Sensorial Decanomial Square
Materials:
10 Squares and corresponding rectangles in colors corresponding to the bead stair, representing the ten factors in the decanomial square
The squares and rectangles are stored in separate compartments within a wooden box
There can be a prepared frame to build the square on
Purposes:
Building the square
Discrimination of size, shape, and color
Preparation for mathematics: squaring (a+b+c+d+e+f+g+h+i+j)²
Age: 4 and up
Preparation: The child will have worked with the Graded Geometric Figures
Presentation 1: Building the Square
Introduction
Invite the child for the lesson on the Decanomial.
Bring the frame to the floor and have the child unroll a rug next to the frame.
Show the child how to carry the box and then bring it to the rug.
Sit at the short end of the rug.
Remove all the squares and place them at random at the bottom of the frame.
Close the box.
On the frame, start to form a concentric pattern with the square and let the child finish.
Building the Decanomial Square
Take the red square off the concentric pattern and place it in the top left corner of the frame.
Place the green square diagonally to the red.
Remove the green rectangles from the box and place them on the frame.
Place the green rectangles in the open spaces.
Place the pink square.
Remove the pink pieces from the box and place them one at a time, alternating placement from one side to the other side of the square, building from the square to the sides. Invite the child to help.
Let the child take over at the yellow.
Stay with the child to offer help as needed.
Note: Depending on the child, they may be done and need to be shown how to put it away. Otherwise, continue to Presentation 2.
Presentation 2: Shrinking the square
Remove a square and then the pieces in order to stack them in a stair on the frame.
Put them in the box.
Shift the lower row upward starting with the narrowest pieces moving toward the square. You will do one side and the child does the other.
When you find pieces that no longer fit, remove them, and set them in the lower-left corner of the frame.
Have the child select the next color to remove.
Remove the color, stack as before, and place in the box.
Repeat the “shrinking” process.
Let the child continue shrinking the square until the last gold square is left.
Control of Error:
The child’s own judgment/visual discrimination of disharmony
Language: None
Following Exercises: Done at a table
Building Squares of One Color:
Have the child select one color to remove from the box.
Spread out the shapes in order.
Move the square to the top of the table.
Build a square and then superimpose the square over the top to check.
Make as many as you can. Count the total number of squares of that color you made.
Making Binomial Patterns:
Place the gold square in front of the child
Find two squares that perfectly fit corner to corner on the gold square.
Find the two rectangular pieces of the same color as the large square to fill in the spaces.
Slide them off and invite the child to find two more squares that would fit, and he could continue finding binomial patterns.
Making Trinomial Patterns:
Same as above but find three squares that fit on the gold square.
Fill in the spaces by the largest square with the same color, and then the second row will be the same color as the middle square.
Memory Games: None
Pedagogical Notes:
Don’t start shrinking with the gold pieces, the child won’t find the pieces that do not fit.
There may be four-year-olds that do not have the manual dexterity for this exercise which will lead to frustration. You may have to wait until the child is closer to five. A 27 inch square bulletin board with straight sides and good right angles can be used as a frame.
This can be a two-child work.
The colors in the box match the color-coding of the bead bars. Each color has a numeric value. This does not need to be indicated to the child but is good for us to know.