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Revised March 5, 2001 |
The #1 Maria Math page on
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(as of November 23, 2003) |
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Revised March 5, 2001 |
The #1 Maria Math page on
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(as of November 23, 2003) |
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She thinks math is very fun. Here are some of the math games she likes. NEW! The Factor Game! Numbers Maria began to
recognize numerals when she was about fifteen months old, and could write
all of them around her 4 1/2 Counting We don't remember
when Maria began to count, but she was counting most two-digit numbers correctly
before she was
Maria started to do addition when she was about 4 1/2. Daddy told her that adding was a game you played when you put things together and wanted to know how many there were. At first, she played the adding game with marbles. After a while, she started using paper and writing adding with numbers and the plus sign. She has been doing long addition correctly, including carrying, since about three months before her 5th birthday. Recently Dad took her to work, and she started writing long addition problems on the board in the computer lab where a group of Rose professors were working. One of them looked at the board and commented, "This is a joke, right?"
Maria started
doing this a few months before her 5th birthday. Daddy told her that subtracting
was a game you played when you took some things away and wanted to know
how many were left. Currently, Maria knows most subtraction facts although
occasionally she has to think about a harder one like 15-9. Daddy also showed
her long subtraction and she even does borrowing -- sometimes with a little
prompting. The first time Dad gave her a long subtraction that required borrowing,
he felt bad -- she almost started crying because it upset her that a bigger
digit was being subtracted from a smaller digit. Maria also knows how to switch
the answer and the number being subtracted, like 12 - 9 = 3 and
Multiplying Maria knows that the times sign is used for multiplication, and she knows many of her multiplication facts. She knows that anything times one, like anything plus zero, is always the same number. Uncle Andrew once asked her what was a million times one, and she told him "a million." Using Mommy's calculator, she taught herself all the perfect squares from one times one equals one, up to twenty times twenty equals four hundred. Sometimes she describes these as "seven rows of seven equals forty-nine" since Daddy told her that multiplying is a game you play when you have rows of things and want to know how many there are.
Maria said dividing
was too hard for a young kid, so she would do it when she was five. On the
morning of her 5th birthday, she asked Daddy to play adding with her.
After that, he showed her how to do dividing by putting marbles into piles.
They checked their answers with her calculator, and Maria wrote some dividing
problems on paper. Fractions Maria has known the concept of one-half since we celebrated her 4 1/2 birthday. We told her when she was 4 3/4 on April 7, 4 5/6 on May 7, and 4 11/12 on June 7. Although she doesn't completely understand what those mean, she knows it means she's getting closer to five. Daddy did teach her how to tell that a number is half of another number by adding it to itself. She usually answers questions like "What is half of fourteen?" correctly, including knowing that half of an odd number is something and a half. About a month before her 5th birthday, we cut an apple into quarters, and she put two of the quarters together and correctly identified that 2/4 was the same as 1/2. Decimals Maria sees these on Mommy's calculator, especially when she uses the divide sign, but doesn't really know what they mean in general. She does know that something point zero is just the same as the number, and she knows that point five is the same as one-half. Percent Maria knows this
is a button on Mommy's calculator and you see it a lot when things are on
sale in a store. I believe she Maria first got interested in factors when Mom helped her use the spiral stencil. Mom showed her that the prettiest patterns happened when you moved the stencil by a number which was a factor of 24, because it had 24 positions. Recently, Maria has asked Dad to play the Factor Game with her. She knows how to tell if a number is a factor, and she knows several tricks of factoring -- that odd numbers only have odd factors, that even numbers always have 2 as a factor, and that it's best to find factors in pairs. She even knows what prime numbers are! When she is done finding factors, she draws circles to connect the pairs. Then Dad sings a song to the tune of "The Muffin Man": "Let's all play
the Factor Game Algebra About a month
before Maria's 5th birthday, Mom saw a newspaper article that mentioned a
4-year-old that knew algebra.
2nd trick: Do the same thing on the other side of the equal sign. With a little
prompting from Dad, Maria did the tricks to get {box} = 12, so she wrote
12 in the box at the first step and was happy to see the right answer. To
make the game more fun, sometimes we use a different shape like a triangle.
We tried a circle once but had to be careful not to confuse it with a number
zero. Dad told Maria that big kids and grownups like to use letters instead
of the shapes when they play "The Guessing Game."
Geometry Dad told Maria this was a math game played with shapes and other things like lines and angles. Maria knows lots of shapes so we will have to play geometry sometime. Dad will give it a catchy name like "The Drawing Lines and Shapes Game." Integers Maria knows that
when you subtract a bigger number from a smaller number, a minus sign comes
on the calculator, and Infinity One day, Maria
asked Dad what was the biggest number. She knows that infinity's not really
a number, because it's not Shapes of Numbers When Maria was about 4 1/2, she used to describe the pattern made by three objects as "the Mickey Mouse shape." Dad told her it was also a triangle shape, and used marbles to show her that six and ten also made triangle shapes. Maria likes to arrange marbles and other objects to see what shapes they make -- "five is a house," "six can be a triangle or a rectangle or a hexagon." The biggest triangle number Maria knows is 78. She learned this using a counting game from preschool. After counting one item into the first compartment of an egg carton, two into the second, etc., she dumped all the items together and counted 78. Dad showed her how 78 made a triangle shape, and from then on, every time we played the game, we had to end by dumping everything together and arranging them into a triangle of 78. Maria knows that rectangle shaped numbers have to do with multiplication. More Maria Photos Maria's Story Page Maria's Horticulture Page Maria's Art Gallery |
Adding 
Subtracting
Dividing 
1st trick: Get
the box all by itself on one side of the equal sign by canceling the other
number on that side. Maria calls this "Making the zero" because she saw how
it was done by canceling an addition with a subtraction or vice versa.