BW and AR have been working on the checkerboard multiplication. This work has required that they focus heavily and work on skills they haven’t used before (ie: multiplication tables).
However, AR and I needed to discuss percentages in her latest project. She didn’t understand what the book meant when it said that the Amazon River moves 20% of the earth’s ground water. Without fractions an adequate discussion about percentages can not occur. So AR and I made a date for the next day to provide AR with the classic Montessori fraction presentation. The next morning out came the apple and the knife and the powerful discussion of “fair.” BW was off site on Wednesday but was entranced by AR’s discussion of the apple cut fairly into so many pieces that he had to have the lesson.
AR joined BW and myself for the same lesson on Thursday. BW is the perfect age for this lesson. He was fascinated by the fraction pieces. At one point I questioned whether I should stop where we were (which was farther than the impressionistic lesson) with the introduction of equivalencies – they had asked about the 2/4 and the 1/2. BW appeared to be waining in interest and he got up and left the lesson! (“Humph.” said I.) He whipped open his drawer, extracted a piece of paper, grabbed a pencil, and with characteristic exuberance exclaimed, “This is something I’ve got to write down!” (Did you hear this: “write” – he wanted to write! Coooolaaaa, Cooolaaaay!) He wrote the word “Equivalence” and drew illustrations of each of the equivalencies. I then asked if they wanted to come up with universal rules for fraction friends. They decided that would be wonderful.
“2 – Twos can find equivalencies with all even numbers.”
“3 – Threes can find equivalencies with 6’s and 9’s.”
As we continued with the process of thinking this through. They became even more enamored with the idea that 2/4 is the “same” as 1/2. They began to jump with it. 20/40 would be friends with 10/20. Here is the response from them.