Concepts in Action: Smaller hexagonal box

Age
6-9.

Presentation

 * 1) At first the large yellow equilateral triangle and the six obtuse-angled isosceles triangles are removed from the box.
 * 2) The remaining triangles are all small equilateral triangles: six grey, three green, two red.
 * 3) The child begins as usual.
 * 4) He names the figures he has formed: hexagon, trapezoid, rhombus.
 * 5) Then values are assigned to the three figures.
 * 6) Superimpose all of the triangles to show congruency.
 * 7) Reconstruct each figure and count the number of congruent triangles in each.
 * 8) The trapezoid has 1/2 as many pieces as the hexagon.
 * 9) Separate the hexagon to show two trapezoids.
 * 10) The rhombus has 1/3 as many pieces as the hexagon.
 * 11) Separate the hexagon into three rhombi.
 * 12) Comparing the trapezoid to the rhombus, we see that the rhombus is 2/3 of the trapezoid, or the trapezoid is 3/2 of the rhombus.
 * 13) Examine the relationship between the lines of the three figures.
 * 14) Note this time that the diagonals of the hexagon connect opposite vertices. classify the trapezoid.
 * 15) It is an isosceles trapezoid, but it is more than isosceles.
 * 16) Since it is made up of three equilateral triangles, it has an extraordinary characteristic.
 * 17) The longer base is equal to the equal legs.
 * 18) Present the inset and the label and add it to the other insets.
 * 19) Just as the equilateral triangle is an isosceles triangle plus, the equilateral trapezoid is an isosceles trapezoid plus.
 * 20) Show also that bilateral symmetry exists in the hexagon and rhombus.
 * 21) At this point the large yellow equilateral triangle and the six red obtuse-angled triangles are returned.
 * 22) When the child joins the triangles, three rhombi are formed.
 * 23) The triangles are stacked up to prove that they are congruent.
 * 24) Thus the three rhombi are congruent.
 * 25) Put the three rhombi together to form a hexagon, thus the hexagon is formed of six equal triangles.
 * 26) Open the hatch of the hexagon and take out the three red triangles, replacing them with the yellow equilateral triangle.
 * 27) Observe that the equilateral triangle is inscribed in the hexagon.
 * 28) Superimpose the red triangles (that were just removed) on the yellow triangle to show that the equilateral triangle is made up of three red triangles.
 * 29) Since the hexagon is made up of six red triangles, the triangle is 1/2 of the hexagon.

Points Of Interest
This hexagon will be called H2 and the large yellow equilateral triangle is called T2. Therefore T2 = 1/2 H2 and T2 is inscribed in H2. The smaller equilateral triangles which are congruent to the small equilateral triangles of the first box, and therefore have the value of 1/4 T1, will be called T3.