#### Material

6 gray equilateral triangles, black lines on two sides.

2 red equilateral triangles, black lines on one side.

3 green equilateral triangles, two with black lines on one side, one with black lines on two sides.

#### Presentation

- Invite the child to the lesson and with the child sit by a rug.
- Take out the red triangles first, one at a time.
- Stack them on top of each other, then slide them together by combining their sides with the black line, forming a rhombus.
- Slide the rhombus to the top corner of the rug.
- Take out the green triangles, one at a time, stack them on top of each other to confirm their congruency. Then slide them together by the black lines to form a trapezoid.
- Take out the grey triangles, one at a time. Stack them on top of each other, then slide them together by combining their sides with the black line, forming a hexagon. Keep the hexagon in the middle of the rug.
- Place the green triangles onto the upper half of the hexagon to show the child how a trapezoid can fit into a hexagon.
- Invite the child to place the trapezoid on the other half of the hexagon.
- While keeping the triangles together, slightly separate the hexagon into two trapezoids to insinuate that the hexagon is made of two trapezoids.
- Place the green trapezoid to the right of the red rhombus.
- Push the hexagon back together.
- Place the red rhombus onto the grey hexagon.
- Separate the hexagon into three rhombi, leaving about half an inch of space between each rhombus.
- Invite the child to do.
- Return the rhombi into a hexagon formation, and place the rhombus back at the top of the rug.
- Let the child explore.

#### Exercises

Child works independently.

#### Language

None.

#### Control of Error

The black lines on each triangle, and the colors of the triangles.

#### Direct Purpose

Further the child’s exploration with equilateral triangles.

#### Indirect Purpose

Preparation for geometry, showing how all plain figures of straight lines are made of triangles.

#### Age

4 to 5

#### Notes

Dealing with equivalence will promote understanding of geometry in later life.

More triangles usually come with the ox, but these are not used at the primary age level and are instead used at the elementary level to illustrate mathematical theorems. The triangles that are removed are 1 large yellow equilateral triangle (without black lines) and 6 red obtuse-angle isosceles triangle (with black lines along the longer side).