Part 2

The little boys with some overlap of the smallest girl, tend to get some free “Mommy Math”  thrown in while she’s fixing dinner.  Whether is getting the right number of plates to set the table or putting the right number of broccoli or carrots on each plate that works.  They also get free play time with puzzles, blocks and music.

We use a mix of flashcards for different areas.  The little girls start with recognizing numbers with picture flashcards, and larger numbers with School Zone flashcards.  Now I really try to get them to understand the numbers what they represent and how they relate to eachother.  I am happy when they can recognize a 5, and also know it is more than 3 and less than  6.

The oldest in this group has progressed to two-digit numbers.  I have gotten her to understand that each number can be broken down in may ways.  The easiest way it the number of tens, and then the number of ones.  We drill on that a lot.  But then I try to slowly introduce other skills sh as counting o sixteen by steps of 4.  How many steps of 4 did you climb?  Or rounding the number to the nearest 5 or ten (comes into play later in larger math and multiplication and division..

The older two from this group have also voluntarily (that’s not a hint of competition, is it?) moved themselves into the first addition flash cards and basic computer games up to about K – 1 level.  If the computer is on, there is usually a flock of helpers attracted to that area, and we in effect have our own version  of “Cloud computing”.

I will write more about the three older ones and the specific learning tools and programs I use in Part 4.  But it is very cool to see that the ‘learning how numbers work and relate to each other’ really works.  My oldest three have shown me that they have figured out multiple ways to get to an answer in multiplication or division.

Take 4 x 8, for instance.  My 7- and 8-year olds will actually verbalize their thought processes and let me know they can start with 4 x 10, then subtract two 4′s to get 32; or they can take 5 x 4, and add three 4′s to get the answer; or they can take two 8′s, and double it (there’s that binary, which really blows me away that they can process like that).  It’s really cool since I did not realize they were learning that way, and I did not tell them to verbalize their thought processes, but I think they have just learned it from me generically teaching them how to get to an answer.  This is kind of weird, since I am an engineer by training, and very visual by nature (I do most everything on paper–”the shortest pencil is better than the longest memory”), but I think we learned much of it in the car driving around so they have learned a lot of math by hearing it.  Kind of cool!

Now my oldest just wants to get to the answer and move on, but tonight in his long division I let him know he had an incorrect remainder. The equation was 49 / 3.  He answered 16 with a remainder of 5.  The remainder should have been 1.  I have taught him to do long division working it out with a pencil and multiplying each digit and subtracting from the dividend in the classic “division-multiplication-subtraction loop”.  However, being our firstborn, and always an original, he has to do it a different way (mostly in his head so I can’t figure out how to help him if he makes an error).  What I saw him write out on paper was very different from what I taught him, and also very heartening to see he understands how it works, and that there is more than one way to get to the answer.  Here is what he wrote on his paper:

12.36

13.39

14.42

15.45

16.48

At first glance I didn’t understand what he was doing with the decimals (since we haven’t worked with them yet).  He explained that he knew he was in the ballpark with 16, so he starting at 12, he worked his way up, multiplying each number by 3 to get to 16×3.  Then he subtracted the  from 49 to get a remainder of 1.

I am humbled.