0:01

Hey fellow

0:01

mathematicians! Welcome to the

0:04

podcast where Math is

0:04

Figure-Out-Able. I'm Pam Harris.

0:09

And I'm Kim Montague.

0:10

And we make the

0:10

strong case that mathematizing

0:13

is not about mimicking steps or

0:13

rote memorizing facts. But it's

0:16

about thinking and reasoning

0:16

about creating and using mental

0:21

relationships. We take the

0:21

stance that not only are

0:24

algorithms not particularly

0:24

helpful in teaching, but that

0:28

mimicking algorithms actually

0:28

keeps students from being the

0:32

mathematicians they can be. We

0:32

answer the question, if not

0:36

algorithms and step by step

0:36

procedures, then what?

0:40

So we're in the

0:40

holiday season for a lot of us

0:43

and you may be home with your

0:43

kids. So last week, we talked

0:46

about some of our favorite games

0:46

and suggested some things that

0:49

maybe you wanted to add to your

0:49

list.

0:52

For gift giving,

0:52

right, and so we want to share a

0:52

For gift giving. little bit about ways that you

0:55

can bring math into your

0:59

family-time while you're home with your people. So if you're

1:02

spending a little bit more time

1:04

with your people, this time of

1:04

the year at home, I know I'm

1:07

going to be, we're gonna have

1:07

all of our kids here this

1:10

holiday season. I'm so excited

1:10

to have them whole home. We're

1:13

kind of empty nesters a little

1:13

bit. And so having all four plus

1:16

the two new is just going to be

1:16

really fun. What kinds of things

1:21

might you do if you have littles

1:21

at home and you want to kind of

1:25

bring math more into your home

1:25

and your experience with them?

1:28

We often get questions from

1:28

teachers about what they can do

1:33

with their own littles and what

1:33

they can tell their parents, so

1:36

parents of their students, what

1:36

can they do as they have their

1:41

students at home with them? And so we thought we'd spend just a minute talking about some of the

1:43

things that we've done in the past, some of the things we

1:44

think that would work well, as

1:47

you're just sort of going about

1:47

your normal everyday stuff. So

1:52

I'm going to just say I like to

1:52

bake. And I don't bake a lot,

1:56

but I do around December. So

1:56

when it gets near Christmas, for

2:01

me and my family, I'm a baking

2:01

machine, which also means I do

2:06

tend to put on a few pounds, I'm

2:06

not going to do that this year.

2:08

This year I'm gonna exercise. There's some math! Yeah, there you go. I'm gonna

2:10

exercise, exercise, exercise so

2:13

that I can imbibe just a little

2:13

bit. But anyway, I do like to

2:17

bake, we like to make fudge. We

2:17

like to make sugar cookies and

2:20

decorate them. And in fact, a

2:20

colleague of ours, Holly, has

2:23

just told me a new recipe for

2:23

frosting. I'm excited to try it.

2:27

And as I try that new recipe for

2:27

frosting, I'm going to be

2:30

talking out loud with my kids.

2:30

I'm going to say things like,

2:33

"What if we were only making

2:33

half of this recipe?" So

2:36

especially when you're talking

2:36

with students, or kids that are

2:40

just starting to learn

2:40

fractions, grab something that

2:43

needs like a half a cup, or a

2:43

half a teaspoon and say things

2:46

like, "What if we're only making

2:46

half a recipe? What is half of a

2:50

half?" And when they say, "Well,

2:50

we could just eyeball it." You

2:53

could say, "Well, sure we could.

2:53

But do we have a spoon or a cup

2:57

that is that measurement? Like

2:57

could we think about that?" I

3:00

know, I've been talking to a

3:00

friend in South Africa that

3:03

measures things in milliliters.

3:03

And she was talking about how

3:07

they're often thinking about a

3:07

quarter of 1000 milliliters. And

3:10

so what does that look like?

3:10

Well, what is a quarter of 1000?

3:13

Can you think about a half of

3:13

1000? Can that help you find a

3:17

quarter of 1000? So instead of

3:17

just using the cup that it says

3:20

start wondering about half of a

3:20

batch, you don't even have to

3:23

make half of a batch. Just

3:23

wonder about it out loud. Or

3:27

triple it or quadruple it or you

3:27

know, in some way, kind of - and

3:30

then when you're tripling and

3:30

quadrupling recipes, and even if

3:34

you're actually doing it or

3:34

wondering about it, don't choose

3:37

the thing, where it's like, hey,

3:37

we need one cup of flour. If we

3:40

triple this, how much are we

3:40

gonna-? Like don't use that one.

3:44

Ask the one where you need three

3:44

tablespoons of something. If we

3:47

triple this, how many will we

3:47

need? And then - let me just

3:51

stay there for a minute. So I

3:51

don't make pancakes very often.

3:54

Except when all my kids are

3:54

home! Then I'm like, "Hey, let's

3:57

have some waffles or pancakes or

3:57

something." Well, I have a

4:01

homemade recipe that calls for

4:01

three teaspoons of baking

4:04

powder. So three teaspoons of

4:04

baking powder. Well, if I'm

4:07

going to quadruple that batch, I

4:07

can put in three times four, 12,

4:10

teaspoons of baking powder. I

4:10

can do that. At one point I said

4:14

to my son, I was like, "Dude,

4:14

figure out what other

4:17

measurement that is. I don't

4:17

want to sit here and measure 12

4:20

of those, like, can we figure

4:20

out is there some..." can it be

4:23

a quarter of a cup plus another

4:23

teaspoon? Like there's got to be

4:27

some kind of - and honestly, we

4:27

wrote it down. I don't remember

4:30

what it is anymore. But that's

4:30

the kind of conversation that

4:34

you could just have just like

4:34

sort of raise it like, I'm lazy.

4:37

I don't want to measure all

4:37

these out, could you kind of

4:40

help me think about that.

4:42

Yeah. So I I'm not

4:42

a real big baker.

4:47

Okay, you're not a baker at all.

4:49

It's not my thing.

4:49

But I do have a son who loves

4:53

the things. He loves dessert.

4:53

And so I have started saying to

4:56

him, fantastic. I'll buy the

4:56

stuff, but you're going to help

4:59

me and it's been wonderful. He

4:59

has his own little cooking set

5:03

with, you know, spatulas and the

5:03

measuring cups and things. And

5:07

he's really, because it's for

5:07

him, and because he's invested,

5:11

then he has spent more time

5:11

talking about measuring tools

5:15

and different amounts and

5:15

fractions probably earlier than

5:19

he would have had he not been

5:19

involved. So just involving them

5:22

in general, I think gives a lot

5:22

of opportunity to have those

5:25

conversations. Also, my kids

5:25

often, thanks grandparents, get

5:31

money around this time, and they

5:31

spend time planning out what

5:38

they think they want to get for

5:38

spending on their money, right?

5:41

So because they have Amazon,

5:41

they can look on the Amazon.

5:46

Find out how much something

5:46

costs, and they want to know,

5:49

are you covering tax for me?

5:49

Which is the answer: no. So they

5:52

have to calculate how much money

5:52

do they have? And how much are

5:56

they gonna have left when they

5:56

spend it? Do I want to spend it?

5:59

So lots of adding and

5:59

subtracting decimals

6:02

considering, you know, saving

6:02

and spending every year.

6:07

I'm sure they're

6:07

also doing some estimating and

6:10

rounding and making sense of

6:10

things.

6:12

Oh sure.

6:13

Yeah, nice. And so

6:13

rather than just a bit of trial

6:16

and error, you're actually encouraging them like, let's plan this. Let's actually, you

6:18

know, like, make some sense of

6:20

things. Isn't this the time of

6:20

the year for book orders too?

6:25

Well, lots of

6:25

different times throughout the

6:27

year are Scholastic book order

6:27

times, and so same kind of

6:30

thing. You know, a lot of them

6:30

are 99 cents, or 2.99. And so

6:34

there's a lot of opportunity, we

6:34

get holiday book orders most

6:37

often. And so there's a lot of

6:37

opportunity for nice round

6:41

numbers, right? No. They're all

6:41

99s. But it's been so much fun,

6:46

because we can have

6:46

conversations about estimating

6:49

or thinking about the total

6:49

amount and then backing off a

6:53

little bit since they have a lot

6:53

of 99 or 98 cents compared at

6:56

the end.

6:57

Absolutely. Lots of

6:57

over strategy going on there.

7:00

Uh-huh.

7:00

Very cool. So

7:00

another thing I'm thinking about

7:03

is involving my kids, when they

7:03

were younger, in wrapping

7:06

presents. And just like, "Hey,

7:06

this is a rectangular prism.

7:09

Like are you gonna do this the

7:09

long way, the short way?" And

7:12

kind of the spatial sense of

7:12

wrapping presents and sometimes

7:16

letting them use too much

7:16

wrapping paper. And then

7:18

noticing that. I mean, "Wow

7:18

because you did it that way,

7:21

look how much extra if you would

7:21

have done it this way." But

7:25

also, we have kind of a funny

7:25

thing in our family. My husband

7:28

refuses to wrap anything that is

7:28

not a rectangular prism. So

7:31

whatever it is - now I'll like

7:31

jury-rig it. I'll like make a

7:34

big, like bon-bon out of it, you

7:34

know, where you sort of like

7:38

wrap it up and kind of have the

7:38

ends and put ribbons on it. And

7:41

he looks at me like, "Are you

7:41

serious?" Because it's lumpy,

7:44

whatever. And he's like, "No,

7:44

then we can't stack it." And I'm

7:48

like, "Why do we have to stack

7:48

the presents, can't we-?"

7:51

Anyways, every year it's an...

7:51

argument? It's a discussion

7:54

between him and me. He will find

7:54

a box, no matter what. He will

7:57

find a box to put it in, and

7:57

then he'll wrap the box and it's

8:00

whatever. So a couple years ago,

8:00

I decided, Oh, yeah. Oh, yeah.

8:04

So I bought a box of boxes.

8:04

These beautiful, like they're

8:07

already kind of like they're,

8:07

well they aren't really wrapped,

8:10

but you don't wrap them because

8:10

they're like already wrapped.

8:14

And I'm like, "Here, here,

8:14

honey, here you go." And he

8:16

loves it. Like it was a big joke

8:16

for me. And he loves it. He's

8:20

like, "I'm just putting

8:20

everything in those boxes."

8:22

I might need those.

8:23

It kind of saves

8:23

wrapping paper too. So that's

8:25

kind of a nice earthy thing.

8:25

Yeah. All right. I'll give him

8:28

that. Fine. Fine. Alright, so

8:28

another thing that we do around

8:32

our house is after we make all

8:32

that stuff, like Christmas

8:36

cookies and fudge, and can I

8:36

even think of all the other

8:39

things? Mostly those. We make a

8:39

ton of different kinds of

8:42

cookies though, there are kinds you can - you don't care. Anyway. So after we make all

8:44

that stuff, then we will take

8:48

them to our neighbors and carol.

8:48

So we like to sing in our

8:51

family, which I know - "Don't

8:51

sing on air," my kids are saying

8:55

right now. "Please, Mom, don't

8:55

sing on air." So I'm not the

8:57

soloist in the family. I could

8:57

carry a part, I can carry a

9:00

tune. And so out of us we have

9:00

good four parts. So we go

9:03

caroling. As we do that, I will

9:03

often have the discussion. Okay.

9:07

So if we're going to go carol to

9:07

our six neighbors, or whoever we

9:10

choose that we're going to, you

9:10

know, deliver some goodies and

9:12

go caroling. How many of these

9:12

kinds of cookies should we make?

9:15

How many batches of this should

9:15

we make? Like, how many plates

9:18

do we need? How much plastic

9:18

wrap, like whatever, all the

9:21

things, I just don't do it all

9:21

myself. I just involve my kids

9:25

in the conversation. It has

9:25

actually been interesting to

9:29

then have my daughter come back

9:29

and say, "Hey, I was asked to

9:32

make this stuff for this thing.

9:32

And because you're always

9:35

involving me when you're

9:35

deciding how much to make, and

9:37

how many of all the things,"

9:37

she's like, all of her peers -

9:40

so she's at university level,

9:40

she's 20 years old- she's like,

9:44

"All my peers they were like,

9:44

how do you know how much to make

9:46

and how much to buy?" And she's

9:46

like, "We do this all the time."

9:48

Anyway, so just the more you can

9:48

kind of involve them in that

9:51

kind of whatever it is that you

9:51

do, just involve them in the

9:53

conversation. You know, like I

9:53

mentioned, we're gonna have a

9:56

new frosting recipe, alright,

9:56

like let's decide. It's new. So

10:01

I got to like, figure out how much are we making, how much of the ingredients we're gonna

10:03

make. All that kind of stuff.

10:05

You're giving them experience, right? So that they can fall back on that

10:07

experience, just like we talked

10:09

about a couple of weeks ago.

10:11

Yeah, that's what teaching is all about, let's give them the experience.

10:13

Absolutely.

10:15

So I will admit

10:15

that because we are a little on

10:18

the go and a little busy, we do

10:18

not do a super often regular sit

10:24

down dinner together. So this is

10:24

especially common during this

10:29

time, lots of like, face to

10:29

face, fully intentional meals.

10:34

So wait, wait. So when you said you don't? That's because typically -

10:37

Typically it's

10:37

sports and things and all the

10:40

clubs and whatever. Right? So

10:40

this time of the year, there's a

10:44

lot more of that. And so we

10:44

actually like to play dinner

10:48

games as well as board games.

10:48

And so we will play games like

10:54

Guess My Number or play I Have,

10:54

You Need a little bit with

10:57

something a little funky, a

10:57

little bit different, maybe some

11:00

fractions now that they're

11:00

older, maybe with some decimals.

11:03

Not long. Not long enough that

11:03

it's 30 minutes of me, you know,

11:06

drilling numbers at them. But as

11:06

they're setting the table, we

11:11

will play a little something. We

11:11

have pulled up MathStratChat and

11:16

had conversations about it. Now,

11:16

that might not be super

11:19

interesting to everybody. But it

11:19

might be. If you've never tried

11:23

it, it might be interesting for

11:23

your kids to just hear you talk

11:26

out loud about how you're

11:26

thinking about something. And

11:29

the more experience they have

11:29

with that, the more natural it

11:32

will become.

11:33

Nice, nice. And you

11:33

mentioned setting the table. So

11:37

ya'll, if you have littles a

11:37

thing that you can do is say,

11:40

"Okay, let's set the table. How

11:40

many - pick it - plates do we

11:44

need?" And then when the little

11:44

you know, I'm talking three,

11:47

four or five year old, when that

11:47

little says, "Well, I don't

11:50

know." Then you can say, "Well,

11:50

how many people do we have?" And

11:53

if they say, "Well, we need lots

11:53

of plates. We need 100 plates!"

11:56

So you go, "100 plates, wow!" Or

11:56

if they say six, and they're

12:00

just guessing, then give them

12:00

six. And when they put them

12:04

around the table, and there's

12:04

extra, you can say, "Oh, how

12:06

many did we really, actually

12:06

need? How many extra do we have

12:09

then? Because since you said

12:09

six." Or six would be exactly

12:12

what my family would need until

12:12

I just got two new

12:14

daughters-in-law. But yeah, the

12:14

point is like estimate first,

12:19

give them the number that they

12:19

said, kind of build that one to

12:21

one idea. How many do we need?

12:21

You think that many? Let's try

12:25

it out. Oh, that wasn't enough.

12:25

How many more do we need? Okay,

12:28

well, that's interesting. We

12:28

needed five plates. We needed

12:31

five cups as well, who knew?

12:31

You're just sort of noticing and

12:36

kind of bringing it up as you're

12:36

kind of just doing the stuff

12:38

that needs to happen anyway.

12:38

Yeah, totally cool.

12:42

I think something

12:42

that you and I both do is go on

12:45

walks with our families.

12:46

We can do that.

12:46

because we're in Texas. So the

12:49

weather is usually ok.

12:50

I mean, it's like

12:50

82 yesterday, and it's December.

12:53

We can hope it'll

12:53

get down into cooler weather

12:55

when it's time to go on walks.

12:55

Yeah.

12:57

So we do go on

12:57

walks. And I don't know if you

13:00

guys do anything besides chat.

13:00

But a lot of times my kids are

13:03

not super excited about going on

13:03

walks. And so we'll play games

13:06

as we're going on walks, and

13:06

we'll count steps and then

13:09

predict how far we've gone when

13:09

I announce the time. So it's

13:12

been 10 minutes, how many steps

13:12

have you gone? Or we've gone

13:16

this many steps, how much time

13:16

do you think has gone by. Just

13:20

to start estimating like, time

13:20

and space and distance. So just,

13:26

you know, little conversation

13:26

about little mathy stuff.

13:30

I'm wondering, do

13:30

you ever look at the house

13:33

numbers and say, "Hey, can you

13:33

factor that? Or is that a

13:36

prime?"

13:37

That's a me running thing, not a a kid walking thing.

13:39

Oh, that's only when you run?

13:42

I should totally

13:42

do that though. I hadn't

13:45

considered that.

13:45

I mean, you used to

13:45

chide me a little bit, you're

13:49

like, "You know, Pam when you're

13:49

running." Because yeah, I jog,

13:51

Kim runs. I used to jog, until I

13:51

had knee surgery, long story.

13:54

Anyway. But she would say, "You know, like, when you're doing that, don't you you know, look

13:56

at the license plates and begin

13:59

to wonder." And I was like, no,

13:59

until I built more

14:02

relationships. And now I can.

14:02

Now I own more. So I actually

14:07

can play with stuff. So play

14:07

with whatever numbers that you

14:10

see, that totally can work. We

14:10

also talked about things that we

14:13

do on car trips. Now I'll be

14:13

honest, my kids are not as

14:17

excited to play car trip games.

14:17

So I have tried lots of games. I

14:24

think is partly because a couple

14:24

of mine get car sick. And so

14:27

they're like stop with making me

14:27

think kind of things. We do play

14:31

a game called Cows On Your Side.

14:31

Whereas we're driving down the

14:36

road, if you see cows on your

14:36

side, then you say cows on my

14:39

side and you get a point. If you

14:39

first see the cows on the other

14:43

side of the car, then you say

14:43

cows on your side then you get

14:45

two points and they have to lose

14:45

a point. Oh, so you can totally

14:49

keep track of points if you want

14:49

to. We have totally gone on car

14:53

trips with the team especially

14:53

when we're going to film and so

14:55

we're all in my van. And no one

14:55

will play with me, which is

15:00

tragic, except Sue. Sue play

15:00

with me kind of. She has her own

15:04

version where she just will

15:04

randomly yell out, "Cows on my

15:07

side," or she'll yell out things

15:07

like, "Buffalo on your side or

15:10

sheep on my side," or it's just

15:10

kind of like it almost could be

15:13

road sign on my side, it doesn't

15:13

really matter, Sue will just

15:16

yell out some funny thing on her

15:16

side. And we don't really keep

15:19

track of points. But anyway, so

15:19

if you want to play points, Cows

15:22

On Your Side can be fun,

15:22

depending on if you're driving

15:25

somewhere that has cows. So I

15:25

guess I always grew up in a

15:28

state that had cows. Do all of

15:28

the United States states have

15:31

cows? No? Alright, on Twitter, I

15:31

want to hear from you if you are

15:34

in a state where you will never

15:34

see a cow. I want to hear from

15:38

you. I mean, if you live in a

15:38

city, a big city, I get it. But

15:41

if you get out of the city, I've

15:41

been in New York state there are

15:44

cows. Anyway, moving on. Kim you

15:44

actually play games with your

15:47

kids in the car. Give us just a couple quick ones.

15:49

So I think we've

15:49

talked about this before. We

15:52

wonder a lot. So my kids will, I

15:52

have always tried to just wonder

15:57

aloud, like we've suggested

15:57

several times here. And so they

16:01

will wonder aloud as well. And

16:01

so we'll wonder things about

16:04

mileage signs or how long until

16:04

or if we're going this fast how

16:08

long until we get there if it's

16:08

this many miles? Yeah, I think

16:15

we've talked about this before, maybe not.

16:16

How far are we

16:16

going? How far have we gone? So

16:21

if we've gone that far, is it

16:21

gonna take us you know, we're

16:23

gonna speed up, slow down? Yeah,

16:23

just all sorts of rate

16:26

questions. Totally cool. So

16:26

y'all maybe the most important

16:30

thing to think about as you're

16:30

sort of maybe spending some more

16:34

together time if you're trying

16:34

to bring some math conversation

16:37

into it, is just involve

16:37

everybody in your thinking,

16:41

wonder aloud. Ask them how

16:41

they're figuring things, share

16:45

your thoughts. Just sort of put

16:45

it out there and kind of see

16:49

what happens. So if you want to

16:49

learn more math and refine your

16:53

math teaching so that you and

16:53

students are mathematizing more

16:57

and more, then join the Math is

16:57

Figure-Out-Able movement to help

17:00

us spread the word that Math is

17:00

Figure Out Able!