related to the magic squares out
there.
But I'm gonna turn off my presentation and move over to my
camera to show you a little bit about how these magic squares
work because you might use these as like uh a challenge with
your students to see how they understand multiplication,
division, addition or subtraction.
So these magic squares here, this is a set for multiplication.
And so what I do is I have a target number here 24.
And I'm gonna figure out, well,
what are two numbers that I can multiply together to equal 24?
And so I know that 12 times two equals 24.
And so I'm gonna put them in the column so that I see 24 right
there. Now,
I have another two numbers that also multiply to 24 I'm gonna
put them in this row. And so if I look at my numbers, I see, oh,
there's a six and there's a four and six times four is 24.
Now, right there, before I even look at my other numbers,
I would ask students. Well, what about the division?
Well, 12 divided by two is 12 or I'm sorry?
24 divided by two is 12 or 24 divided by 12 is two or 24 divided
by four is 6, 24 divided by six is four.
Probably your teachers are talking with your kids all the time
about relationships between numbers.
That's a lot of the relationships that I can see right there.
But then what I do with the rest of my magic squares is I figure
out, well, what can I multiply here?
Well, two times three is six.
And if I do, let's see if I can figure this one out.
Might have these backwards here. Two times,
one is two and three times four is 12 and one times four is four.
And so it doesn't work on the horizontals.
I'll go ahead or I'm sorry, on the diagonal,
but it works horizontally and vertically.
So here I now see six different multiplication facts as well as
six different division facts.
And so there's a lot of tits that you can use to make these
magic squares.
It's like a nice fun way for students to practice their
understanding of adding subtracting, multiplying and dividing.
And if you want the templates,
email me or you can also find them on the internet machine.
Usually just call those magic squares.
I probably shouldn't even flipped over to my presentation
because I'm going to show you two.
I'm gonna show you all the games.
I'm gonna go back to not showing my presentation but showing my
camera and I'm gonna show you some other cool games as well.
Uh Have any of you ever played banana grams?
Probably some of you have.
So um if you want to see the math version of banana grams,
that's here with Moby.
And so Moby has a bunch of colored tiles in it,
they're turquoise number tiles.
And then we have our symbol tiles there as well.
And what students can do is they can make different equations.
So I can see that seven plus five equals 12.
And then the next person can go to build off of that.
Oh, I see that 12 minus six equals six and so on.
All right.
So the whole idea here is that you're kind of like building this
uh really large um like equation mat uh to show different types
of equations. There's another similar game to Moby.
And I, I think some of you have probably played this one before.
Um This game is called S math and it looks exactly like the box.
So I'm not going to open it up here,
but S math is where you can create equations and it actually is
a lot like Scrabble.
So if you've ever wanted to play Scrabble, but for Snap,
um Snath might be the game for you. Now, a few other games,
um they're gonna make some noise there as I put those away.
Um A few other games that you might be interested in mathematics.
Well, if you've got some young kids,
there's a lot of really fun little games like count your
chickens or this game is called Rooster Race.
Um Proof is a really fun game with proof goodness sakes.
I don't have enough room in my office.
Um You create a three by three grid with these number cards and
then the group has to make equations with the different cards.
And so as I put the cards out here, I'll mix them all up.
So then if you make an equation and if you have proof that that
equation is true, then you get to keep those cards.
And so sometimes I really have to think a little bit about this,
but maybe I want to figure out what are some of the cards that I
can make to add to 33 or what if I start with 34 I subtract some
numbers or here?
What if I goodness my proof is gonna be hard to do today.
But, um,
I think all of you could probably figure out a proof there and
I'm not gonna do it because I want to go to the next game.
But this is a, a very inexpensive game called Proof.
And that might be a nice fun mathematical thing to do as well.
All right,
I've got three more games before we get into some of our other
stuff. Actually, four sorry block.
Uh This is the travel version of block.
But um, some of you might play the big game of block,
you might say, well, that's, that's not a math game.
Oh, contrary, it totally is.
Um, block is, is a great game for spatial reasoning.
Spatial reasoning is really essential in math and also block,
you have to do a lot of accounting and a lot of planning.
And so that would be a nice math game to play there as well.
If you've got some older students,
you might be interested in this game called Prime Club.
Um This is a really nice one.
It's got like this really nice big mat and it, there's,
you can play that game. Lots of cool things going on in there.
And I said I had a few more things. All right, two more.
Um probably a lot of your kids are into puppets and if they're
not, they will be soon or maybe they're past puppets.
I don't know. But on this puppet,
uh so this one is labeled on one side with the numbers 1 to 100.
So if you want to practice counting, you could go 12345.
And as the students say, the numbers, they pop it through.
But the puppets have a lot of other cool things that you could
do. So maybe you are working, have a,
an older child and maybe you're working on multiplication.
And let's say we're working on the fact four times two.
So I could say OK, that's 1234,
I'm gonna pop that through or pop it back and then,
but four times two and I could even pop.
There's my four oh my gosh. And then I do that times two.
So four times two is eight.
And so I can show multiplication in that grid.
Just like many of your kids probably work with a multiplication
table or um a multiplication chart.
And then another activity that you can do with students are
these wrap ups.
Um These are little plastic keys that always have a string
attached.
Um And here the operation is listed on top um with the wrap ups
let's do plus five today.
Um You isolate that key and then how this works is you start the
string on the top left hand side in the first notch.
So on this key, I'm always adding five. So first I have four,
you see the number four there four plus five is nine.
So I take my string over and I put it by the notch that says
nine and then I bring the string to the back to the second notch
below four. Now I'm gonna do seven plus five. That's 12.
Now I'm gonna do three plus five, gonna get it there.
That's 88 plus five is 13,
2 plus five is 7-Eleven plus five is 16.
Um five plus five is 10.
And I'm not just showing you that I know my math facts,
but I wanna finish here to show you what happens at the end.
So as I get to the end, six plus five is 11, 10 plus five is 15,
I can match it in there and then if you turn it over and
sometimes I know this is hard to see on my document camera.
If the string,
there's like a kind of like a very gentle ribbing on the back of
this key. And if the string matches the key, you know,
you've answered the facts correctly.
So it's like a really just nice little practice thing.
Maybe just give this as you're driving your kid to soccer
practice. Or something,
you just give it to them and they could just practice their
facts, um, in that way as well. All right.
Oh, that was a lot of games but it's not all of them.
And so what I would like you to do is in the chat.
Tell us some of your favorite games. What are your,
some of the games that you like to play at home or some of the
math activities that you like to do at home that your kids
really like to do?
So go ahead and start to drop those into the chat and then I'll
join you in a minute with them with my presentation.
Now, some of you are probably ahead of me.
So I'm gonna join you. OK. So we got the Golden Snake game.
All right. That sounds super fun.
Any game with that has a snake in it? I'm gonna like that.
Some of you might say uh shoots and ladders or candy land.
We don't always think about those as bad games,
but there's a lot of math that's involved in all of those games.
Um Some other games, hopefully you're gonna drop in there.
Uh Count your chickens or Getty in my spaghetti.
You know how many noodles have, have you taken out?
How many noodles did it take till the getty dropped into the
Spaghetti. Ginga is somewhat mathematical. Um 24 is a fun game.
This is an oldie, but a goodie. I really like 24.
I showed you Prime Club there before.
Monopoly, uh, money involved in there as well.
So, yeah, what are some of your favorite games?
So, we've got, uh, one in the chat at the restaurant.
Who can guess the bill? Oh, I like that. The estimation there.
Maybe. Who can calculate the tip beyond that? That's a good one.
See if any of you would like to share any of your other favorite
games.
I've got a few other games.
I've got a pizza fraction game that seems, uh, kind of fun.
It's just that trouble. Yep. Robbi Cube. Oh, these are great.
I love it.
We play a lot of card games beyond war that, uh,
do involve mathematics.
So, yeah, like uno, yeah, that's a great one.
I'm glad that one just got dropped in the chat as well.
Does anybody pay? Play phase 10? That's a good one.
How many tiles are at the doctor's office? Yeah, I like that.
Yeah, math is really all around us.
I'm glad you bring up that example because there's really math
is everywhere, but we don't always talk about it.
So, speaking of next, I'd like to talk about books.
There are hundreds and hundreds.
I will actually say thousands of books about math and they're
not books about math,
but they're books that are stories that about math and so on my
website, I did put these,
if you go to my website there or follow that QR code,
I put them under presentations and it's just an Excel
spreadsheet. And you're welcome to download it.
And what we've tried to do is um categorize these books by area.
So if you want to talk about patterns with your kids,
here are some of the pattern books.
If you want to talk about comparison,
here are some of the comparison books.
If you want to talk about counting,
counting books are the most prevalent.
So they're probably not hard to find counting books.
Um But there's just a lot of really cool things that we can do
with books.
So I'm going to come back over to my camera here to show you
some of these books.
Uh So I try to pull, pull books for everything.
So do you have a kid who's really interested in Star Wars?
Well, there's a counting book for that. Now with counting books,
um you want to be looking for typically three things.
One is that the number form is represented here.
So I see that with the, the numeral eight,
the number word is represented.
So I see that with the E I G H T and then you want to be able to
be able to uh you want to be able to count eight things and they
should be clear and easy to count.
So as I look at these little Jawas on this page, 12345678,
they are easy to count. Now,
the other thing you wanna look at with number books is do they
count past 10? Which is why I chose this Star Wars book.
Not just because I love Star Wars,
but because about 65% of counting books stop at 10.
And do you know what the two most difficult numbers are for
students across um, zero through 20? It's 11 and 12.
And so think about, do your counting books,
do the teen numbers or do they go to numbers that are greater
than 20?
So really think about that as you're selecting some of these
counting books to do with kids, do they have the number,
the number word and a representation of that number?
Is it easy to count? And does it go above 20?
But there are books for so many other things.
Um This is a really cute book, 100 Hungry Ants.
Um This book helps us get into thinking about uh place value.
So sets of 10 and sets of 100 the different ways that we can
organize 100. Um Here is one of my favorite books.
This author Greg Tang has a lot of really great books.
Some of you probably already have some of these.
Um this book of his is about multiplication and it's about
multiplication of squares.
And so here it talks about two times 23 times 34 times four and
so on.
And it has some really nice little visuals and stories that go
along with that as well,
but not all books are just about number probably geometry is
gonna be important for some of you to talk about with your
students.
This is a really nice book about three dimensional figures that
has this kind of cute story about these kids going to the
pyramid and working with um different three dimensional figures
like these here.
Uh This is a nice book that involves a broken tile and this
relates to a tool called the Tangram.
Some of you probably use these in school or some of you,
your kids use these.
But a tangram is just seven shapes that you can put together to
make a square and also a lot of different shapes such as
alligators, bunnies, cats, dogs, et cetera.
Some other things you might want to emphasize with your books in
math. Uh This is a book about time.
So it's called Just a second and it talks about different
variations of time.
This is a book about size and so on this one.
Um This one has some like things about the actual size of
different creatures because that's always hard to conceptualize
if you actually haven't seen um you know,
different animals in the wild. This is a book about fractions.
So pizza is often one of those things we think about about both
fractions.
And then this last book I'll share with you called Mapping Sam.
Um This is a book about where we are in the environment and how
we can map different things.
And so um Sam is this cat and we can map Sam in different ways.
So this is like the neighborhood of Sam.
Um This is Sam in the universe and then this is even Sam's body,
we can map bodies.
Um And so thinking about our spatial awareness in our world.
That's part of that book right there.
Now, with books, I'll share just like one more thing here.
I'll go back to the presentation and then I'm gonna ask you
about some of your favorite books.
Um, books are helpful when they are reread.
And so if you're doing bedtime stories or maybe you're just
doing some reading with your kids, it's OK to read the book.
And in fact,
we have a thing we've been doing with preschoolers and
kindergartners where we read the book three times with them in a
week.
Um At first we talk about some of the vocabulary that they might
see in that book and so much of the vocabulary is just general
vocabulary, but some of it might be mathematical in nature.
Um And then we talk about making real life connections.
And so maybe thinking about just reading the book,
but are there activities that you could do at dinner or on the
way to school the next day that would then tie those connections
in the book to the student's real life and that's when hands-on
activities come in.
So this is, um, for the book called the Mitten. Um,
you can play a mitten match and then look at all those questions
for discussion,
like how many of you have or how many mittens and gloves do you
have? Or why do we wear mittens or why do you think the animals
crawled into the mitten? And why, how big are your mittens?
And how big is a bear? I mean,
all of this just seems like we're asking kids a lot of questions,
but all of it is mathematical in nature.
There's a lot of really cool things we can do as we read
children's books that have a mathematical focus and as we do
activities and ask a lot of questions along with those.
So, in the chat, would you please share?
I'll go back to our page,
some of your favorite children's books about math.
So, what are some of the things that you're reading, um,
or that you've found that your kids really enjoy?
Go ahead and drop those in the chat.
And as I said, I, um, and Jordan dropped, uh, on my web page.
I put in a spreadsheet of some different math books.
I think the last time I updated it was 2021.
So I'm sure there are many books that have been published since
then. So in the chat, I see, um, tent Friendly Fish,
I just got a new book about um eight little planets.
I like that. Counting book.
I also bought a new one recently called billions of bricks.
It's about billions.
Um Jordan says counting books in both English and Spanish. Yeah,
there's quite a few of those uh these days and actually a lot of
mathematics books are in both English and Spanish or English and
other languages. Pearl likes bedtime math. That's a great one.
Yeah.
Counting Kisses is probably one that some of you have used with
your kids before.
So there are a lot,
I would kind of encourage you that if you are still at the age
where you are doing bedtime stories with your kids, you know,
at least once a week,
choose a math focused book or you might have to check out some
from the library or maybe if you wanna purchase some, um,
online or at your local bookshop. But, you know,
not every kid has a lot of math focused books in the home.
In fact,
researchers go into the home and do account of what they call
the student's home numeracy environment and often the number of
math focused books to just non math books. Um,
usually about only 10% of a child's books are focused on math.
So that might be away on their next birthday or maybe at the
next holiday if you want to buy some books for your child,
maybe get some math focused books in their homes and then
there's books for older kids.
So Julia talks about the Math Inspector series and I, I'm,
I'm sorry, I'm looking past you.
But over here on my shelf, I have quite a few of these as well.
But there's some books that are like anime, math books.
And there are also some books for middle schoolers and maybe
even into high school where there's like these math
investigations that students have to solve, um,
in order to read through the book.
So some ideas there might be helpful as well.
And then we get to some virtual tools.
Um Our virtual tools go back to this idea that we want students
to see math in lots of different ways.
Um There are many, many, many virtual tools available right now.
Um If you follow this QR code or you follow this bit,
it'll take you to landing page that I created where you can
explore some of those virtual tools.
And so what I'd like to do right now is I'd like for you to show
you uh that landing page and and explain some of the virtual
tools that you might be able to find if you are working with
your student in math. So let me go ahead and get there.
So I got to share my screen one more time. All right.
So if you go to, we'll just go to,
we'll say Google is my search engine of choice today.
And if I go to bit at dot slash S R Pal.
And I'll also give you the QR code.
It gets you to this landing page here of just a number of free
virtual manipulatives.
So let's say that your student comes home with some homework on
place value. So click on place value here.
So here are free virtual base 10 blocks.
So they might be using the hands on version at school.
Now, you have access to those at home.
If I just click on any one of these,
I'll go ahead and click on this from.
Maybe you want to show students what it means to show uh 122.
So I could show 122 and I can just drag and drop those virtual
manipulatives there.
Maybe your student comes home and they are wanting to focus on
things with counting.
So there's a lot of really great early manipulatives that you
might want to use here.
Um Speaking of dice, look, we have virtual dice,
but I like these virtual unfix cubes. So here,
maybe I want to show what happens when I add two plus three.
So I could take two red counters and add three green counters,
two plus three equals 12345.
So I've got some virtual manipulatives that can help me with
that.
Maybe you have some kids that are working on fractions and um
fraction strips are a really helpful thing to have there.
So I could click on this tab here.
Um, here are some different fraction strips perhaps.
I want to show, uh, one what happens when I have one half,
I've actually got to move that back.
Um, plus I just want one third. I'm gonna take that.
And so what have I got to scroll this? There we go. One third.
I can put those together to show is one half,
plus one third is less than one or greater than one.
Is it less than one half? Greater than one half?
And there's a lot of really cool stuff that you can do with
these different fraction bars.
The virtual geo boards are some of my favorite things.
Probably some of you have some nightmares from when you were in
school and having these geo boards and the rubber bands flipping
all over the place. These virtual geo boards are awesome.
Maybe you want your student to play around and make some
rectangles. Um They can also show fraction.
So if I was trying to show the fraction two thirds first,
I might show a rectangle with 1 to 3 equal parts and then I can
use a different color rubber band to rubber band over two of
those three parts.
So right there, I've showed the fraction two thirds.
Uh many cool things we can do.
Um And then just a few other things if you're working with kids
that are doing algebra,
algebra tiles are really popular manipulative these days.
So here's an example of those.
And so I can just um drag and drop these algebra tiles to show
different types of things in algebra.
If you are working with kids uh with geometry, there's here,
we've got virtual pattern blocks, geo boards,
the pen Tomio and the Tetromino. These are ways to help.
Um I have to click on those. There we go.
Um These are ways that I can uh show how,
how to put sets of things of four together or things of five
together. Probably many of you.
This looks like Tetris and that's pretty similar to what it is.
There's the 10 g there. I showed that book about 10 g earlier.
Um There are also virtual manipulatives for time and money.
There's virtual manipulatives for like graphing.
Probably some of you are asking your students to do that or
creating spinners.
And oh what happens when we land on this number and then there's
a few extra things, you know,
if you want timers or thermometers or just numbers or fact cards
or, you know, whatever it might be.
Um There are so many virtual manipulatives these days,
you all um I would just like you in the chat to drop in any that
you've used or that your kids have found helpful.
So if you want to go ahead and put those in the chat,
I'll join you in just a minute and return to our presentation
and there's the QR code. If you want that landing page again.
Um,
and I'm not the only person who's put a landing page of virtual
manipulatives together. Um,
but I find it helpful to have them all in one location instead
of spread out across a lot of different websites.
So I'm gonna come to the chat to see, um, oh,
I'm not showing my face. There we go. Ok.
Um, so I'll see if, let's see what we go. Here we go.
Um See if anybody has dropped any of their virtual manipulatives
into the chat.
Uh uh has a lot uh toy theater, has a lot uh demos,
has a lot of virtual manipulatives.
There's a lot of different ones that you might wanna try.
Um Some of you probably are using technology to practice facts
or computation.
So there's a lot of programs out there that you might be
interested in.
Um And then I put in a few other resources I was able to develop
a free course.
So this is a virtual tool for you for best practices for
teaching math, particularly when students struggle with math.
And so if you visit intensive intervention dot org,
you can see that resource there.
Um And I also created a bunch of videos for um this project
called Project Stare.
So this is how to compare 3/5 to 4/5 with the fraction circles.
And so there's a lot of virtual videos that you might want to
check out or even watch with your student to see how to do some
of these different things in math.
So people can drop their first favorite virtual tools.
Maybe you don't have one yet. That's OK.
Um But I do wanna let you know that there's a lot out there now
before we close for today,
probably one of the things that some of you are doing is
supporting your kids with word problems.
And um Jordan knows this, But when I talk about word problems,
you're probably gonna hear me talk for hours about word problems
because it is a pretty complex task and there's a lot that goes
into it,
but I'll just leave you with a party thought about word problems.
And one of the things to not do when it comes to helping your
kids with word problems and that is taking keywords and tying
them to operations.
So over here on the left hand side is what we would call a
keyword poster.
And I'm gonna go ahead and put my animations on this slide
because I want to cover it up.
Um a keyword poster takes words or terms and it organizes them
by operation.
So when students read a word problem, like at the one in green,
so Lincoln had eight pencils fewer than Rosco.
If Rosco had 18 pencils, how many pencils did Lincoln have?
There? Many times kids will identify that keyword to fewer,
they'll look at the keyword poster over there where fewer means
subtraction. And if they subtract to solve the green problem,
they will solve that problem. Correct.
But look at the red problem.
Lincoln had eight pencils fewer than Rosco.
If Lincoln had 18 pencils,
how many pencils did Roscoe have there? I see fewer.
I look at my keyword poster. Few.
I uh fewer tells me to subtract.
And if I subtract to solve that word problem,
then I'm not going to solve the problem, correct.
So every time that a keyword works in a word problem,
I will challenge you and also say that a keyword will not work
in the word problem as well.
Now, these keyword posters are very prevalent.
Um This is just a casual search on my favorite search engine for
keyword math posters gonna go ahead and cover it up.
So none of you take a picture of it there.
Um You can also purchase these um but they're problematic and
here's why.
So uh we did an analysis of all the released items for a series
of word problem tests across grades three through eight.
And we organize these by problem type which I can talk to you
about another time if you're really interested.
But what we first did is in yellow and we calculated the
percentage of the time word problems have a keyword in them.
And you can see across these different problem types that
keywords are in these problems anywhere from, you know,
60 70 80 to 100% of the time.
But then we solved the word problems using keywords.
And here our success rate for solving those problems varied
anywhere from 26% of the time to 80% of the time.
So, not terrible, right? But not great.
But then it got to multi stepp word problems,
which is where many of your kids are going with their word
problem solving skill starting in grade three and beyond.
So the first question was how much do keywords appear in these
multi step word problems?
And here the percentage of the time was anywhere from 76% of the
time to 100% of the time, almost always in the nineties.
But then how often does that keyword help me solve the problem?
Correct?
Then it's less than 10% of the time and I'll just show you some
word problems that your students might be asked to set up and
solve. And if I ask you, well,
what is the key word in this word problem?
That's almost an impossible question to answer.
So if I look at the orange problem, is it before?
Is it taken out? Is it total? If I look at the blue problem?
Is it total? Is it same?
Is it each or if I look at the purple problem? Is it decreased?
Is it per is it overall, is it change?
So most problems that students solve,
especially beyond 1st and 2nd grade have multiple keywords And
so for that reason, you cannot rely on this keyword strategy.
But I will say,
and I think this gets to one of the comments that came into the
uh chat where someone said their daughter has learned a lot from.
I read her math vocabulary is amazing.
Yeah, because it's focused on math vocabulary.
So these math vocabulary terms,
these keywords are really important.
We want to talk about them, we want to discuss them,
we want to see them in books and have conversations about them.
But the thing that we want to avoid is we never wanna say,
oh when you see that word,
that means you do this thing like add subtract multiply or
divide, that's the thing that we don't want to do.
So that will be all that we talk about for today to just leave a
few minutes here at the end to answer any questions or um you
know, have you drop some more resources into the chat?
But the idea is that if you're doing math at home, um you know,
often you're doing homework, right?
But think about playing games and doing activities,
think about math through reading books and talking about those
books and talking about the vocabulary in those books.
Think about some of the virtual tools that you might want to
access,
whether those are programs and games or whether those are
different types of virtual manipulatives.
And then if you are helping your student with the solving of
word problems do make sure that you're not falling into that
keyword.
Um Hole, we do not wanna use keywords to solve word problems.
So I'll finish there. Um See if there are any questions,
please go ahead and drop those into the chat.
I'm totally happy to talk about those now.
And if you don't have any questions,
I just want to thank you for joining me tonight.
I want to thank Jordan um and the school for inviting me to talk
with all of you. And if you do want more resources,
please feel free to reach out to me. You can email me,
you can find me on social media and I just um you know,
hope you continue the math conversations with your kids at home
because so many of the math conversations at home will then
really help your students at school.
So thanks so much for joining us and I'll go ahead and finish up
there. I have a question for you. Yeah, take it away.
So um sorry,
I I um I my question is like for older kids like kids who love,
love math. Um What?
Because obviously your your information was great.
Um Little for younger.
Yeah, but I'm thinking like, you know, advanced elementary,
middle school and even on to high school, like,
do you have a list of resources you could possibly provide I
with just that, you know, like I know kids like, you know,
the advanced geometry.
Like if you start, you're interested in a protractor how,
how you can extend it or even, yeah,
even your bibliography of math books for older kids.
Um That would be super cool. Yeah. So if you uh email me,
we have some list of manipulatives by content and also by grade
level.
So um I will tell you Michelle all of my stuff really kind of
goes through grade eight.
I don't spend a lot of time in the high school space,
but I do have a colleague that only works with math and high
school. So he would be able to share some stuff with you.
But yeah, there are a lot of really great manipulatives.
Um So I'm looking at my office and I'll show you I'll show I'll
tell you about some and then I can send you the resource.
But um so in the middle school grades there, there's these,
the manipulative called coordinate peg peg boards that first
help students understand one quadrant and then you can actually
move the X and Y axes on these. They are literally movable.
So you can either create,
create a two quadrant grid board or four quadrant and then
students can plot ordered pairs and they,
I can actually like plot quadratics with a rubber band.
It's a very cool.
Um There are also some really great algebra manipulative.
So how you as you get to understanding integers,
things with zero pairs.
So you know if I have a negative one and a positive one those
canceled to zero and then whatever you do to one side of the
equal sign you do to the other. So properties of equivalence,
both the algebra tiles and what they call the alga blocks.
The alge blocks are absolutely amazing and you can do some
really cool stuff with fact screen all the way with cubes.
Um And so they actually have all these different yellow,
orange and green manipulatives and these really cool mats so
that you can use those through like through eighth grade algebra
and into high school because often middle school teachers will
tell me like, oh those, you know, these are for kids, right?
These are for little kids, they're colorful and I'm like, oh no,
there's algebra manipulatives,
there's the hands-on equations which are another really great
tool and um there's some really neat stuff you can do with
balance scales and positive and negative numbers there and I'm
happy to send those to you as well. Thank you so much.
This was great. Thank you.
Any other questions?
All right. Well, if there are,
if there aren't any um I know that was a lot of information in
only one hour.
Um But I do wanna thank you Sarah or uh Doctor Powell for
joining us today, you know,
um and uh spending your own time on this as well.
So, um if, if uh what I will ask is that actually,
if you can send me actually maybe a link to those resources and
like a Google doc,
then we can even put that on the website for uh for us to uh put
on our website for our parents to um use and uh and at you,
you know, like this is hopefully gets the conversation started,
but probably a lot of people are doing things at home and it
would be really great for people to learn from one another as
well. Correct. Correct.
Well, thank you everybody for joining us tonight.
I, I hope this was a fruitful presentation and um,
and for a school that, you know,
is highly performing in mathematics,
there's always room to get better. And so, um,
let's continue this conversation and have a good night,
everybody. Thanks Jordan. Bye bye. Thank you.