Shapes and Number Patterns is a new block for me so I am grateful to be in his capable hands. For this story, we had Farmer Joe, whose farm had lovely straight edges and was just the same length on each side. He loved having a square farm. Each morning he would get up and walk the perimeter of his farm and think about how much he loved the shape of it. Then Farmer Joe's wife announces that they are having a baby. Naturally he is thrilled at the news. This goes on until finally he has four children, two boys and two girls. I named the children (and Farmer Joe -- E.F. doesn't include names in his write up of the story) Fred and Fern and Jack and Jolene. One day they come to their father and say, Dad, we want to be farmers too. And he is very pleased. Then they tell him that they want a piece of the family farm. So he goes off to think. He wants them each to have a fair and equal share but he also wants to still have a square farm and you can't divide a rectangle into five sections and have them each be squares... Is he stuck or does he find a way? So I draw the diagram of the initial division on the board. The children are copying as I go. We labeled each section with the name of the child who inherits it but E.F. suggests having them color the child sections all one certain color. Don't color in his farm yet, though, because he'll have to divide it again. Grandchildren are on the way. Each grandchild receives a portion of the farm adjacent to their parents' property. Farmer Joe has a still-smaller square farm in the middle of it all. He doesn't mind giving away the property, of course, because he loves his family. He is just happy to still have a square farm. You can color the grandchild portions in a second color. I let the students name the four grandchildren. They loved that! We drew Farmer Joe's tiny little farmhouse smack dab in the center. Then I showed the students how to draw the four roads extending from his house to the four corners of his property. You can then color in his farm a 3rd color. The students are asked how many squares are in the design, then cut and rearrange them per Eric Fairman's instructions to create new squares out of the triangles.
My students really enjoyed this lesson!!!!
I would recommend starting each child with a piece of paper that is already square. This drawing is hard to do if you are imagining a square on your 8 1/2 by 11 paper. Don't use graph paper or there will be waaaaay too many lines and it will become more confusing.
You can get square main lesson books from Paper Scissors Stone, and much of the work in this block would be suitable for a square book -- like Dorothy Harrer's Square Kingdom which we did as our next lesson. I would recommend a blue square MLB for this block.
We lucked out in that I have the Montessori math materials in my classroom. For students who hadn't drawn straight neat sides to their triangles and thus the triangles didn't match, I was able to call the class together to the floor and show them how this same design can be made -- Hooray! -- with the Montessori Metal Squares. Fortune certainly smiled on me that day. The EXACT design! And then with the precision cut metal triangle fractions I was able to demonstrate how they create new squares. Students were allowed to trace this work if they wished as a follow-up.
Unfortunately, online I can't find any templates for these pieces, showing squares broken down into different sizes of triangles. Does anyone know of a pdf somewhere of the Metal Squares material?
Read Maria Montessori's book on Google books: The Advanced Montessori Method: The Montessori Elementary Material