Nito was presented with an extension of the Distributive Law today. This brought in the idea of arithmetic exploration. I apologize in advance for these pictures. I didn't really how bad the glare was until I put them on the computer. So, for your reference, the brown cards are 3 and 5 respectively.
The first set of parentheses has the 7 bar and the 2 bar that he will be multiplying by the brown 3 card and the 5 card.
He first turns over the brown 5 card so that he can multiply both bead bars by the brown 3 card. He then places his beads below.
Now, he turns the brown 3 card over and multiplies by the brown 5 card and places the beads below on the right hand side.
He then totals the individual columns and places that below.
He pushes all of the beads together.
Then he simplifies and trades in beads for the final answer. He ends up with the answer of 72.
CHECK USING COMMUNICATIVE LAW
So the great thing with the Montessori way of learning is that the child always has some way to check his answer. He doesn't really have to rely on the teacher to know if his answer is correct or not (which is great because I'm not always available!) For this problem, he can check his work using the communicative law.
Nito basically just flip flops the beads and the cards. He now has the 3 and 5 beads on the left with the brown 7 and 2 cards on the right. The same process is done as before. The brown 2 card gets turned over and the bead bars get multiplied by the brown 7 card with the answers being placed below.
The brown 7 card is flipped over and now the bead bars will be multiplied by the brown 2 card, placing the beads below.
Sum the columns individually.
Push all of the beads together.
Simplify and trade the beads in for the final answer. 72! Yay, his answer checks out.
No comments:
Post a Comment