Concepts in Action: Relationship between T1 and T2

Age
6-9.

Presentation

 * 1) With the pieces of the small hexagonal box, form various figure: hexagon, trapezoid, rhombus, and equilateral triangle and hexagon.
 * 2) Superimpose the grey hexagon on the red and yellow hexagon to demonstrate congruency.
 * 3) Recall the value relationships already established.
 * 4) Since the equilateral triangle is equal to 1/2 the red hexagon, then it is also equal to 1/2 of the grey hexagon - or a trapezoid.
 * 5) Bring from the triangular box the grey unit triangle (T1) and the four small red equilateral triangles (T3).
 * 6) We know that the yellow triangle T2 is equivalent to the trapezoid which is 1/2 of the grey hexagon.
 * 7) One of the triangles of the trapezoid is congruent to one of the small red equilateral triangles (T3).
 * 8) Superimpose them.
 * 9) Thus, one red triangle is 1/3 of the trapezoid.
 * 10) The red triangle as we know is 1/4 of the large grey unit triangle (T1).
 * 11) Four of these red triangles are equivalent to the grey unit triangle.
 * 12) Because the yellow triangle (T2) is made up of three of the small red triangles (T3), then we can say that the yellow triangle (T2) is made up of 3/4 (T3) of the grey unit triangle (T2 = 3/4 T1).