Posted in wwlw

what we’re learning wednesday, episode 10

To incorporate some math into our current space-themed enthusiasm, I came up with a new game that we have been calling Space Race. All you need are three dice, a deck of cards, and some sort of token for each player, so it’s pretty easy to set up.

Using all 13 cards from one suit, we have enough cards to represent the sun, all 8 planets, and 4 dwarf planets (Limerick’s favorites). While you could line up the cards from 1-13 in order from the Sun outwards, Limerick prefers to assign each card to the appropriate planet according to its ranking by mass, as follows:

Sun13 (King)
Mercury5
Venus7
Earth8
Mars6
Ceres1
Jupiter12 (Queen)
Saturn11 (Jack)
Uranus9
Neptune10
Pluto4
Haumea3
Makemake2

In the table above note that the dwarf planets are italicized and that Uranus, despite having a larger diameter than Neptune, has less mass and is therefore given a smaller number. If you had cards going up higher than 13 you could incorporate more dwarf planets, but that would also make the game longer.

On a player’s turn, they roll the three dice and attempt to use the three numbers rolled to make the number of the planet to which they wish to launch a probe. Once they show how they can reach a planet’s number using basic arithmetic (addition, subtraction, multiplication, and division), they can place a token on that planet’s card to symbolize the successful mission of their spacecraft. If the player is unable to make the number of any planet to which they have not already launched a probe, that turn is considered a “failed launch” and play proceeds to the next person. The goal is to be the first player to send spacecraft to the Sun and all the planets.

We have these awesome cards with non-standard suits, one of which is little rocket ships! And the face cards, while still called J, Q, and K, have the correct number of rocket ships on them which is helpful for this sort of game. We use brain flakes for our tokens since we have a lot of them in multiple colors, but Legos or coins would also work well.

If the game is too easy or goes by too fast with open-ended launch destinations, a more challenging variation is to select a specific order in which the planets need to be reached – smallest to largest or center of the Solar System outward, for example. Limerick prefers this variation; it forces him to be more creative with his use of the numbers while also removing the need to decide which planet to choose when there are multiple options. Rondel prefers the original more flexible version, however, since it allows him to launch to the first planet he is able to find a solution for and lets him play with the math skills he is more comfortable using. I would encourage the more flexible version if you have players who are primarily relying on addition and subtraction, and the ordered variant for players who are comfortable with simple multiplication and division as well. Either way, it’s fun and it’s good math practice – always a winning combination πŸ™‚

Posted in family life, sqt

{sqt} – just living life

This is a real {sqt} post this week: just seven updates from our life πŸ™‚ Visit This Ain’t the Lyceum for the rest of the linkup!

  1. I now officially have my autism diagnosis! So if you read my series for Autism Acceptance Month, which I wrote during the diagnosis process, you can now be comfortable in the knowledge that it comes from a “real” autistic person instead of an imposter. Not that I think most self-diagnosed individuals are – but it was how I was afraid I would be perceived (and honestly, I was deeply afraid that it was true of myself). It was a lot easier than I thought it would be, and also a lot more uncomfortable. I was so afraid, the whole time, that the psychologist would tell me I was just intelligent with typical gifted quirkiness – and then I would be left wondering, if that were so, why I seemed to struggle so much with things that came naturally to the gifted friends I grew up with? But fortunately for my peace of mind, I can now say I’m autistic with confidence, and I say it to myself a lot when I need to advocate for myself or address areas of weaknesses in my life, and it helps to stop the perfectionist depressive thinking patterns from asserting themselves.
  2. I have realized how much game play helps with the development of strategic thinking and forethought, by watching Rondel grow in those skills. I’ve seen him take the initiative to plan a course of play at the beginning of a game; stay aware of the events of the game so that opportune moments for deviating from that plan can be seized; look ahead at his opponents’ possible moves to make the optimal choice for his own; and see several steps ahead on the pathway to his desired end – in several different game settings. These are really valuable skills for life, not just for games! This is all about considering options, observing the environment, planning for the future, and making decisions in the moment that affect long-term goals. When I write up his kindergarten year summary, I may include some of these games in a SPED section under executive functions…
  3. Teaching something that I don’t remember learning is challenging. In other words, while we are all into math and science over here (definitely at least a grade ahead in math, and more for Limerick), we’ve barely done more than the alphabet and letter sounds when it comes to reading, and I’m struggling to know where to go next. I have a few ideas from my sister-in-law and I looked up some phonics/beginning reader games online that look fun (my kids are always up for a new game) – but to me, reading is like breathing. I can’t imagine (or remember) life without it. And how would you go about teaching someone to breathe?
  4. I may have a new favorite food, and I think Aubade would agree. I whipped up some heavy cream, added some yogurt and maple syrup, and discovered paradisiacal creaminess with just the right balance of airiness and weight, sweetness and tang. We’re calling it “breakfast cream”, over here.

    IMG_5466
    Picture is of Aubade in a black and white striped polo shirt at a kitchen table with a bowl of whipped yogurt, eating a spoon of it, with white smears all around her mouth and nose.

    The recipe is very straightforward: two parts heavy cream, whipped until very stiff; beat in three parts plain Greek yogurt (I used full fat); sweeten with one tablespoon maple syrup for each quarter cup of yogurt. Last time I made it, I rolled it up inside fresh crepes with diced peaches; Aubade just ate three bowls of it unadorned πŸ™‚

  5. The cantaloupe vines have reached the top of the trellis (8 feet high!) and are beginning to claim the other side. It makes for a beautiful shady green retreat from the world, tucked under the trellis on a camp chair, looking out at the sunflowers starting to bloom. The fruits themselves are not overwhelming in number (which could be because I planted too many too close together), but they are massive. Paul keeps asking me if I’m sure they aren’t actually watermelons and I can’t really blame him because I have never seen cantaloupes this size in my life…

     

  6. Every few months for the past couple years, I’ve pulled out my old pattern blocks to see if the kids are interested in them – and now at last their interest and their fine motor skills are there! Limerick and I make patterns (he prefers to work with me rather than on his own, even if he’s making all the decisions), and Rondel tends to build animals. Aubade isn’t really ready – but she has fun playing along with the boys πŸ™‚

    It is such a great foundation for an understanding of geometry and the more mathematically abstract styles of art, and having the hexagonal base is a nice contrast to our other building toys which are either octagonal (Brain Flakes) or rectangular (Legos). And it’s just so much fun… I could make patterns for hours.

  7. This past week was rather interesting for me in terms of theological discussion. My sister-in-law and I had a discussion about Protestant/Catholic differences that spilled over onto Facebook (where actual Catholics got involved, to my delight) and many text messages days later. Then, I spent a morning with two Protestant missionaries on home assignment, and finally was accosted by two Mormon missionaries that same afternoon. These are all concepts and divisions I have thought about and researched a lot, but I don’t often have the opportunity to actually discuss them in real life very frequently. And I realized that while I still am officially Protestant, I was arguing the Catholic side and thinking in Catholic terms more often than not during all of these interactions. So, having surmounted the autism diagnosis hurdle, addressing this theological hurdle is next on my list of Important But Uncomfortable Things To Address. I’d be interested in any resources, thoughts, or experiential wisdom you have to offer here!

Again, don’t forget to visit the linkup today! If you share your own blog there let me know and I’ll make sure to read it, or I’d love to hear some of the highlights of your week in the comments as well πŸ™‚

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 πŸ™‚ 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 πŸ™‚

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 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 πŸ™‚

  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 πŸ™‚

    IMG_5113
    Limerick’s coloring page – don’t be too critical of his handwriting! He is only 4 after all πŸ™‚

  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 πŸ™‚ 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 wwlw

what we’re learning wednesday: episode 5

This week, we’ve been playing math games!

While Aubade takes her naps, I’ve introduced the boys to dominoes (just the number matching beginner version – they aren’t quite ready for the multiples-of-five scoring version yet, but I wanted to lay the foundation for it as it is one of my family’s traditional games) and to war with playing cards. For war, we mess with the rules a bit by either playing addition war, where we pull two cards at a time and the person with the highest sum wins, or subtraction war, where we again pull two cards but the person with the smallest difference wins. (Multiplication war – highest product wins – and division war – smallest remainder wins – are other possible versions of the game but Rondel isn’t able to do that math quickly enough yet for the game to stay engaging and fun.)

I thought it might just be a fun novelty, but the boys have both really enjoyed it. Handling the cards, especially with our old sticky set, is good fine motor work, and the game itself is great math practice since the symbols on the card allow the boys to count to the answer if they need to. I also spent one game writing down the rounds in math language, to introduce the boys to symbols like “-“, “+”, “=”, “>”, and “<“; they liked the greater and lesser than signs the best, of course, because they are alligator mouths trying to eat the bigger number!

When we play games like these, Limerick gets super excited every time he figures out what his sum or difference is, and Rondel gets super excited every time he wins the round πŸ˜› It’s interesting to see Rondel developing a sense of competitiveness, though I’m definitely grateful that he still has no negativity associated with losing. It’s also interesting to see how little Limerick seems to care about who wins or loses: he just loves the process of playing the game, and I wonder if that is connected more to his age/developmental stage or to his personality.

A note to add is that we don’t approach these games as a “math lesson” or as “doing math.” It’s just a way to have fun together – to incorporate Rondel’s newfound love of games (thanks to speech therapy) and Limerick’s passion for numbers. Especially at their age, it is far more productive to follow their interests than to try to force them into something they don’t want to do or aren’t ready to learn yet!

Posted in wwlw

what we’re learning wednesday: episode 4

Rondel and Limerick are very different academic beings. Rondel’s first love is stories – he tells them, he listens to them, he invents them, he demands them, he constantly (since before he could talk) brings us books so he can hear their stories too. He soaks up facts about animals, and then populates his worlds with monsters generated from conglomerations of the different animals he loves. Limerick, on the other hand, has always been intrigued by symbols and patterns. He knew all (and could write most) of the letters and numbers by 18 months, spent a good 6 months nearly inseparable from a Duplo pattern board he created, and currently puts a lot of energy each day into creating symmetrical designs and exploring the world of numbers.

When we introduced Cuisenaire rods (a really great math manipulative, by the way – I grew up using these with the Miquon math curriculum and have always felt that they gave me a strong conceptual foundation in mathematics) for the first time this week in preparation for more kindergarten-type activities, this difference in their inclinations was immediately evident.

Limerick went through each color rod, noticing how long each one was as compared to the small white unit blocks. When he reached the longest rod, he began to line up the smaller rods next to it, to see how he could split it up. Ten is ten groups of one, he realized, and five groups of two, but when you try to split it into groups of three you end up with one empty space.

We made squares (one group of one, two groups of two, three groups of three, etc.) and talked about the difference between the perimeter of a shape (how long all the edges are, put together) and its area (how many white unit squares could fit inside it).

IMG_0239.jpg

Meanwhile, Rondel was using different sizes and color of blocks to retell the story of the Three Little Pigs with house-building fleas and a predatory lion (I think he chose fleas because they are too small to see, and he didn’t have any prey animal toys on hand to use with the lion figurine). He went through all the steps of the story with sound effects and drama, creating and destroying as necessary, completely immersed in his imagined world.

When the boys play together, I see these inherent differences leading to growth in each of them. Rondel’s love of imagination draws Limerick along with him into wildly creative and unrealistic pretend games, while Limerick’s fascination with numbers and patterns motivates Rondel to learn the vocabulary and concepts of math also. It makes me glad all over again that they have each other to grow up with.

So what are we learning, this Wednesday? We are learning about how numbers work together, how they split apart and recombine in consistent ways. We are learning about the trial and error it takes to finally build a house that can keep out a powerful lion. And we are learning about each other, and how we can help each other learn in grow in different ways.

Posted in wwlw

what we’re learning wednesday: episode 3

Today we went to the grocery store and learned about the way peaches smell when they’re ripe and good to eat (and also plums). I learned that Limerick will pull the leaves off of strawberries before he eats them, while Aubade will eat them leaves and all.

We learned about the strength of the wind in a storm when we saw huge branches torn off of trees by the monsoon that came through last night.

We learned about the hiddenness of the wind, how it can only be inferred by the consequences of its presence, last night as we watched that storm crash down the street and read Christina Rosetti’s poem about the wind:

Who has seen the wind?
Neither I nor you:
But when the leaves hang trembling,
The wind is passing through.

Who has seen the wind?
Neither you nor I:
But when the trees bow down their heads,
The wind is passing by.

Rondel wondered at how we can feel the wind when it presses against us even though we can’t see it coming with our eyes.

Today, we talked about how scary things can be when they are new and unfamiliar and unknown, when really they are good and beautiful things, because we discovered some books on that theme at the library:Β Tiny’s Big Adventure by Martin Waddell,Β What Do You Do With a Chance? by Kobi Yamada, andΒ Little Frog and the Scary Autumn Thing by Jane Yolen.

Earlier this week we made a 10×10 number chart and discovered that if we covered up all the odd numbers with flakes (all the numbers that can’t be split into two groups, as the boys say), the even numbers that were left all lined up in neat columns and had 2, 4, 6, 8, or 0 in their ones place. We also spent a lot of time figuring out which numbers would be visible if we covered up the ones that couldn’t be split into three groups, but we didn’t discover a reliable pattern yet for those numbers. (Limerick loved figuring it out for each number though, so I’m sure he’ll find the pattern pretty soon).

Rondel watched a documentary about the Galapagos islands and learned about an iguana that laid its eggs in nests of volcanic ash and so couldn’t leave the volcano summit of one of the islands, and also learned about the blue-footed booby for the first time and was impressed by how blue its feet really are!

And I learned that the best way to turn around a bad day is to apologize directly for my irritability and impatience, instead of just hoping it will go away and be forgotten.

Those are our recent highlights! What have you all been learning and discovering in your lives lately? What riches of knowledge and adventure have your curiosity and hunger to learn unearthed for you?