My 8-year-old, Annie, started learning multiplication last year in 2nd grade at public school. Now I must admit, I seem to be raising math geniuses. I'm not bragging (much). I did not grow up with the same math skills that my children have, but of the 4 I've given birth to, it just seems to come naturally to them.
Of course, maybe it could have something to do with the fact that I always provided them with educational and developmental toys from toddlerhood on. We counted as babies, we sorted and grouped as toddlers, and we learned to recognize numbers as preschoolers. My babies were raised in an atmosphere of "learning," so this might be what led to their ease with Math. One can hope.
Now that we have begun homeschooling this year, our first time ever, I wanted to cover multiplication as soon as possible with Annie. Luckily, her 2nd grade teacher was fabulous (if Annie could've had her every year for the rest of her school life, I would've left her in public school -- maybe). Annie has retained her understanding of how multiplication works, so now my goal is to give her a "Classical Education" twist. We are going to memorize the facts, factors, and multiples.
We started a Math Notebook today (just a regular spiral notebook). Annie wrote "factor x factor = product" as her first note. I covered this on the whiteboard, showing examples, and labeling one number "factor 1" and the other "factor 2" at first, then showing her that we can have these switch places, with the second number becoming "factor 1" and the first number becoming "factor 2" but the product staying the same.
She then wrote the rule for "zeros" -- Any number x 0 = 0 -- and "ones" -- Any number x 1 = that same number.
She already has a very firm understanding of the 2's since the answers are "the doubles" (this is how she thinks of it -- it works for her, so I'm not changing it). Thus we didn't worry about a rule for two's today.
We then turned to a clean page, and I made 4 sections by drawing a line across the middle horizontally, and one vertically as well. I labeled the top two sections "0's" and the bottom two sections were labeled "1's." I then got her started so she would know exactly what I expected from her and to make sure she understood the commutative property of these facts.
In the top left section, I started her off with writing 0 x 0 = 0 on the first line. Across from it, in the top right section, I wrote the same thing. On the next line down, I wrote 0 x 1 = 0, and 1 x 0 = 0 ... and the next down line, I did 0 x 2 = 0 and 2 x 0 = 0. I then did the same thing on the bottom half, using the 1's facts. She got the idea of what to do to continue the pattern, and was able to complete these on her own.
She was so excited about the fact that she knew what she was doing, and that she already knows her 2's also, that she wanted me to go on with the next page, so I did! Why stop for the day when the child is engaged?!? However, I wasn't going to just set up the top half of the page with the 2's and leave the bottom half blank. I set it up for the 3's. AND, since we had basically covered things she already had a good grasp of, I decided it was the proper time to cover the 3's.
At this point, I pulled out the Legos (she didn't feel like it was just "more of the same" this way) and picked out 12 little Lego pieces that each had 3 circles on top. I also pulled out a Lego that they would describe as a 2x3 brick (read: 2 by 3). I asked if she could tell me a multiplication sentence that describes that brick. She could! Yay!
I then showed her the chart in her notebook, with the beginner problems I had started for her, and showed her how we could "show" this with the Legos. I also showed her how she could count the circles on top if she needed help. We used that method to "count on" once she knew how many she had so far, and just "counted on" 3 more. Annie then used the manipulatives (Legos) to physically illustrate each sentence as she continued filling in her chart. She loved it. By the time she got to 9, she was able to pick up on the pattern she was making (adding 3 more to the previous product).
As she finished the chart, I grabbed a sheet of construction paper and cut a ctrip from the long side, about an inch and a half wide. I then used my Sharpie marker to write the multiples of 3 (although I just realized I didn't teach her the word "multiples!" Bad mom!!) from 0 through 36 down the length of the strip. When Annie had finished her chart, I showed her the multiples strip, and asked if she could tell what the pattern on it was ... she could! Again, yay!
We then spent a minute looking at it, reading the numbers down the strip, and then I asked her (she likes a challenge) how far she thought she could remember without looking. She loves praise, so even though she only got to 15, I praised that. We then taped this strip to the front door, which she passes many times a day. I told her we would see how much of it she could memorize before Daddy gets home. A few hours later, she had the whole thing memorized and was able to recite it for Dad when he got home.
Tomorrow we will do the 4's, and maybe the 5's, since they are so easy.
Oh, I should mention that we did try filling in a multiplication chart (a 10 by 10 chart) first, but that idea didn't seem to click with her, so I scrapped that idea and went on with the notebook idea instead. I personally feel like you need to treat the most important subjects for your children (math, reading, etc) like you do potty training: you just keep trying the known methods, and maybe some of your own, until you find one that works with your particular child.