Thinking about Math

Here are some things I learned about math since homeschooling.

*Zero*
Zero is not merely nothing. Zero is the balance point between positive and negative numbers. Zero itself is neither positive nor negative.

*Multiplication is NOT Repeated Addition*
Multiplication is not repeated addition. Repeated addition works for whole numbers, but not fractions. I like to think of multiplication as groups of objects. For 2 x 3, start with a three, and take two of them: 6. For 1/2 x 3, start with a three, and take half of it: 1 1/2. For 1/2 x 1/3, start with a third and take half of it: 1/6.

*Are there more even numbers or whole numbers?*
I guess this is obvious, but I never thought of it before. There are half as many even numbers as whole numbers. Yet, there are an infinite number of both.

*A Parallelogram IS a Trapezoid*
And along those lines, a square is a rectangle. All the formulas and propertes that apply to a rectangle also apply to a square. All the formulas and properties that apply to a trapezoid apply to a parallelogram.

*Algebra Manipulatives Exist*
There's a host of math manipulatives for early elementary math: addition, subtraction, multiplication, division, place value, fractions, decimals, etc.
I don't remember using them in school, but they are easy to find nowadays. Slightly less common are manipulatives for algebra. My favorite algebra manipulatives are the ones used in Hands-On-Equations, and algeblocks.

*The Distributive Property is Very Useful*
I learned about FOIL (first, outside, inside, last) in algebra class when multiplying things like (x+3)(x+4). The manipulatives for showing (x+3)(x+4) are also ideal for explaining 13*14 = (10+3)(10+4).
traditional algorithm: ((4*3) + (4*10)) + ((10*3)+(10*10))
FOIL: (10*10)+(10*4)+(3*10)+(3*4)

*Cuisenaire Rods shouldn't have notches*
Dear me, other people have written at length about this topic. Suffice it to say that I am firmly in the Cuisenaire Rods should't have notches camp.

*Grading math worksheets is BORING*
I guess this also goes without saying. However, I never had to do it before homeschooling and I now actively look for ways to avoid grading math worksheets.

Happy Birthday Glitter

Glitter wore that "Birthday Girl" pin from the early morning when her sister put it on her, until bedtime.


To celebrate, we went out to eat. Originally Glitter requested the same Chinese restaurant where we went for Chinese New Year. Wander and I were looking forward to yummy food. Then, at the last minute, Glitter changed her mind and wanted Chuck E. Cheese. The grown-ups in the family are not fond of Chuck E. Cheese. But, as Glitter cried, it was her birthday, so off to Chuck E. Cheese we went.



Okay, the food at CEC wasn't so great, but the smiles evoked by those silly games and rides were awesome.

Once home, Glitter got her present, a Panda PillowPet. She named *him* *Jane.* Yup, she said that the panda is a boy, and she named him "Jane."

Now both sisters have pillow pets! (And it's easy to tell the pillow pets apart, yay!)

P.S.
When I ticked Glitter into bed, she was surrounded by extreme "puffyness." "Jane" joined her existing zoo of stuffed animals and Glitter announced in amazement that there were NINE in bed, and watch out, because the bed might break.

Monday's Nature Walk

We saw lots of wildlife on Monday's nature walk.

Sparkle caught this lizard and carried it all around the gardens, releasing it only when it was time to go. We didn't see any other lizards; it must be too cold for them.


Several squirrels showed their bushy tails. Most were too fast for my camera.


The trees were teaming with birds. We saw a few cardinals, and several other songbirds of various sizes. Unfortunately, my camera doesn't take decent pictures of tiny birds hidden among the leaves and branches.

On the other hand, Sparkle and Glitter ooh'ed and aah'ed for a while over this bride who posed quite nicely. It's not really the season for brides, but they do appear every now, as well as girls celebrating their quincenerias.


I don't think I've gotten photographic evidence of the ritualistic hand stamp the girls get each week. I'm surprised that Sparkle hasn't outgrown it yet.

English lesson

Analyzing a sentence is like creating a jigsaw puzzle. You start with a beautiful picture, and then separate it into parts.

Creating a sentence is like making a mosiac. You search for just the right pieces and fit them together to make a pleasing whole.

Youtube videos

Here's some youtube math videos that I just discovered.