“I need to work with Seric (4) on his letters for a while, so I want you, Sarah (7) and America, to sit at the table and do math with the big, glass beads. If you can't figure out a problem, use the beads.”
I swung the heavy plastic jug of flat, glass, marble pieces onto the center of the table as I spoke. We use these glass pieces to play Mancala, Go, and Pente; all games which help the kids understand basic math and strategy. The heavy weight and shiny appearance of the glass beads resemble a currency of intrinsic value, and the kids prefer them over other manipulative math tools.
“America, I want you to take out all the green pieces and divide them into piles of two. Then put them all back together in a big pile, like this.” I demonstrated each instruction directly in front of her with my arms around my eager little girl. “Then separate them into piles of three, like this… and then piles of four. Do you think you can place four in each pile?”
America hesitated, then counted one pile of glass pieces. “One, two, three, four!”
“That's right. When you have three kids at the table and one more kid comes to sit at the table… ”
“There are four!”
“Good. Okay, so you do that for a while with the green beads. Put them in piles of two, then in piles of three, then into four each. Got it?”
Next I turned to Sarah who was opening her 2nd-grade math book and finding the last page she had done. The book she was using was a three-dollar math supplement book from the School Zone publishing company.
“Okay, Sarah, do you need any help?”
“Uh, maybe… is this all adding?”
“No, these are called fact families. This set is about 10, 7, and 3. Look at all of the problems. See how some are addition: 7+3, and some are subtraction: 10-7, but they all use the same three numbers, 10, 7, and 3. So pull out 10 glass beads. Now look at that set again.”
Sarah: “Oh, yeah. I see. And that set is… 14, 5, and 9. Yeah, I can do it.”
Using the glass beads, Sarah quickly finished a page of math and America sorted her piles of beads.
JudyLucy (8) was working on her multiplication tables and David (10) was working on fractions.
I find that by the time a child makes it through about second-grade level, using glass beads as physical representatives of the symbols, all numbers become real objects in their minds. When the next levels of calculation are introduced, they are much more easily understood and, more importantly, applied.
Later, for snack time, David asked if he could divide up the last four pieces of banana cake between the eight of us. Even Seric (4) understood that meant cutting each piece in half. Large families have an advantage in understanding division, multiplication, and fractions!