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 π

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 π
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.
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 π 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 π 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).

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?

Posted in wwlw

## what we’re learning wednesday (episode 2)

Limerick is currently in love with numbers.

He counts everything he can, comparing amounts and sizes: he counted all the straps on the plastic pool chairs at the public pool Saturday afternoon, at least ten times in a row; he makes long chains of flakes and counts them over and over again as he builds to find out how long they are and which color is the longest; he counts the number of bites or slices on his plate and recounts each time he eats one. Essentially, he is spending time with the numbers and quantities, becoming friends with them, getting to know how they interact with each other and discovering their unique qualities.

Limerick figuring out how many sticks could fit on the length of our big wooden cutting board – I think it was somewhere around 40.

He will break numbers down into their component groups: if he builds a tower with fourteen wooden blocks, he will tell me proudly that it is two groups of seven. When he expanded his tower to eighteen blocks, I asked if it could split into two equal groups and he lined them up into two equal lines and counted each one to make sure that they both contained nine blocks. When I then asked if it could split into three groups, he made many little groups of three blocks and found out there were six of them – so, six groups of three and three groups of six. Since he’s been doing this on his own anyway, I introduced the vocabulary of “even” and “odd” to him.

“See this group of seven? I can’t break it into two groups of the same size – one of them is always bigger than the other. Numbers like that are called odd.”

Limerick pondered, then declared, “But eight is two groups of four!”

“Exactly! Numbers that can be split into two groups of the same size are called even!”

“Nine would be five and four,” Limerick told me with a slight frown, “but ten would be five and five!”

“So nine is odd, and ten is even!”

We’ll see if he remembers – he tends to hold a new word to himself for a week or so after he learns it, before he brings it out for everyday use.

Emboldened by all the math talk going on, I pulled out one of my favorite math tools from my own childhood (one that I believe my mom created, and that she now uses in her job as a remedial math professor at the community college):

It’s a physical representation of place value – the numbers on the cards in front show what the number would look like written down, while the buckets hold the appropriate number of craft sticks. In this picture, there are three single craft sticks in the box on the right, six bundles of ten craft sticks each in the middle box (the tens place), and nothing in the box on the left (the hundreds place).

We pulled out some huge foam dice and decided to take turns rolling and adding the number we rolled to the number already in the buckets:

Sometimes the boys knew right away what the answer would be; other times they would line up all the sticks to count them to make sure, and to bundle up the new ten-pack if needed.

Before this we hadn’t done much with written numbers – the boys know all the digits, but they didn’t understand double digit numbers. So it was a bit confusing at first for them, but by the time we stopped I think they were beginning to understand what the numbers meant and looked like, which is really cool!

Math tools and games like this aren’t necessary for learning math – Limerick has certainly been picking up on concepts ranging from quantitative comparison to division (with even a touch of fractions) just from everyday conversations about the numbers around us – but they are definitely helpful for illustrating a specific concept, challenging the mind to use a concept in a new way, or just having fun together with numbers! And since all you need for this particular tool are buckets, sticks, and paper, it doesn’t get much easier π