Posted in wwlw

what we’re learning wednesday, episode 9

Every spring, as part of her job as a math professor at the local community college, my mom goes to a math education conference and brings home all sorts of interesting books, games, and ideas. One of these was a set of playing cards containing the integers from -12 to 12 (two sets of -12 to 0 and two sets of 0 to 12), from Eureka Math. I can only find the cards sold in packs of 12, which isn’t very useful for a single family in terms of either quantity or price, but if you have an interested support group or co-op I’d definitely recommend them.

So far we’ve come up with two different games to play (neither of which is the game for which instructions are provided with the cards, though that also looks fun). First, we’ve been playing addition war, where whoever’s sum is closest to zero wins the round. Limerick picked up the concept of negative numbers really quickly – I introduced them with a number line while we were waiting for Rondel’s speech therapy, and he understood them and was picking up speed in figuring out the sums in our game of war by the end of the 45-minute session. Rondel is more visual and tactile than Limerick, and was struggling with the concept and calculations when they were presented that abstractly, so we made a large helpful number line that has really helped.

Unlike a traditional number line that runs horizontally, this one extends vertically, with negative numbers at the bottom and positive numbers at the top. So positive numbers are like steps up a mountain, while negative numbers are steps down into a hole underground. When we make the sums during war, Rondel knows that he can start with either number and count the number of steps either up (for a positive number) or down (for a negative number) to calculate the result. After a week or so of playing with this board every day, he’s now grasped the concept well enough to be able to figure out most of the sums completely in his head, just like Limerick.

The board also gave us an opportunity to develop another game using the Eureka Math integer cards, this one cooperative instead of competitive. Each of us starts out with one playing piece (a small animal counter, usually) on the zero tick in the center of the board. Taking turns, we draw one card at a time from the pile and move that number of steps from our current position. Every time someone goes off the board (28 or -28 – my tick marks are centimeters on standard printer paper) or lands exactly on 0, everyone gets a chocolate chip ๐Ÿ™‚ The board is large enough that the amount of chocolate earned is fairly small, but small enough to keep everyone from getting frustrated. I usually end this game (to loud protests) when we’ve gone through the entire deck three times… more than that could lead to excessive amounts of chocolate and the concomitant hyper silliness ๐Ÿ™‚

From what my mom says, negative numbers were apparently one of the more difficult mathematical concepts for me to grasp (along with distance-rate-time problems), though I don’t remember learning (or struggling with) them. So I’m glad that these two fairly simple tools have made them intuitive and fun for my kids.

Posted in hikes

hiking with littles: superstition mountains – treasure loop trail

Now that our very wet winter has come to an end, the desert has burst into life with a wild spring bloom, and I’ve been trying to take the kids out to see the mountains turned green with wildflowers decorating the slopes. My mood always tends to improve as the colder and grayer season ends (can’t imagine what I’d be like if I lived elsewhere), so I’ve had the energy and motivation to hike again – and the prospect of flowers definitely adds to that motivation!

The day we chose to hike the Treasure Loop trail in the Superstition Mountains was unfortunately cloudy and rainy, so many of the flowers stayed hidden away, but it was still a beautiful hike.

Treasure Loop trail is almost 2.5 miles long and moderately difficult – the trail is broad and well-marked, but it can be steep and slippery in places. We took a few hours doing it… in out defense, we stopped to smell the flowers a time or two (and count their petals, in Limerick’s case):

We also took time to climb up some boulders near the path and pretend to be mountain lions:

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And of course we took breaks for snuggles and snacks (the bench at the overlook was really timed perfectly for the kids’ hunger):

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The cold and wind did make the hike considerably more challenging, as Aubade really dislikes being cold and getting wind in her face (we’ve had this issue on other hikes). Because the trail ended up being a lot colder than our home just 30 minutes away, Aubade wore my jacket for most of the hike, which helped and was adorable but left me rather cold as a result ๐Ÿ™‚ I guess it’s just a reminder to check the weather at the actual trailhead before deciding what to wear!

For others considering Treasure Loop, I’d say it would take much less time with just slightly older kids – we were mostly slowed down by Aubade (and our spirit of exploration!). Good footwear is important though as the trail can get quite slippery once you start coming back down the slope. This is a fairly popular trail from what I could tell, based on the number of other hikers we saw on a weekday, but it wasn’t overly crowded. It can be accessed from free parking spots by the First Water trailhead, or through the Lost Dutchman state park for a $7.00 entrance fee (as well as a shorter hike and good bathrooms, both of which were needed with my little hikers). We enjoyed it and I’m sure we’ll be back next spring ๐Ÿ™‚

How to get there from the East Valley: take the 60 to Apache Junction and exit on Idaho Road; turn right onto Apache Trail and continue until you reach the entrance to the Lost Dutchman State Park. The entrance fee is $7.00 and the ranger will give you a map of the trails and state park roads/parking lots.

Posted in family life, sqt, wwlw

{sqt} – because limerick loves numbers

If you ask him, Limerick will tell you that his favorite thing in the whole world is numbers. More than milk, more than cookies, more than hugs – numbers are the best. So I thought I would capture seven ways he shows that love for this week’s {SQT}! Join Kelly for the rest of the linkup ๐Ÿ™‚

  1. Limerick’s favorite numbers of all are 1, 11, 111, and so on – anything that is all 1’s. So the other day as we were skip-counting back and forth together the way we do, he decided we should count by 11. When he got to 1111 (and he was the one who got to say it!), he was so happy that he stood up on his chair and clapped his hands together while laughing for joy.
  2. This past week he’s been asking me to make number coloring pages for him, where I’ll draw the outlines of numbers on a page and he’ll color them in. Well, for one of those pages, he decided the best way to color them in would be to fill all the little spaces with smaller versions of the number he was coloring – very meta ๐Ÿ™‚
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    Limerick’s coloring page – don’t be too critical of his handwriting! He is only 4 after all ๐Ÿ™‚
  3. In addition to coloring numbers, Limerick likes me to make skip-counting number boards for him – this week alone we’ve made one that counted by 499, one that counted by 999, one that counted by 4, and one that counted by 1 but had all the multiples of 3 drawn in a different color. After a board is made we’ll play a game with it once or twice but then it is on to the next one! I sometimes think he just likes watching the numbers appear on the paper as I write them…
  4. Speaking of watching numbers, Limerick’s favorite book, You Can Count On Monsters by Richard Schwartz, gives him plenty of chances to do just that. He will sit for hours poring over every page of the book, noticing how the focal number of each page breaks down into its factors and figuring out how the accompanying monster illustration incorporates those factors (or the number itself, if it is prime). He’s been through it at least three times this week, taking 2-3 hours each time, and it doesn’t seem to be growing old yet.countonmonsters
  5. I pulled out a math workbook for Limerick this week also, thinking he might be interested, and so far he has just been turning the pages looking at all the numbers and math problems and shapes. He isn’t interested in writing anything down, but when I ask him about any of the problems he knows the answer instantly, or knows how to figure it out. There are some fractions later in the book that would be more of a challenge for him, though, so maybe that will catch his attention eventually. It’s a bit of a tightrope balancing between guiding him towards new information and allowing him the joy of freely exploring numbers without pushing or interfering.
  6. I did, however, get to explain different base systems to him this week! I just sat down at the table and started counting in hexadecimal on a piece of paper, and he glanced over and was immediately intrigued. We discussed what place value means in the context of the various base systems, and ended up writing out 1-32 in decimal, hexadecimal, binary, and base 6. I think binary was his favorite because there were so many 1’s and the numbers got long so quickly!
  7. One other fun book we’ve read through a few times (though not as recently) is Bedtime Math by Laura Overdeck. It’s been a great introduction to the application of numbers, and a challenge for Limerick to translate the words into the more familiar arithmetic. He’s actually quite good at tracking along with the question as I read it, deciphering the logical connections, and doing the math in his head – he can for most of the stories do even the most difficult problem on the page already!

All in all, I just have to echo Limerick and say that he really does love numbers the best ๐Ÿ™‚ And he has, honestly, since he was 18 months old and would sit on the driveway drawing them in wide circles around himself until he was familiar with each one, and since he was 2 years old and would count the bites remaining on his plate at dinner and practice subtracting them as he ate. I’m looking forward to watching this love continue to grow with him in the years to come!

Posted in family life

playing in compost

More than a year and a half after moving in, we’re finally nearing the end of the backyard project: we’re putting in the lawn!

Most lawns out here are bermuda grass in the summer, overseeded with rye in the winter, which makes for a nice grass lawn but takes a lot of effort (and water) to maintain. So since we had a blank slate to work with, I wanted to try something different, and I’ve been researching the question for the past year or so. Most lawn alternatives aren’t quite hardy enough for the summers here, but I ended up choosing a miniature clover variety, interspersed withย Herniaria glabra and Roman chamomile (and wildflowers for fun, in hopes of butterflies).

The exciting part for the kids, of course, was spreading compost out over the native soil (which seems like clay to me, though it once supported cotton fields). When you’re little, rolling around is soft dirt is pretty awesome, especially when the air is cool and the soil is warm enough to steam up into the air.

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And of course there’s jumping into the piles before they get raked down.

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Not to mention running all over it, soft underfoot, warm against the chill of the morning, cold air rushing in your face and lungs:

Or digging in it, rolling around in it, burrowing into it, and just generally becoming covered in it!

You could even help spread it out, if you were feeling so inclined.

It was definitely an adventure getting them all cleaned up afterwards, but the happiness of getting dirty was more than worth it. They lasted almost two hours before wanting to come in and eat breakfast, and went out again later in the morning! Now, while we’re waiting for the seeds to germinate, they are pretending it’s all lava and creeping around the completed edges of the yard instead ๐Ÿ™‚ And I’m just waiting to see if all the effort pays off and green can come out of all that brown.

 

Posted in family life

spontaneity and snow storms

Last Wednesday I looked at the weather forecast and realized that two days of cold rain here in the valley would most likely mean two days of snow up north. I thought to myself that a day trip might be nice, on Friday or Saturday depending on the road conditions, but when I bounced the idea off of Paul and my mom (both of whom might have appreciated a day trip being scheduled when they could join me), my mom suggested that I go up before the storm and stay through it so as not to worry about the roads at all. And Paul thought that sounded like a great idea and a good reason to take a few days off of work, so I set about planning it.

Note: this idea was forged late Wednesday morning, and the storm was scheduled to hit around 9 o’clock that evening. So that left me with about six hours to find a place to stay, pack two days worth of food in case we ended up snowed in, buy or borrow snow gear for the entire family, and pack clothes, activities, and other necessary items. I definitely had some moments where I regretted ever having had the idea to play in the snow in the first place! (Like when Paul called to tell me his car battery died so I would also need to pack for him and pick him up at work on the way up, when I had been hoping for his help as the crazy late afternoon itch hit the kids…)

In the end, however, I am so glad that I didn’t let my anxiety or insecurity change my mind.

Thanks to Air BNB allowing same-day booking, we found a little house in Prescott Valley that didn’t seem likely to necessitate four wheel drive (I lost a couple hours agonizing over a different cabin that was absolutely gorgeous but whose owner was very concerned about us being stranded there), and took the kids to experience real snow – not just flurries or random patches on the ground – for the first time in their lives. And this was serious snow. Prescott Valley averages 5 inches of snow in the month of February, but this storm brought in about two feet in just two days (the official totals range from 21 to 28 inches depending on location in the city) – and we were there to watch it all come down, to feel the fluffy lightness of the new snow and the dense strength of the old, to wake up to icicles on the eaves and a world glittering like a preschool art project, to taste the ethereal coldness of snow dissolving like cotton candy in our mouths, to catch individual flakes on our jackets and marvel at their complexity, to be pelted by hard fast-falling half-melting and refreezing almost-hail flakes, to see the world turn suddenly white and new.

Rondel was a huge help preparing for the trip, because he was so excited about the chance to go up to the mountains to see snow, and so he cooperated with all the crazy last-minute packing and helped keep Aubade and Limerick happy all afternoon – and when we got there, he loved the snow just as much as he anticipated (though I think he didn’t realize just how cold it would be!). He ate the snow, he pretended to be the unstoppable boar from a Kung Fu Panda short (in other words, he knocked people over and was knocked over into the snow quite often), and he just generally relished in the opportunity to run and play in it!

Limerick had a slightly harder time with the snow – the depth made it harder for him to move around, and he got cold more quickly. But he still enjoyed it quite a bit, in his quieter way. On one of our excursions, when Rondel was chasing me around as Boar Unstoppable, I made a snowball for Limerick that just didn’t seem to break, no matter how many times he threw it at me, so we dubbed it the Indestructible Snowball of Doom. Every time Rondel would knock me over Limerick would come up with the snowball and drop it on me and the look of mischievous glee on his face was so hilarious that I could hardly push myself up out of the snow from laughing so hard.

Aubade really wanted to like the snow; she wanted to go out anytime anyone else went out; but she got cold really fast and struggled to walk through the snow as well. It didn’t help that I couldn’t find more waterproof mittens in her size and had to settle for lined fleece ones, either – the few times I put her in Limerick’s mittens she seemed to last longer despite having almost no control over her hands. She did have a lot of fun until she got cold, though, and she definitely enjoyed getting all bundled up in the snow clothes ๐Ÿ˜›

All in all, it was one of the best times we’ve had as a family (and definitely the most spontaneous!). There was so little tension and so much laughter, as all of us were able to relax into the wonder and excitement and peace of our time away. And as Rondel keeps reminding us, each time he sees the snow-capped mountains in the distance, we will definitely go back north again some day.

Posted in family life

bikes!

For Christmas, we used part of our Christmas gift from my grandpa to buy a bike for each of the boys – their first pedal bikes! I’d been scouting Craigslist for months and hadn’t found much besides princess and unicorn bikes with pink streamers… so I figured this would be a good use of the Christmas money, and the boys were excited.

That is, until they tried to ride them, and realized how different it was from the little push bike they were used to. I think they avoided the bikes for at least three weeks before agreeing to try them out again, and for another week or so they wouldn’t want to go farther than down the driveway.

Now, however, they are finally starting to figure things out!

(No, my children never wear shoes if given a choice. Yes, they get that from me…)

While riding down the wide sidewalks at the park, Limerick was passed by a teenager going quite fast on his own bike, and decided that he could also go fast, and started pedaling as hard as he could. He got some speed, and had to go around some corners, and fortunately slowed down before reaching the parking lot or crashing ๐Ÿ™‚

Now I can look forward to family bike rides in the not-so-distant-any-longer future! You know, once they get the hang of braking, and can go more than once around the block without getting tired. Baby steps. Or in this case, training wheels, I suppose?

Posted in family life

when a boy turns four

When a boy and his big brother have been singing happy birthday to all their toys for four months straight, and it is finally his birthday and he is going to beย fourย now –ย 

ย That is a big deal.

That is cause for delighted giggling, and for concentrated practice with the little sister so that she no longer calls himย three. It is reason to curl up into a cozy ball and snuggle all squirmy with Mommy and Daddy.

Turning four means a cake shaped like a four, with four candles on top, and his whole face lighting up with excitement because the cake is aย number, and it is his number now!

Turning four means opening the most wonderful new book, one he never even imagined, in which prime factors and counting and modern art meet, and it hardly even matters that there are other unwrapped presents on the bench beside him because this, this book, has to be the best thing ever.

Turning four means getting to spend the afternoon at Grandma’s house, and swim in the hot tub, and choose what food everyone will eat for dinner, and generally spend the whole day enjoying himself.

And it is such a happy thing to be able to give him, a day of joy for his birthday, a day all about him, when he is so often the one who thinks of others first. He is the one who, seeing his sister’s favorite toys lying around, will bring them to her; he is the one who notices what his siblings are building with the Legos and finds pieces that they could use; he is the one who is always willing to share his cup or his snack with someone else who is hungry or thirsty; he is the one who will voluntarily take apart his flake creations so that his brother can have the color flakes he wants.

At four (and really at three, since a day doesn’t make much of a difference), he is keenly intelligent, deeply enamored with the world of numbers (he has broken down in tears because we had to stop reading a math book at bedtime; he invents his own simple word problems to ask us; he can multiply any two single digit numbers together and loves to skip count with chalk on the driveway to see the patterns in the series of multiples), and beginning to read; but it is his attention to the small details of his siblings’ lives, and the sweet care he gives them as a result, that mean more to me. And so just as I nurture his academic strengths with number games and puzzles to solve and books to read, I try to nurture his budding compassion and sensitivity by pouring into him connection and love. I hold him and when he looks at me I look straight back into his eyes because I know that is significant for him. We play the silly and sweet games of early childhood, meaningless save for the connections formed.

Because ultimately? No matter how intelligent he is or what he does with that intelligence, he needs to be assured of his parents’ unconditional love for him more than anything else. Maybe because he has this talent he needs that assurance even more – he already shows me that he has perfectionist tendencies regarding himself. But that assurance has to happen on his level. And he is four. He has just turned four, after all!

So for now? We are – we strive to be – his safe haven, his rich soil, his clean air, so he can grow in wisdom and knowledge. Happy fourth birthday, my Limerick.