Posted in family life, learning together

learning together: infinite series

I asked Limerick the other day what was, in his opinion, one of the neatest things he knew about math and numbers.

In response he told me he thought the neatest thing was that if you start with the powers of 2 (say, 128 for example) and kept dividing by 2 (32, 16, 8, 4, 2, 1, 1/2, 1/4, and so on, he said), you would go on forever and never actually reach 0.

Basically my five year old uncovered on his own the concept of an infinite series approaching a limit and (very naturally!) decided it was just about the coolest thing numbers do. I love how his brain processes numbers and analyzes the world in their light!

Posted in learning together

learning together: erupting citrus!

Inspired by one of Limerick’s class experiments at our co-op, we spent an afternoon watching baking soda and citric acid react explosively in our kitchen 🙂

Limerick applying the baking soda to the lemon! (and his shirt, lol)

One thing I really liked about the way his co-op teacher presented the baking soda/lemon juice reaction was that she asked a lot of questions designed to help the kids come up with hypotheses and logically critique those hypotheses. Each lemon volcano had three components: the lemon, the food coloring (to make it look more like lava!), and the baking soda. So she asked them what they thought made the eruption happen, for example, and when a lot of the kids said the baking soda, she pointed out that the baking soda wasn’t making fizzy bubbles when it was all by itself in the bowl!

Limerick at co-op, right after adding the baking soda to his lemons.

So when we replicated and expanded upon the experiment at home (Rowan was so jealous that Limerick got to do it at co-op and he didn’t!), I tried to ask similar leading questions. We also decided to test other citrus fruits with the same reaction, so I had the kids think about the differences between the fruits and guess which would make the biggest reaction beforehand, so we could compare our hypotheses with our results.

To my surprise, the two types of oranges we tested had drastically different results. The big navel orange was even less reactive than I’d expected, while the small juicing orange was almost as explosive as the lemon! The grapefruits were also quite dramatic, being overripe and thus extremely juicy and very fun to squeeze everywhere to create great “lava flows” of fizzy reactive liquid. I do think the lemons were still the most reactive, although the results were not anything like quantitative 😛

While we didn’t draw chemical diagrams and get into the atomic reason acids and bases react, we did have a lot of fun exploring the reaction itself! It’s such an easy and exciting way to see how different types of substances can interact.

Posted in learning together

learning together: biomes

While the kids were playing together, I set up an activity for the next lull in their imagination. Pulling out two of our giant whiteboards, I quartered them and placed a biome card (from our Waseca materials) into each of the eight sections: Oceans, Wetlands, Tropical Forests, Temperate Forests, Grasslands, Desert, Mountains, Polar Regions. Pulling out the box of toy animals, I began sorting them into the biomes: zebras in Grasslands, tigers in Tropical forests, dolphins in Oceans.

It wasn’t long before Rondel came out and was instantly engaged, asking if he could help sort the animals. So we sorted together, talking about which biomes would make the most sense for animals which are domesticated, for example, or adapted for a range of habitats. When we had at least a few animals in each biome, I brought out the biome question and answer cards.

There were six questions altogether (asking about temperature, moisture, soil, plants, animals, and humans), and each one had an answer for each biome, so Rondel’s task was to match each answer to the correct biome after I read the card. He only needed help on one or two of the cards, and showed a good conceptual understanding of how the environment differs between biomes, how plants and animals have adapted to different biomes, and how humans have interacted with biomes in different ways (both positive and negative).

I noticed that our animal representation was heavily skewed towards African grasslands and oceans; the Waseca teacher’s guide recommended using animals cutout from magazines, which would increase the diversity, but I didn’t have any that I was willing to cut up. I may just need to buy a big batch of old National Geographics or ZooBooks off of Ebay – old magazines can be really useful craft and learning supplies!

This activity was a good summary of the information we’ve learned about biomes as well as a good overview before diving into more detail on any one area; I think we’ll explore animal adaptations next but I have a lot of ideas.

Posted in learning together

learning together: a “3R’s” treasure hunt

Rondel really enjoys looking for treasure (thing-finding in the tradition of Pippi Longstocking, where almost anything can be considered treasure), and as I pondered what to do with our morning (unexpectedly open since Aubade had too bad of a cold to handle the hike we’d planned), I thought he might enjoy following a series of clues to find a treasure at the end.

Because there is always some way to incorporate math, reading, and handwriting into life’s activities (please take that with some humor!), I decided that each clue would be a numerical cipher but that the numbers in the encoded message would have to be determined by calculating a series of math problems. I made short messages like “under the desk” and “lego box”, converted them to series of numbers using a key, and then came up with arithmetic problems at Rondel’s level. He started out with the key and the first clue, which led him to the second clue, then to the third, and all the way to the treasure after six clues in total (probably about 50 math problems all together, which is a lot more than he’d normally do otherwise!). In addition to the math, he got a lot of handwriting practice in from writing down the numerical answer to each problem as well as the corresponding letter value from the cipher, and then even got to do a bit of reading to put all those letters together for each clue.

Above are two examples of keys and clues – the orange set was for Limerick and the red set was for Rondel. Changing the key values to larger numbers would let you create even more difficult math problems without needing to alter the method of encryption. Limerick kept commenting on how the problems corresponding to the letter “A” – where the answer was 1 – were too easy, and a different key value would have eliminated that issue.

Rondel did a whole treasure hunt, despite the difficulty of focusing with two younger siblings running around at high volume and also being very interested in everything he was doing and not giving him any quiet or space! I was really impressed with his determination and motivation, because nothing about this was easy for him but he didn’t give up.

Rondel sitting at the kitchen table with sound-reduction headphones, writing out the answer to one of his clues.
The sound-reduction headphones were a huge help! I could see him relax and focus more easily the instant he put them on.

Limerick wasn’t interested at first, because he isn’t all that into finding treasure, but he like the idea of following a path of math clues so I made a set for him later and he finished his as well! He does not like to write or draw often so pulling him into an activity where he writes this much is a rare and pleasant thing (I think he couldn’t resist the math).

Limerick standing by the kitchen table writing on his clues

One thing I did notice from the activity was that both boys have legibility issues, and I’m going to have to find a way to work with them on pen grip and letter formation that hopefully doesn’t result in daily fights. Rondel’s letters in particular are like people, each with their own personality and opinions, and they dance around the page and swing by their toes and jump on each other’s heads and sometimes sword fight – and they are highly offended by the idea that they should arrange themselves in a neat orderly line! So if you have any ideas or suggestions I would love to hear them.

Posted in family life

independent writing

The boys were trying to be sneaky, scampering through the kitchen when my back was turned, hiding behind the trellised sweet potato vines when I said hi through the kitchen window, running into their bedroom when I peered down the hall.

(They’re not particularly sneaky, but they are very adorable when they’re trying to be.)

At one point Limerick crept silently into the kitchen and proceeded to stare at the water and ice dispenser on the fridge for several minutes, then disappeared again. Shortly thereafter, the boys appeared with the following note:

A piece of printer paper with the message, “PLEEZ MOM CAN U FILL UP MIE WATER”

Rondel needed more water and they wanted to ask in a sneaky way, so they worked together to figure out how to spell the words and Rondel transcribed the message (they had a dispute about whether “water” should be spelled with an “a” or an “o”, thus explaining Limerick’s mysterious visit to the fridge: he’d been checking the spelling (and proving himself right!)). They told me they didn’t know how to spell the word “you” so they just used the letter even though they knew it wasn’t correct 🙂

This is the first time they’ve used writing to communicate, besides a few happy birthday cards, and definitely the first time they’ve written without any external prompting. So I’m most likely inordinately excited about it and am looking forward to more notes of this nature!

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 family life

lift off!

Our biomes curriculum started off by introducing our planet’s location in the Solar System – it’s kind of important, after all, since the sun plays such a crucial role in shaping climate, determining the seasons, and maintaining life. It’s intended to be just a brief overview, before diving down more deeply into Earth itself, but both Rondel and Limerick have become completely, utterly captivated by outer space.

Limerick in particular has attacked it with his rather academic and obsessive bent, spending hours poring through images of the sun and the planets (always in order, from Mercury outward, including the dwarf planets), asking me to read and reread the books we have in the house, getting out the play dough day after day to model the solar system and using the kitchen scale to make his planets as close to an accurate scale as he can. (Since it’s finicky in its old age and won’t switch from standard to metric units, he’s gotten some practice working with pounds and ounces as well. It is rather irritating when something needs to be 1000 times larger than something else and you have to divide by 16 to get the correct number of pounds.)

 

(I may be to blame for his obsession with accurate scaling… for our first solar system activity, we made a scaled model of the solar system with play dough, based on NASA’s mass estimations for each planet, and measured out the appropriate distances between the planets so we could set them up down the hallway. Jupiter was so much larger that we ended up making a new double batch of play dough, using it all for Jupiter, and scaling everything else in relation to that.)

From top left, clockwise: all eight planets before placing them relative to the “sun” (the bookshelf); the whiteboard with calculations (and on the bottom a comparison of Jupiter’s mass in kg to various family members in kg); Jupiter looking out toward the other gas giants; Neptune looking in toward the “sun”; Jupiter looking in toward the inner planets.

Over the weekend, both boys decided to make paper models of the solar system as well, not to scale, but showing all the planets and the sun. They even wrote labels for each planet, which is the most handwriting they’ve ever done at one time! (Rondel’s picture is on the left and Limerick’s is on the right – Rondel included Ceres, a dwarf planet in the asteroid belt, and Limerick gave his sun quite a few solar flares.)

They’ve also been asking to read from our (admittedly small but at least quality) space book collection at bedtime and throughout the day. We’ve been cycling through Our Solar System by Seymour Simon (published in 1992, and lacking a lot of newer information), The Magic School Bus: Lost in the Solar System (published in 1990, so the same problem), and Astronomica by Fred Watson (published in 2011, absolutely massive, with amazing images and detailed information which I have to skim through to read at a level the boys can understand).

I’m planning on finding some supplementary books from the library about different space missions and picture book biographies of people involved in space exploration, so we can incorporate some history into our space study as well. We’ve already made a timeline with the lives of family members and individuals from books we’ve read, so it would be natural to include important dates in space exploration. Since ASU has a large space exploration exhibit and 3D show open to the public, I’ll probably try to incorporate that as well. And while Limerick has already used math with all the scaling he’s done, I’d like to find a way to show the boys how much math was used in designing spacecraft, planning missions, and charting the orbits of planets – Rondel enjoys math far more when it involves a topic he’s interested in. It might not have been my original plan for the beginning of the school year, but what’s the point in homeschooling, after all, if you can’t be flexible and use your children’s interests to motivate their learning?