Posted in wwlw

learning to love math

Rondel never took to the “3 R’s” of education quite as naturally as Limerick (most people don’t, honestly), though he is an information sponge for the things that interest him, which have throughout his life been mostly science-related. We’d tried a couple of different approaches to learning and practicing math before I came across the Life of Fred curriculum (and I don’t even remember where, or I would definitely send them my thanks!).

Life of Fred is very, very different from any other math curriculum I’ve used. Every math concept is introduced in the context of a story about Fred Gauss, a five-year-old math professor (yes, it’s strange, but you have to just roll with it), and the end of each short (ridiculous, hilarious, bizarre) chapter has a few practice questions that work in both new and old concepts. So kids reading through the stories begin to see math as something useful, lovable, and even beautiful as it snakes its way through Fred’s everyday life (and his very odd adventures). And the stories will have kids laughing out loud along the way, if they are at all like Rondel (and myself!).

The elementary series for Life of Fred starts with Apples and Butterflies, which are both kindergarten level, and goes from there – through decimals, fractions and percents, through pre-algebra and algebra, and all the way through calculus (which was actually the first book the author wrote, oddly enough). While the books are published by Polkadot Publishing, I couldn’t find a way to purchase directly through them and ordered from ZTwist Books instead (free shipping!).

We are just beginning Cats now, having spent an average of 3-4 weeks each on the first two books. Rondel has been asking me to read Life of Fred all the time – more than I can right now with my lingering sore throat, and more than Aubade has patience for at times – and I can see his confidence with math growing week by week (we’ve been using the books for over two months by now). He will now tell people that math is his favorite because of Fred; he doesn’t get overwhelmed by basic addition and subtraction problems; he is starting to understand analog time-telling; he is getting better at remembering the days of the week and months of the year; he will skip-count for fun; and he is learning to notice patterns and sets in the things around him. The practice problems force him to focus as he has to recall information and use concepts in new contexts, but there are never so many in a set that he can’t make his way through them all.

In short, I am so glad we found these books and highly recommend them for anyone else, particularly those kids who are struggling with a traditional approach to mathematics.

Posted in family life, wwlw

what we’re learning wednesday, episode 11: field trip to lowell observatory

Through a fortuitous combination of a Groupon deal for tickets to Lowell Observatory and my mom’s travel bug, we were able to travel up to Flagstaff for a weekend and take Rondel and Limerick to the observatory one evening while we were there, without worrying about a late night drive home or an overtired Aubade.

I had been to Lowell before, but not since before college, so I didn’t remember much, and it was of course all new to the boys. Paul and I split up near the beginning, and I went with Limerick who absolutely loved every inch of it. He sat through an entire 45 minute talk about the solar system, explored the old telescope through which Clyde Tombaugh discovered Pluto, and got to see both Jupiter and Saturn through the massive telescopes set up for public use. (He was so cute looking through them – he had to climb all the way up the ladder to look through the view piece, and he kept pausing to tell me about everything he could see: storm bands on Jupiter, the four Galilean moons, Saturn’s rings, and some of Saturn’s moons as well, until the observatory volunteer told him that it was time to let someone else have a turn 🙂 ). Lowell also has a large globe that can display in three dimensions images of various planets and moons, and Limerick enjoyed experimenting with that as well.

I think both boys’ favorite part, however, was the Solar System walk stretching through the heart of the observatory grounds. The walk starts with the Sun and has a sign for each planet along with two bronze markers in the sidewalk denoting the aphelion and perihelion of each planet’s orbit. The distance between the markers is all to scale, of course, and reveals just how close together the rocky inner planets are compared to the outer gas giants. We’d done a smaller scale model in our house, but when you have to keep walking and walking to find Neptune, because the scale is larger, it has more of an impact. We did the walk through twice, marveling at how elliptical some orbits were compared to others (Mercury, for example, has a distance of almost 24 million kilometers between its aphelion and perihelion, while the near and far points of Venus’s orbit are only 1.5 million kilometers different), and probably would have done it again if it hadn’t gotten too dark.

While Flagstaff at the end of October is cold in the evenings, it was definitely worth it to be above the city in the dark, clear air; the boys had never seen the sky so full of stars, and I was able to show them the cloudy glow of the Milky Way arching across the night sky as well. It made me think of how humanity must have seen the heavens throughout history: a tapestry of light spread wide above them, telling the stories of their people, singing the praises of God. For both science – the desire to learn, to know, to explain – and story – the desire to remember, to understand, to give meaning – are fundamentally human and find a home in the stars above.

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 🙂

Posted in wwlw

{wwlw episode 10} – CVC words

All credit for this game goes to Ruth Beechick! Her books are full of good ideas and perspective on education.

The boys had been walking around talking about different letter sounds and trying to find objects that started with each letter of the alphabet in order, so I thought that it would be a good time to introduce more phonics games. CVC words are the easiest place to start, so we started there.

I cut two pieces of card stock into sixteenths. On each of the sixteen blue rectangles I wrote a consonant; on five of the orange rectangles I wrote a vowel (some consonants don’t show up that often in three-letter words, so it wasn’t hard to find a few to leave out). We spread them out, face down, on the table, and took turns drawing three cards.

The first time we played, we earned a chocolate chip just for sounding out the potential words. The second time, though, we only earned the chocolate chip if our three letters spelled a real word. So our beginning level helped to build confidence in the rules of sounding out words, while the harder level forced the boys to think of the collection of letters as a word instead of just a series of sounds.

Chocolate chips are an exceptional reward in our family 🙂 By the end of our second game, the boys were almost literally rolling on the floor in laughter at some of the words (real and otherwise) that our randomly-drawn letters spelled – and in the meantime, their speed at decoding those words had increased significantly.

I think next time we play I’ll make an extra “e” card with the chance to earn an extra chocolate chip for successfully sounding out a real word made with the three random letters and an “e” at the end – it’ll be a good way to practice the short-to-long vowel change!

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 🙂 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 🙂

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 🙂

  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 🙂

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

  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 🙂 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 8

We have been learning about writing letters and sending them in the mail!

Rondel has been coloring pictures by the handful (although not finishing them all), and he wanted to send some of them to the people he loves that live far away. So he has been learning about how to write letters by dictating to me the things he wants to say, and we’ve been tucking a letter and a picture into an envelope and mailing it off. It turns out that writing is a lot different than talking; I’ve been writing for so long that I had kind of forgotten, but when you are communicating with someone who can’t see you or what you’re talking about, and who can’t ask clarifying questions in real time, you have to use words in a different way than when those perks of conversation are available. So Rondel has been figuring out how to word things for a letter vs. a conversation, which is pretty neat.

He’s also been learning about addresses and the mail system – how does the mail man know who Grandpa Bob is? How do they find his house to bring the letter there? What do all those numbers and letters mean on the outside of the envelope? And so on. Rondel’s first question was actually about why we needed an address on the envelope, so I had to explain to him that the mail man here in Arizona who will pick up the letter doesn’t know his Grandpa Bob and wouldn’t know what state to send it to 🙂 I think he is starting to understand it, and it is a good step towards learning his own address and understanding why that is important information to know.

So far he has only sent pictures to his aunt, his great-grandma, and his great-grandpa – but I think if he could think of more recipients he would send pictures to others as well, especially if there were a chance of getting a letter in reply. Mail is so exciting – you never know when something special may surprise you!