Squares and rectangles in colors corresponding to the bead stair, representing the factors of the decanomial square (Square of Pythagoras):
(a)^2 = a^2
(a + b)^2 = a^2 + 2ab + b^2
(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
…and so on, through the square of the decanomial.
A wooden board, or a black/gray felt underlay.
- Place the wooden board on the rug, so that the two wooden edges show the right angle in the top left corner.
- Remove lid and place it underneath the box.
- Take out the square of each color from largest to smallest.
- Place them in sequence concentrically.
- Disassemble the squares, keep them out.
- Take the small red square and place it in the upper left hand corner of the board.
- Align the green square so its top left corner touches the red squares bottom right corner.
- With the other two green pieces, place them adjacent to the green square, forming a larger square.
- Repeat this process until all the squares and rectangles have been placed on the board. Go from smallest to largest, one color at a time.
- Admire the completed board.
- Show the child how to return the squares and rectangles to the box, leaving the squares on top.
Exercise 1, Presentation
The child performs the presentation.
Exercise 2, Removing a Square
- With sensorial decanomial all laid out, remove a square from its place.
- Look at the gap, place the square on the rug and remove its corresponding rectangles.
- Slide the rectangles into the new gap towards the direction of the top left corner.
- The rectangles will fit into the gap, except for the rectangle with the corresponding width of the removed square.
- Remove the rectangle of the same width from each color, then push the rectangles towards the upper left hand corner.
Exercise 3, How Many Squares Can be Made?
- Explain to the child that we are going to see how many squares can be made.
- Start with the red square and put it into the top left corner of the rug.
- Remove all the green pieces, and place the green square below the red square.
- Using the other two green pieces, form a square and place it next to the green square.
- Remove all the pink pieces, and place the pink square below the green square.
- Use the remaining pink pieces to make squares, place them next to the pink square.
- Remove all the yellow pieces, and place the yellow square under the pink square.
- Use the remaining yellow pieces to make squares, place them next to the yellow square.
- Repeat this process until all squares of all colors have been made.
Exercise 4, How to Make a Larger Square
- Take out a square from the box, place it on the rug.
- Take out a smaller square and touch the top left corner of the smaller square to the bottom right corner of the larger square.
- Find corresponding rectangles to fill in the gaps, forming a binomial square.
- Superimpose a larger square on top of the binomial to verify it’s a square.
- Invite the child to explore.
Control of Error
Preparation for mathematics.
4 1/2, 5 for later exercises.
Just help the child get started with the material, but don’t build the whole thing yourself.