On the positive side, the kids are enthusiastic in their work, glad to be moving into new topic areas in several subjects. Both children have initiated projects for the science fair. Tessa has decided to raise lettuce seeds in different soil types to discover which is best. Josiah is going to make a weta hotel and observe the numbers and kinds of weta that use it.
Maths with Josiah has been interesting this week. Yesterday, I began to present the Geometric Decanomial. (This is an activity involving arranging squares and rectangles of grid paper into the decanomial formation. Each square or rectangle has a number written on it corresponding to the product it represents, e.g. a two by three rectangle represents the problem 2 x 3 and has “6” written on it.) Josiah very quickly got bored and declined to proceed but suggested a variation on the activity: for me to draw the decanomial formation onto one large sheet of grid paper and for him to write the products into the squares and rectangles.
Today I dutifully drew up the decanomial as Josiah suggested. He wrote in the products in the top row and the left hand column, i.e. the one times table. That was boring so he lost interest and said that was enough for today. I teased him jokingly that he'd be able to tell his friends that for maths today he did the one times table. (He liked the joke.) I suggested he fill in the squares on the diagonal. He complained that that was easy too but began writing the products in. I moved on to something with Tessa, beginning to doubt the value of the activity for Josiah.
After writing in the products of the squares, Josiah came over and handed me a piece of paper with “4096” written on it, saying, “This is 64 squared. [He'd used a calculator to get that.] Let's have a race to work out 65 squared.” Giving me the piece of paper, he added, “You can use this.” We had our race and afterwards Josiah showed me how he had reached his answer by adding 64 + 65 + 4096. He took me over to the decanomial and showed me how he had noticed that each square was larger than the previous square by the length of the larger square plus the length of the previous square.
Basically in his own words he was pointing out that (x + 1)2 = x2 + x + (x + 1). We discussed it a bit, superimposing, in our imaginations, one square on the next square and looking at the column and row remaining uncovered. We did that with a few squares then left it, me feeling a lot more satisfied of the worth of the activity! Isn't Montessori great :)