## Enclosed Surfaces

*Material Description:*

The Box of Sticks: This is a box which is divided and contains a collection of:

Wooden sticks

Plastic Arcs

Pins and Tacks of different colours

Nails

Paper Fasteners

Plumb Line

A right angle (snipped on the hypotenuse to distinguish is from a triangle, it is called a measuring angle.)

Large board, paper, pencil

Wooden Geometric Sticks

*Method:*

Give a general introduction to the box of sticks, measuring angle etc.

Take out two solid sticks and join them to make an angle, place them loose on the board. Add other sticks to the end until there are five in total, Say,* ‘It loos like a broken line, let’s see if I can join it up’.* Put the ends so it meets. * ‘When I take it apart it looks like a broken line’.* Join it again. Say, *‘If I join it up again I have an enclosed part of my plane, the boards, so I have a place inside and a place outside,’ *Indicating the centre, *‘Here what I have is an enclosed surface’.* Open it, ask,* ‘Have I got an enclosed space now?’ *(no) Close it*,’Have I an enclosed space now?’* (yes)* ‘What we have to figure out is how many sticks we need to enclose a space.’*

Take one stick and ask,* ‘Have I an enclosed space?’ *(no)

Add a stick to put two sticks together and ask* ‘Can I make an enclosed space with this?* (no)

Add a stick to put three sticks together and ask, *‘Do I have an enclosed space? ‘*(yes)_

Give one child four sticks and fasteners, another child five and another six. Ask them to make enclosed spaces with the sticks and fasteners, give one less fastener so they cannot be closed.

Gather the shapes together and ask,* ‘Is this an enclosed space?’ *. Open up one or two and then close them. Ask the children to make more examples with 3 to 6 sticks.

Say, *‘These figures that enclose a space, having a part inside and a part outside, these figures are called polygons. Polygons with three sides are called polygons, polygons with four sides are called quadrilateral and polygons with more than four sides are called just that, polygons with more than four sides. Polygon comes from the Greek meaning ‘many’ and ‘gonia’ which means corner or angle’.*

*‘We are going to sort the polygons we have made into groups. We will arrange the polygons with the least number of sides into one group, those with four into and other and those with more than four into a third group*’. Do this and write tickets, for ‘polygons’, ‘triangles’, ‘quadrilaterals’ and ‘polygons with many sides’.

Do a loose three period lesson, mixing up the figures and asking the children to arrange them around the labels. Give the labels and ask the children to identify the shapes. Say,* ‘A polygon really is a figure bound by straight lines’ *

*Aim:*

We bring the classifications and characteristics of the polygons to the children’s consciousness. Encouraging them to become aware of what they already know.

*Notes:*

The children know the names of the polygons from their work with the geometric cabinet.

This is the end of the first presentation. It is a general introduction to polygons and enclosed space.

A polygon is a plane shape bound only by straight lines. We begin with general polygons and go on to examine specific polygons starting with the triangle, the polygon with the least number of sides.

*When to give the lesson:*

This can be given parallel with lines and angles

*After the lesson:*

### Also give the ideas of diagonals and arc

Diagonals – show that the triangle is a solid shape, but the quadrilateral can be pulled out of shape, add a diagonal and it becomes firm. This is a further key to the triangle as the constructor.

Arc – make an arc, ask the children, “Can I call this a polygon? Why? (no, it is not bound by straight lines).

*Follow up work:*

- The children can use the box of sticks as for the presentation, joining the sticks together to make polygons. Straws, yarn and needle can be an alternative activity.
- The children can explore the environment; look at the surfaces of solids to see what polygon results. The surface of a solid is called a face.Then the children can make their own labels.
- The children can draw polygons and decorate them with specific nomenclature.

Triangles

*Material Description:*

The Box of Sticks: This is a box which is divided and contains a collection of:

Wooden sticks

Plastic Arcs

Pins and Tacks of different colours

Nails

Paper Fasteners

Plumb Line

## Triangles

*Method:*

Building triangles according the sides, angles and according to size and angles

Remove

- 3 equal sticks
- 2 sticks of the same length and one different one
- 3 different sticks

Use them to make three different triangles and give them names

Do a loose three period lesson asking the child to show you triangles and later name them,

Write labels and ask the children to match.

*Aim:*

To show triangles from a new perspective, to give the etymology of the names of the triangle which the children already know.

*When to give the lesson:*

Children have already worked with triangles in the casa and with the divided figures and Constructive triangles to see similarity, congruency and equivalency.

*Follow up work:*

Make labels and have the children read and place them.

Make sure the children are comfortable with the nomenclature for the three types of triangles according to their sides before continuing.