Eight is Great

Eight years ago today was a pretty big day in the whole scheme of things--a new eternal family began. That's pretty huge to begin something that doesn't have to end. And I'd say after these eight years that this adventure called family life is beyond great. I've told Aaron many times that he should give good husband lessons. He is just so unbelievably good to me. It makes me think of some sweet, wise words spoken by Aaron's Dad. We were down in Texas celebrating their 50th anniversary and I heard someone ask him, "Wow, 50 years, how did you do it?" He replied humbly, "well, it wasn't hard, being married to her." That's how I feel about Aaron; it isn't hard being married to him.

Well, I was going to do something all cute and sappy and list eight of the reasons I love him, but then Hazel woke up screaming. Followed by Xander, who had a fever, and then Elodie, who heard the crying and figured she should join in. They are all sleeping snug in their beds again. But now I'm not feeling it, so no sappy list tonight. Just a simple, "Happy Anniversary, honey!"

Ode to Kotzebue

Shortly after we'd gotten home from our Arctic Adventure, I was just doing dishes and found myself singing an impromptu song about Kotzebue. I was just kind of making it up as I went along, so I decided to write it down and extend it to capture our Kotzebue experience!

Oh, Kotzebue!

(sung to the tune of "O, Tannenbaum," which is "Oh, Christmas Tree" for you English-speakers out there)

Oh, Kotzebue, oh, Kotzebue,

There’s no place that’s quite like you.

The tundra may not have real trees,

But who needs these with blueberries?

Oh, Kotzebue, oh, Kotzebue,

She made this Kuspuk just for you.

Oh, Kotzebue, oh, Kotzebue,

They say no roads connect to you.

With boats and planes and snow machines

And don’t forget your sled dog teams

You get to where you need to go,

No matter how deep is the snow.

Oh, Kotzebue, oh, Kotzebue,

There’s no place that’s quite like you.

In villages the Inupiaq

Eat caribou and meat that’s black.

Oh, Kotzebue, oh, Kotzebue,

Muktuk and fish are snack foods, too.

Oh, Kotzebue, oh, Kotzebue,

Yes Arctic is the name for you.

You’re not just white in winter moons.

No, icy snow lasts up through June.

Oh, Kotzebue, oh, Kotzebue,

The frozen ocean is your view.

Math Monday 3

So Many Ways to Make a Dollar

Age: 5 & up (depending on the challenge you give, even adults could be challenged by these)

Concept/ Skills: Money, Interval Counting, Place Value (foundation), Organizing your Thinking, Flexibility in Thinking, Reasoning & Logic (foundation of proofs), Problem-Solving

Materials: a big pile of various coins

Object: To figure out lots of different ways to make one dollar.

How to play: For a 5-7 year old, simply dump out a bunch of money and ask them, "How many ways do you think you can make a dollar?" Tell him to show each way and leave them all laid out so you can look at them. If the kid pretty good at working on this independently, but you want to up the motivation a bit, you could say, "How many different ways can you make a dollar in 10 minutes?" Then at the end of the time, you can lather on the praise when they have found SO MANY different ways to make a dollar. Or if they answer your original question by saying, "I think I can make a dollar in 12 different ways." Then ask, "how long do you think it'll take you to do that?" "OK, I'll time you to see how long it takes you to come up with 12 ways."

For an older kid who's more familiar with counting money, you can ask the more challenging question, "how can you make a dollar using exactly __ coins?" If you think they really need a challenge, ask them one you don't know the answer to and let them really think through it! Remind them to keep track of what they tried so they'll be able to tell you about the process. Older kids don't even need the actual coins, they can just use paper. Even if they do use coins to figure it out, you might want them to keep track on paper.

How to maximize the math learning going on: Let's say you're doing this with a 5-year-old. You ask the big question, "How many ways do you think you can make a dollar?" and they tell you one way. Xander's first response was the simplest, "A Sacajawea dollar!" Ask, "is that the only way to make a dollar?" He replied, "No, we could do 100 pennies." "OK, let's show all the ways we can make a dollar right here on the floor." He is kind of new to counting money, so I found I had to ask him leading questions like, "How many dimes do you think it would take to make a dollar?" And then, "How can you check to see if that guess is right?" I also needed to guide him to organize the money in rows to make checking your counting easier. We grouped the pennies by 10s, each cluster arranged in a 2x5 array. Doing this together helps him to develop the skill of organizing his thinking and his work, which will help him solve math problems more efficiently. Looking for patterns is a big part of math, and it's hard to see those patterns if you leave everything in a jumbled pile. I also found that while Xander is great at counting by 2s, 5s, and 10s, switching gears in the middle is really challenging for him. It takes practice to actually think about what it means to count by numbers instead of just rattling them off like he memorized. Counting money is really good for this. And learning that concept of one thing (like a dime) being worth more than 1 is great for the developing sense of place value.

Let's say your doing this with a 7-year-old (or maybe older--you'll get the feel for where she is as you discuss it). You gave her 10 minutes to see how many ways she could come up with. When the time is up, ask her to show you her ways and tell you how she came up with them. "Do you think you found every way possible? How do you know? Can you think of a more efficient way to find every single way possible?" Those thought provoking questions really increase the challenge level of the problem. At that point, if they seem ready for it and haven't come up with it on their own, you could suggest creating a table with all of the different coins along one axis and using tally marks to keep track. Point out simple things like, "There is only one way to make a dollar with 4 quarters, so you could mark it like this. But if I try 3 quarters, I could first do the 2 dimes and 1 nickel way. (Mark it.) Then I could mark 3 quarters again (mark it) and use the other coins to make $0.25 in a different way. Is there a different way to do it that still uses 2 dimes?"

Let's say you asked an even older kid to make a dollar using exactly 5 coins. After working on it for a few minutes, he says, "it's not possible." This is one of the best opportunities to stretch his capacity to reason and prepare him for more formal proofs to come. "Can you prove that this is not possible?" If you can prove that it can't be done, then you'll be done with the problem. Make sure you write it down in a way that I can follow what you were thinking." If you ask one that turned out to be too easy for him and he solves it super fast, ask him, "do you think you can come up with a number of coins with which it is not possible to make a dollar?" You can actually do these kind of problems verbally on a road trip or something. If you come up with a challenging math problem for them to think about every time they complain, "Mom, there's nothing to do," they're bound to learn something. (Even if they just learn not to complain to mom about boredom, which is a valuable thing in its own right!)

I just love to get kids thinking! We surely wouldn't want our kids brains to turn to mush, now would we? Or our own, for that matter!

Math Monday 2

Finger Flash

This is a quick and easy activity. I got it from a book my mom loaned me, called Teaching Number in the Classroom. All you need is your fingers, so you can do it while you're waiting in line at the grocery store, waiting in the car, or anywhere else.

Age: 3-6, depending on the conversation you have with it

Concept/ Skills: Odds & Evens, Addition Fact Fluency up to 10, Flexibility (more than one right way to do it), Subitizing, Mental Math with Fives and Doubles

How to Play: "I'm going to say a number, then as quick as a flash, use your fingers to show me that number." The kid flashes fingers at you and you lather on the compliments when they get it right and fast. That's all there is to it.

How to maximize the math learning: Let's say you called out 8, and they flash 5 and 3. You say something like, "That's right, 5 fingers and 3 more fingers makes 8 fingers all together. 5+3=8. Can you show me another way to make 8?" Give them a chance to figure out the 4 and 4 way, the doubles representation. "Hey, look at that, what do you notice about your hands?" "They're both 4s. They match." "Yeah, the left hand team and the right hand team are even now--they both have the same number of fingers up. That's why we call 8 an even number; 'cause you can split it into 2 even teams (or 2 equal groups)." Do an odd number next to show the contrast. There are all kinds of good thinking and mental math strategies that can start to bud in this simple game. Here’s a conversation I had with Elodie when we played this today.

Me: Show me 9!

Elodie started quietly counting up on her fingers, then she stopped and just showed me 9 fingers.

Me: That’s right! How did you figure that out?

Elodie: Well, this is 10 (shows me 10 fingers) and it goes, “9, 10” so 10 is more than 9, so this is 9.

Me: Wow! That was a really smart way to think about it! Good strategy! 9 is one less than 10, so you knew you could hold up one less finger than all 10.

That is really simple, but it is good mental math. It is a more efficient strategy than counting up, and becoming a good mathematician is all about developing increasingly efficient strategies for thinking and solving problems. I was very proud of my little budding mathematician! When you start to hear how your little mathematician is thinking, I’m sure you’ll be impressed, too!

Hazel's First Food

Maniilaq Health Center did a rather nice job of wining and dining us (minus the wining of course). We met the med staff at the Bayside Restaurant for dinner Monday evening. The food was great and the people were fun and we were having a lovely time. Except for one thing: it was past Hazel's bedtime (9:30 in the time zone she's used to) and she was done being the perfectly cooperative, patient, flexible baby she'd been all day. Aaron and I were taking turns with her, and it was going OK, but towards the end of dinner, she was frazzled and we were desperate to entertain her long enough to get dessert. I mean, we have priorities. The plants you see behind me here distracted her nicely for a couple of minutes, but when she started tasting them and tugging on them, I decided it would be better if she didn't kill the only living plant I had seen in Kotzebue, and Hazel was pretty mad to say the least when I delicately extricated its leaves from her grasp. I looked around in desperation for something new and novel to hold her attention. Aha--an onion ring.

Instantly, the fussing stopped. She loved it. Cool texture. New to look at.

As babies do, she stuffed it in her mouth. Wow! Check out these eyes and her tongue just going at it to get more of that salty fried taste.

Her first real food. She did try bland old rice cereal the beginning of March, but it wasn't going so well so I backed off. I'm afraid we ruined her in one fell swoop. If she won't eat that bland rice cereal when I try again this week, I'll know why. Maybe if I batter and fry it... Hey, desperate times call for desperate measures.

This was some pretty good entertainment for the whole table. When she sucked it enough that a soggy chunk of the fried batter started coming off, we were all a little concerned about how she'd react when I had to take it away. Amazingly, she didn't mind at all when we traded it for a napkin she could shred. Phew. We could finish our dessert. I had an ice cream sundae. It seemed fitting in my icy surroundings. Although it did make me a bit chillier as we walked back to our hotel right after.

Kotzebue Culture

Monday, March 28

I loved the NANA Museum of the Arctic. Berry picking season sounds awesome--I'd love to be here in late summer just for that! I am glad the people here are striving to preserve the values and skills of their native culture--they are impressive and just plain good. But the current culture, which has emerged in Kotzebue as modern conveniences and government aid have been incorporated, lacks the beauty and the character-building sense of community that seemed to exist in the past. In too many instances, resourcefulness, creativity, and physical labor have been replaced with entitlement, addiction, and slothfulness. How sad to lose the traditional Inupiaq values and language. My generation doesn't speak the language, but with the help of the elders and the school, the kids now are learning. And at the museum, they have resources to pass down some really cool skills. Like this book I found that my dad would love--A Guide to Edible Plants of the Tundra--wow. Imagine just surviving off of the land up there, with no food flown in--impressive.

Speaking of food flown in, we also visited the 2 grocery stores in town today. Milk was $11 a gallon at the cheaper store. The selection was actually better than I feared, you just have to pay for it. Cuties were $7.88 a pound, not a box.

Potatoes were $13.99 for 10 pounds, at the cheaper store. Are you serious? Potatoes are supposed to be dirt cheap. Not in the Arctic tundra. A delicious-looking 2-lb bag of fresh snap peas cost $14.95. Even non-perishable items like cereal were plenty expensive.

At least apples were on sale for $1.98 a pound, which is only twice the cost of sale prices up here in Montana, and maybe three times the cost of sale prices in Colorado. Somewhat reasonable. People shared their ways of keeping their grocery bill down. You can order a box of farm fresh produce online and everyone picks it up at a local church, which keeps shipping costs down. People also fly to or through Anchorage quite a bit. While they're there, they head to Costco and stock up. Alaska Air lets you check 4 carry-ons per person for free for in-state flights, so you can get it home without shipping costs. I guess you can make it work, but being as frugal as I am, I would seriously struggle to let myself buy luxuries like green peppers and snap peas.

Could I really see my family living here? People who live here tend to describe it as a struggle. You make do. It's an adventure. The real bush experience. Day-to-day life with little kids? I dunno, it just doesn't strike me as the most family-friendly location on earth. Most of the providers we talked to at the hospital either came within the last year or so or are planning on leaving in the next year or so. I could do it for a couple years, but do we need to, honey?

Math Monday

My sister, the one who convinced me to start a blog back in the day, used to run a "weekly feature" that I thought was kinda fun. It was based on her hobby/pre-motherhood professional life, and it was a way for her to spread what she believed in: promoting health and happiness through better nutrition. Well, today as I was having preschool time with Elodie, I was winging it as I generally do, and I came up with this little game. It worked so well, I thought I would share it. And so, readers, my new weekly feature, Math Monday, is born. As a former (and future) public school math teacher, I like promoting intellectual health and happiness through better mathematical understanding. Feel free to share this link with anyone you know who teaches preschool co-ops or is looking for games to prevent their children's minds from turning to mush over the summer.

Has this conversation ever occurred with your child? "I'm thinking of a number between 1 and 10." "Ummm, 16." If so, then this game is in your kid's ZPD, Zone of Proximal Development. That's teacher talk for something your kid can't quite do yet but is ready to learn. All you need is a deck of Rook cards (or hand-made number cards with the numbers you want to work on). I call the game "In Between?" for obvious reasons. It only takes a few minutes to play, but it's amazing how a few minutes of your undivided attention can make a kid feel so special. Enjoy!

In Between?

Concept: Greater than/ Less than (great for 3-5 year olds, but fun for older siblings, too)

Players: 2 or more

Materials: Rook Cards

Object: To collect the most cards by getting a third card that goes in between the first two.

How to play: Mix the cards well. Place the full stack of cards in the middle of all the players. The first person takes 2 cards and lays them in front of herself. She puts the lower card to the left and the higher card to the right. She then draws the next card in the stack. If it is in between the first two, she gets to keep all three. If it is less than the lowest or greater than the highest, she puts all three in the discard pile next to the draw stack. If the first two cards are either next to each other or an exact match, then obviously no whole number is in between, so she has to discard those (either before drawing the third card or after, depending on how long it takes her to realize that nothing will fit in between). Then the next player takes a turn. Play continues until the whole stack has been used. The lucky player with the most cards wins!

How to maximize the math learning going on: Most importantly, let the kid take his time to think through it himself. Let’s say he drew 4 and 11. He then turns the next card in the stack over, let’s say it’s a 9, and asks himself, ”Is 9 in between 4 and 11?” When he figures it out, ask him, “How did you know?” and help him put words to the strategy he used to figure it out. For example, if he says, “I counted up and figured it out,” you could say, “Oh, very smart, you used a counting strategy and found out that 9 comes after 4, but it’s still before 11. Good thinking!” If he says, “I just knew that 9 was bigger than 4 but not as big as 11,” you can compliment him specifically saying, “Wow, good mental math. You’re developing a really good sense of what numbers are bigger and smaller. I can tell your math brain is turned on!” If he can’t express how he figured it out, ask questions and help him come up with a way to explain his thinking. If he says the number is in between, but that's not correct, you can still ask, "How did you figure that out?" and keep questioning to help him discover his own mistake. This is a very powerful skill in math--self-checking. When it’s your turn, think aloud to model how you solve problems. “OK, I need to compare these two numbers. I know that 6 is less than 8, so I’ll put the 6 to the left of the 8 (I actually make them face the right way for Elodie, rather than for myself) with a little space between them. Hey, I noticed that there’s only one number that is between 6 and 8—7! So if I don’t get a 7, I won’t get to keep these cards!” Have fun learning math together!

The Kotzebue Branch

Sunday, March 27

Church was wonderful. It just seemed especially Spirit-filled and worshipful. The numbers were few, but the Spirit was not at all diminished; if anything, it was increased, to make up for the lack of numbers! What a powerful affirmation that this is the true and living Church upon the Earth.

There were 15 locals there and 8 visitors, including us. They don't usually get visitors; kinda funny that they got so many in one week. Three of them were the stake presidency who flew in from Anchorage with us the night before for branch conference. The other 2 were the branch president's parents who came to visit since they just got back from a mission to Scotland. They didn't have a primary--the oldest kid was only 4, so he just had to repeat nursery. And they had 3 young men, but no young women. Kinda like our ward back in Sidney!

Church was only 2 hours long since they don't have the numbers to keep every auxiliary running. It was totally back to basics, which is not necessarily a bad thing. The branch president was so good at focusing on people. He just radiated the pure love of Christ. After sacrament meeting, the adults and young men had Sunday School while the little kids had nursery, supervised by the branch president that week. And the church building was really cool. It was a big gym with a cool-looking wood-beamed ceiling and classrooms and a kitchen and a stage around the gym. Sacrament meeting was held on the stage, closed off by a nice curtain. No hallways, just doors opening into the gym. I've never seen a church building quite like it. Unique just like the town.

I could picture myself being a part of the Kotzebue branch... We would definitely need to make friends and invite them to church so my kids wouldn't be alone in primary! What an adventure!

(Disclaimer: I did not take this picture, I found it online and borrowed it. When we were there, snow completely covered the ground. You definitely could not see things like pavement! This must've been taken much later in the spring.)

Arctic Adventurers

Saturday Night, March 26

Our first night in Kotzebue (we flew in at about 8pm)

This is what I would have blogged if we were connected to the rest of the world via the world wide web. Don't worry, the WORLD WIDE web has made it to Kotzebue, just not to our hotel. I had to use a notebook and pen. Weird.

WHOA! I am in the Arctic Circle. I just ate surprisingly delicious Schechwan Vegetables, Potstickers, and Orange Chicken (at the Empress Restaurant) as I watched the sun begin to set over the frozen Bering Sea. Beautiful. And surreal.

And the short walk (2 buildings down) back to the Nullagvik Hotel (which you can apparently just call The Hotel because it's the only one in town to speak of)? Completely FREEZING! Like leave my hat, coat, and boots on for five minutes after coming inside freezing. Like, Arctic freezing. Like, what am I thinking taking my baby out in this?!?!?! freezing.

And now it's 10:00, it's not totally dark yet, and I'm being serenaded "I've Got Friends in Low Places" by a group of guys through these thin hotel walls. Karaoke anyone? Looks like "We will Rock You" is coming up next.

Could I really see myself living here? Calling it home, even for a little while? Whoa. The Arctic Circle. My mind is blown.