Four Year Old Fractions

My partner downloaded the app, Slice Fractions 2, onto his iPad, and Little Fox has been obsessed with it. Though he seems to have been able to figure out most of the problems on his own without being formally taught fractions, some of the levels stumped him.

Rather than do the problems for him so his mammoth could move on, earn hats, and rescue cute pets, I talked to him about the problems as we solved them together. He was especially stumped by a particular level where there are two whole blocks, and he has to come up with five-thirds blocks of ice to snuff the lava and let the mammoth go on its merry way.

Just describing it wasn’t working, as it had for other levels, so we got back to practical basics. I didn’t think we’d be doing fractions this early with him, but so be it. He’s interested, so we’re doing it.

I thought of using cuisenaire rods, but what I really wanted was something whole that could be cut up. We don’t have gf pretzel sticks, and I didn’t want to break a pencil for a point (pun intended), and Dragon suggested a banana, but no way am I eating or wasting a banana right now.

We decided on meat sticks, because even if we didn’t eat them, we could put them back in the bag. Fox plucked the paper towel, Dragon fetched the bag of snacks from the pantry, and I set to work.

First we talked about the stick as a whole, representing a block. There are two blocks: two wholes.

Second, I talked about the “number on the bottom” (the denominator) being how many pieces to cut the whole into. In the case of his problem, five-thirds, he needed to cut each whole into three pieces. Cutting was hard with a table knife–these meat sticks are dry and dense–so I did the work. When we had our three pieces, I showed him that each piece represented a single third.

Finally, we talked about how many pieces he needed to complete the puzzle. The problem showed 5/3. I talked about the “number on top” (the numerator), and how it indicates how many pieces are necessary to solve the problem. I asked him to count out five thirds from the pieces we had. Then he went back to the game, used his narwhals to slice the right number of thirds, and passed the challenge.

If you have access to the game and can afford the price ($4), this is an incredible game that my little one loves, and both my partner and I enjoy playing as well, even though we mastered fractions a long time ago because there’s more to many of these challenges than just knowing what numbers are needed to complete each level. (I am not being sponsored by the company to endorse it, I just really, really like it.)

As for the meat sticks, they never made it back in the bag.

Counting and the Alphabet

Lately, the Little Fox loves counting.  We’re counting the lamps in the bedroom, we’re counting our fingers and toes, we’re counting bites during a snack, or seconds while I hold my PT and yoga poses.  We’re counting anything and everything holding my son’s interest.

It’s not the first time he’s been interested in numbers, but it’s a resurgence with an intensity he never showed before.  As I mentioned in last week’s post, he started becoming interested again with the books One Nighttime Sea and Wizard of Oz Counting.

One of his favorite things to count — his absolute favorite — is counting letters.  He especially likes seeking out the letters in his name (he learned to spell his name courtesy of a cousin who sent a wooden bench carved with his name in it).  He’s always looking for the As and the Cs.  Sunday night, I read the whole Animalia to him, slowly enunciating all the words.  We didn’t just count the obvious letters, but also those hidden within the art on each page.  Sometimes we went far beyond his knowledge of counting, but he did his best to repeat the numbers I said.  Some pages went up to 23 instances of the letter in question.

This combined interest in both numbers and letters has become an exciting way of integrating the basics.  Though we’d never push him to start reading or doing math so early, we absolutely support him when he shows such passion for something.  Since he’s so focused, I’ve even started introducing the concepts of addition.  When we’re counting letters or animals or some other items in a book, and the items in questions are split between the folds, I count the whole, and then count those on either side of the page and add them together.

For example, seven lemurs are spread across two pages.  We count them as seven together, and then I count four on one page, three on the other, and say, “and four and three makes seven!”

I don’t expect him to repeat this, but by simply talking about it, the concept starts to sink into his mind, so when he starts to focus on adding and subtracting objects in his world, these lessons will have laid a preliminary foundation.

Random ideas for things to count:

• Legos, ponies, cars, figurines, or other toys they’re actively playing with
• Sticks, leaves, rocks, shells, or other common objects found on a nature walk
• Seconds (while doing something)
• Peas, chips, grapes, or other food that comes in multiples
• People or animals in an area
• Fingers, toes, eyes, ears, bones, etc.
• Shirts, pants, socks, or other laundry items while folding (socks are especially good for counting if they’re learning to fold their socks)
• Dabs of paint, crayons, or other items with varied colors (also integrates color lessons)
• Wooden beads, buttons, yarn pieces, and other craft items they’re using in projects
• The tires on different vehicles (e.g. bicycles, tricycles, car, semitruck, etc.)
• The limbs on varying animals (counting legs: zero limbs on snakes, bipedal humans, quadrapedal animals, six-legged insects, eight-legged spiders and octopuses; wings or arms vs. legs; etc.)

Another part to teaching and learning counting is the concept of zero, nothing, and none.  This is crucial to all levels of mathematics, although the basic vague understanding of it comes along often in a young child’s life when they’re told they cannot have something, or when they insist they want to eat nothing when they’re cranky with hunger.  Nevertheless, as important as zero is, we often don’t remember it in counting, which is why discussions about limbs, for instance, can introduce zero as a number meaning none.

Whenever your little one starts taking an interest in numbers or letters, it’s time to start playing number and alphabet games, and singing songs (e.g. Hickory, Dickory Dock, 10 little monkeys, the alphabet song, and so on.)  Another great resource are “Alligators All Around” and “One Was Johnny” by Maurice Sendak and sent to music by Carole King (these are two books found in Sendak’s Nutshell library).  And if you’re counting months, don’t forget “Chicken Soup with Rice.”  If your little ones are Seuss fans, there’s also Dr. Seuss’ ABC Book; it’s not my favorite, but my son adores it.

 

 

 

What We’re Doing: Justice January

Our year began with a few surprises.  One of them dramatically shifted our plans for the year, as some mistakes came to light — small mistakes hidden from my partner and I until they compounded into something big.  My daughter has withdrawn from Running Start for now.  Though she kept up with the academics and showed full comprehension of the subjects she studied on graded papers and tests, her social anxiety led to a series of events that reflected poorly on her GPA.

For now, we’ve returned to homeschooling, and are seeking a counselor to help give her tools to deal with her anxiety better.  While her choices sadden me, it’s a valuable learning experience for us both.  While it set an unexpected tone for the new year, it’s not all we’ve been up to.

 

WHAT WE’RE DOING

We bought a new subscription to the Pacific Science Center and went there for the final weekend of their Sherlock Holmes traveling exhibit, complete with historical documents and artifacts, film and TV props, and a mystery to solve as a family.  My partner and I attended the Seattle Symphony‘s tribute to David Bowie on the 10th, and this past weekend, we saw Curious George and the Golden Meatball at Second Story Repertory Theater.

The Little Fox can now count to ten consistently, and engages us in counting whenever he finds something interesting enough to count.  Much like the Count from Sesame Street, he’ll stop whatever we’re doing and have us count something.  Most recently, it was the number of lamps in my room: three, and the number of fingers on his hands: ten.  The Dragon wishes to one day work for the FBI as a forensic psychologist, so we’ve been checking out books related to her long-term goals, including Criminology, Psychology, and U.S. History.  We’re also working on essay writing and pre-Calculus, as she’s considering doing AP testing as a way to earn some of her college credits.  With the SATs coming up, we’re also considering my father’s advice to take the PSATs first.

 

Upward Facing Dog

I’ve taken on the Yoga Green Book‘s 21 Days of Yoga Challenge by Carla Christine, and have working harder on improving my strength and flexibility.  Her instructions have been detailed and easy to follow, improving even the basics I already practice (I recommend her for future classes; also, check out my friend Starbird, who teaches one how to flow through yoga). As someone with an autoimmune issue and chronic pain, sometimes it’s easy to lose perspective on the hardest days, so I’m also working on tracking my overall daily outlook using the idea of a Year in Pixels, and a Jar of Happiness. I’ve also been working hard on my writing.  Cress and the Medicine Show, a myth-based novelette, will be available mid-February, and my debut novel, Perdition, publishes in March.  Also, there’s a new class I’m putting together to teach Creative Writing to middle schoolers.

On the whole, we’re finding a new routine all over again, and I’m hoping to incorporate some of these wonderful ideas about gameschooling from SimpleHomeschool.net.  We’ll also be greeting the protesters from the Women’s March on Saturday, and we have some wonderful books checked out from the library to celebrate the memory and message of Dr. Martin Luther King, Jr. all week long.

 

WHAT WE’RE READING

At the time of writing, I have 45 books checked out from the library and 2 curriculum boxes.  Among them, the collection of Nurse Mathilda stories. Since beginning in December, we’ve completed the first book and are in the middle of the second.  If you’re not familiar, these are the three odd little books, which inspired the Nanny McPhee movies, and all center around a family so large, they don’t know how many children they have.  My son enjoys them, but wants to take breaks every second or third night, so we’re doing a few chapters each week.

My son’s favorite counting books right now are One Nighttime Sea (library copy) and The Wizard of Oz Counting (bought at Costco with the shapes book).  When I checked out One Nighttime Sea, it was for his nocturnal animals unit, but it’s become such a beloved book, we keep renewing it.  It not only counts different sea creatures from one to ten, it then counts even more from ten to one.  We take time to touch each animal and say its number as we go and I ask him where the number itself is on the page.  The Wizard of Oz Counting book is far more simplistic and quite jolly, and we’ve had it since he was a year old.
Along with some criminology books, my daughter is working her way through FBI 100 Years and The Adventures and Memoirs of Sherlock Holmes.  There are other books awaiting her, but I don’t want to bog her down.

 

On top of books, we have magazine subscriptions coming in.  We allowed our Ladybug and Click subscriptions to lapse.  I was disappointed when they arrived, as I was expecting the better binding of Babybug, which keep well on shelves as sturdy little books.  Standard sized magazines don’t hold up as well, and the content didn’t inspire as much interest in my son.

While at the library, we found out they have all of the Cricket Media publications available, so we can read them there when we wish each month.  However, I also fell in love with Cricket itself, especially the hilarious stories in the January issue, so I’ve ordered a subscription for it, despite its recommended age range.  Also, we’re receiving Zootles, a fun science magazine for kids given to us as a gift by our cousins.

 

WHAT WE’RE EATING

Recently, my daughter took my banana bread recipe and made a few dozen mini muffins for us in the toaster oven (because our oven still isn’t fixed; we’ve had a lot of trouble ordering the element we need for baking).

Mama Raven’s Banana Bread

1/2 c. butter (salted, because yum)
3/4 c. raw sugar
3 eggs, beaten
3 aged bananas (mashed)
1 1/2 c. brown rice flour
1/4 c. tapioca starch
1/4 c. oat flour
1 t. salt
1 t. baking soda
1 t. cinnamon
1 t. vanilla
7 oz. of crushed or chopped pineapple
1 T. pineapple juice
1 T. soured milk (milk with a few drops of lemon juice; wait 20 minutes to sour) or buttermilk
1/2 c. crushed walnut pieces (not option in my house, but maybe in yours)

Mix dry ingredients and set aside.  Mash bananas and stir in eggs and vanilla.  Blend well and add pineapple juice and buttermilk.  Fold wet ingredients into dry, and add pineapple (the pineapple helps keep the bread moist) and walnuts. Put in a greased bread pan and bake 45 minutes in a 350°F oven (or about 15 minutes in a mini muffin pan).

Alternatives: for dairy free recipes, substitute coconut milk for the buttermilk, and Earth Balance sticks for the butter.  If you wish to add chocolate chips, ditch the pineapple and substitute about 1/4 c. of milk or coconut milk instead.

Enjoy warm and buttered or cold and dunked in chocolate milk.  So good!

Geometry, Design, and Pasta

Fiori-shaped pasta by Barilla. Approximately 0.5″ in diameter. (Photo credit: Wikipedia)

Thanks to a friend, we came across the CBS short video clip Geometry and Pasta about two authors — one an architect, the other, a chef — each wrote books about pasta from a mathematical perspective.  The former, George Legendre, cataloged over 200 types of pasta in his book, Pasta by Design, showing the mathematics of form behind the function, in part as an inspiration for other designers looking for more unique shapes in their architecture, though another part I believe has more to do with his love of mathematics. Meanwhile, chef Jacob Kennedy’s recipes and historical knowledge of noodles paired with hints of geometry in Caz Hildebrand’s drawings, come together in The Geometry of Pasta.  This book looks both informative and drool-worthy, but focuses more on the food’s function because of its design.

For someone like myself who is equally fascinated by architectural design and historical cooking, these books are tempting.  As a homeschooler, I can see them being the inspiration for my child(ren) to explore culinary arts, history, math, and design all at once in an integrated form.  An exploration that could be hands on and delicious!