Tag Archives: math

Measuring the Marigolds

Wow, we’ve been busy the past few weeks. In many ways our busiest days were the ones we stayed home and did nothing.

As we wait for our fence, grass, patio, gardens, and trees we spend the days with our noses pressed to the window dreaming. Today Ella dreamed the weeds growing in our backyard grew into beanstalks. We were able to climb them all the way to space. There were no giants in the clouds though. Because clouds are made of condensed air and nobody can stand on air. Okay then.

We also spend quite a bit of time caring for the plants we have in the house. A grapefruit, a lemon, lime, and mandarin tree. Each tree should have 5 or so fruit on it that’ll be big enough to eat. From caring for these plants the girls have learnt about the different parts of flowers, they’ve loved being little bumble bees pollinating the flowers. They’ve also successfully planted an apple seed from an apple they were eating. Which lead to us getting several pots and growing herbs, tomatoes, peppers, and onions. The different sizes and shapes of the seeds fascinated them.

The citrus trees gave the girls another opportunity. The trees came with a few friends. Besides hundreds of aphids (that we’ve faithfully been squishing by hand every day), they also came with millipedes, pill bugs, and spider mites. We diminished the millipede population very quickly (they were everywhere), killed every spider its and aphid we could find. Added a couple lady bugs to the mix and the girls went to work adding a few pets to our family.

They took our old sugar dish (looks like a  fish bowl) added a few inches of dirt to the bottom, layering the dirt with fallen leaves, blossoms, fallen fruit buds, and anything else they could find that was rotten. We added a spider plant shoot that needed a home and a tomato plant that wasn’t doing very well. They carefully added water to half the terrarium and left he other side mostly dry. They named their new pet pill bug Aliza. It didn’t take long for them to find more. Soon our little terrarium housed four pill bugs. The tomato plant is doing fabulous, the spider plant has taken over the rest of the space, effectively sealing the top. The air below is moist and the dirt stays damp. The perfect environment for pill bugs. The girls can see through the glass to see when the dirt becomes homogenous allowing them to know when to add ‘food’ to the space. In the meantime they have a glass they put all fallen leaves and such until it’s time to feed their little pets.

From here we talked about bugs, what makes a bug? was a pill bug actually a bug? (nope, it’s a crustacean). We talked about bugs, crustaceans, turtles, shrimp, then we moved on to talking about mammals. We spent an hour or so classifying different creatures, then dissolved into fits of being sabre-toothed, crustacean eating dogs. It wasn’t pretty. And there were still six hours until Ryan came home.

Ninjas are deadly and silent. I set up a laser obstacle course out of yarn through our upstairs hallway. The girls had a blast climbing over and under the different strands. Cordelia managed to get herself tied in knots, Chester managed to rip it all down (and get himself tied in knots), Agatha couldn’t tell where her bum was (so it’s a good thing these lasers did not actually slice off the body part it touched), Ella managed pretty well. I’m still working on the overall costume, but did manage to get a couple of black jumpsuits made in a day so the girls have Ninja costumes to play in. Ella wants to start wrestling, but I think if I introduce her to martial arts she might go for that more so now than wrestling. Youtube here we come!

For her birthday Ella received a Mexican cookbook with spanish vocabulary in it. She’s so exceed and wants to learn Spanish so badly. We intended to start her in French (makes sense around here) but think we’ll start with Spanish after all. As soon as we (fill out the paperwork) get funding, we’ll buy the Rosetta stone for Spanish. Ever since she received this cookbook she’s actually started eating food with flavour again! She happily dumped cumin and onion into a pot because her book told her to.

As such she’s really working hard to learn to read and write. She practices writing almost daily, but at this point if she writes a letter it’s just a letter unless Ryan or I give it meaning (within a word). If we spell words for her she can write them down. Certain words she can see and read quite well, but often we have to stop her and actually have her look t the word. She just assumes she doesn’t know it, so doesn’t try until we tell her she either knows it or can figure it out.

As she works on her letters, she also works on her numbers. In fact numbers are very important to her right now. She owns her own store you see. She creates items every day and sells them to unsuspecting passer-by’s   Ryan and me. It started with her asking for a certain number of coins, exact change only. Then moving onto asking for specific coins. She’s slowly moving toward asking for a certain price. Though this is difficult for her. The numbers are bigger than she comprehends yet.

Ella: Mommy this twirly costs two coins.

Me: Which two?

Ella: The ones with the reindeer.

Me: Quarters. This costs two quarters?

Ella: (Beaming) Yes.

I really didn’t think she could count to fifty, let alone try to teach about change for those numbers. And using two quarters to her is easy, fifty cents. She doesn’t have a comparison. As an experiment I did ask if she could count to fifty. She made it to twenty no problem. Then she paused and thought about it. Asked what the next number was. I told her twenty-one. She then guessed twenty-two. I said yes. She then slowly counted twenty-three, twenty-four up to twenty-nine where she paused. I told her thirty, then she went on. Only pausing for the tens to figure out what the number was. We counted to one-hundred ten. in this fashion. She didn’t know it previously, but she knew the pattern and could manage from that point.

Ella: This costs three pennies

Me: Okay. Here’s a nickel. Can I have change please?

Ella: Sorry my store doesn’t work that way.

I explained to her about change. I promised I wouldn’t take her money, but wanted to demonstrate what how change worked. If she liked it, she could make change. Or I wouldn’t buy the item. We took out all her coins we talked about the different coins, how much they cost, size, shape, colour. We then made piles of each one so each pile was worth the same amount. I then showed her how to make change for a nickel from pennies. In the end she wasn’t certain, but her jar had more money than when she started so she’s trying it out for now.

Ella’s been fairly proficient with addition and subtracting. She uses her fingers, or objects to visualize, but she knows the terms and the concepts. Recently we’ve begun multiplying and dividing small numbers as well. Usually in relation to food. She’ll glance at a cake and tell me how many pieces everyone gets. But she can’t tell me how she knows that. So I’ve been helping her figure out how she knows the answer. The whole number we start with is the number of pieces total. Then we get out the same number of plates as people. Before we start we make note of how many pieces she thought were for everyone. Then we divide. She’s usually right. Though now that I’ve pointed out the concept to her I’ve noticed she doesn’t get the right answer as often. But I can see her trying to get the answer.

For the most part everyone seems to do the same thing, just different levels. While Ella’s writing about numbers, Agatha’s counting objects or colouring and Cordelia’s eating markers.

Agatha’s working on letter recognition and writing her own name. We’re also talking about places in the world and where she fits in. I have a couple ideas for projects, just a matter of doing them.

Agatha’s fascinated by Benjamin Franklin and journalists. She’s been creating news daily, writing everything she can down. Her and Ella team up to sell it to us from their news office in the basement. She’s also practicing counting a starting to add and subtract. Though mostly that’s because that’s what Ella’s doing. Agatha’s not interested in ‘actual’ math yet.

Cordelia’s climbing everything and has a ton of words. There is some interpretation needed, but once you know what she’s saying it’s easy to understand the next time she says it. Certain words are clearer than others. Her doggie commands are perfect. “‘Hester Siiiiit” (Hester = Chester) “‘Hester Stttayy” both commands complete with hand signals.

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Probability, Fractions, Addition, Subtraction

At what age should a child know how to count? To 10, 20, 100? At what age should a child be able to add basic numbers? Subtract them? At what age should fractions be introduced, or probabilities?

According to the school district each skill should happen at a certain time – for all students. For this reason I believe many parents don’t ‘allow’ their children to learn the skills earlier. Not purposefully mind you, but rather because it doesn’t occur to the parents that their child is capable of learning them.

Ella at close to 4.5yrs can count to twenty on her own, possibly farther. But that is nothing remarkable the majority of three year old I know can count to twenty. She also adds and subtracts number 0-12 easily, sometimes she uses finger, dots, or some other item to assist, other times she does it in her head. She has a basic understanding of fractions, and is beginning to learn probability.

She enjoys eating sandwiches for lunch. She can practice adding and subtracting as she eats piece by piece. When I cut the sandwiches into different proportions she can practice fractions. As well as adding and subtracting fractions. If you had 8/8 and ate 3/8s, how many are left? If you had five, and have eaten three, how many were there when you started? She’s interested in the ideas, so she plays along. If she weren’t interested we wouldn’t continue, but she is, so we do.

Most recently we introduced her to one of our favorite board games, “Settlers Of Catan”, the board is made up of hexagonal tiles and each tile has a number placed on top. Under the number are dots. The number of dots represent the probability that each number may be rolled, based on the number of different combinations possible with two dice, with 8 and 6 being the most likely to be rolled. We explained the dots to her and took turns placing settlements with her going last so she could place both her houses at once. She choose well. The next time we played she wanted to place first so she could choose the best settlement placement.

We could take the basics a step farther and write down the numbers as we roll them, then at the end of the game see which numbers were actually rolled most often. We could keep that tally and see after 3 games, 5 games, 10 games which numbers really had the highest probability. If 6 and 8 weren’t rolled most often we could discuss possible reasons why.

Next we’ll work on geography. We’ll play “Ticket to Ride” – a game where you build train routes from one city to another. Besides geography it’ll also reinforce colours, numbers, and introduce some complexities of risk taking: taking more time to get lots of points at once, or taking less time and getting several smaller points.

Besides the skills mentioned, the games also teach other skills, but most importantly it provides a fun way for our family to spend time together doing something we all enjoy.

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