Material Description:
Ten square green frames each containing red squares or triangles formed by dividing a square vertically, horizontally and diagonally. Each shape has a central knob to hold the inset by.
On the first shelf are the horizontally and vertically divided insets;
The first is a ‘whole’ square
The second a square vertically ‘halved’ into two rectangles
The third is further divide into four small squares ‘quarters’
The fourth has the ‘quarters’ vertically divided into eight rectangles
The fifth divides the ‘eighths’ into sixteen small squares
On the second shelf are the insets which also have diagonally divisions;
The first is a ‘whole’ square
The second of these is a square and divided into two right angled isosceles triangles
The third has the isosceles triangles with a further diagonal division, to create four right angled isosceles triangles
The fourth has the ‘quartered’ triangles subdivided by a cross, to create eight triangles
The fifth has the ‘eight’ triangles subdivided by a rhombus, to create sixteen triangles
Each shape is either a square, a rectangle or a right angled isosceles triangle
The name of the fraction is not given to the child until much later, it is used here as a reference only
The insets are carried one frame at a time
Much later the child is given the language
Presentation:
- Introduce one inset and let the child look at all of them
- Introduce Similar
- When the child is familiar with all of the insets present by putting all of the square insets in front of the child, one at a time
- Remove the large square ‘Whole’ and place it on the mat in front of its frame.
- Ask the child to find an identical shape when she cannot show her that the third and fifth set contain similar plane figure, of different proportions, not by speaking but by removing the ‘quarters’ and ‘sixteenths’ and placing them on the mat in front of their frames, in a line with the ‘whole’ inset
- Repeat this with a rectangle of the second inset with the fourth inset; the ‘half’ with the ‘eighths’
- The child can do the same with the triangular insets; the ‘half’ triangle is the same shape as two ‘quarters’, four ‘eighths’ and six ‘sixteenths’
- Introduce Identical at a separate sitting
- Take two rectangles from the second frame ‘halves’ and place them back to back to show that they are identical
- Take two squares from frame three ‘quarters’ and show that they fit exactly onto the back of the ‘half’ rectangle
- Let the child find other identical rectangles, squares and triangles with figures of the same plane
Encourage her to draw round and cut and paste the shapes when she is older, or make a booklet.
- Introduce Equivalent, much later than similar and identical
- Take the large square ‘whole’, from the frame and in it’s place put two ‘half’ rectangles from the second inset
- Show that they fit exactly, use the word ‘equivalent’
- Let the child use all the insets together for example, fit the second triangle inset ‘halves’ into the first ‘whole’ square frame
- Show that they are equivalent by placing the rectangle ‘half’ upside down and the triangle ‘half’ on top, complete showing that the ‘eighth’ triangle fits into the remaining gap of both the shapes.
When the child continues to use the materials like this she will discover equivalence.
Exercises:
- When the child later works with fractions she can put name labels on each plane figure
- When the child is able to use Geometric Instruments she can make similar, identical and equivalent shapes, using the set square
Language:
When the words ‘Similar’, ‘Identical’ and ‘Equivalent’ are known revise them in a Three Period Lesson
Criteria of Perfection (Control of Error):
- In the child’s ability, the frame and the insets
Direct Aim:
- To help the child understand smililar, identical and equivalence
- To further explore geometry
Age at Presentation:
Beginning at three to three and a half years, later used in fractions to find the common denominator