Investigate and compare 2-dimensional shapes

Try to make other shapes with four sides. All the sides may be of different length if you wish.

2.4 Can the 4-sided shapes be changed if you pull the corners gently?

2.5 How could you prevent this change from being possible?

Quadrilaterals have four straight sides and are not rigid.

3. Individual work. Use the shapes on the next page, your pencil and ruler, and a pair of scissors to do the following:

3.1 Turn each triangle into a 6-sided shape (hexagon) by cutting off the corners. Cut out your hexagons and paste them in the frame below. (They need not be regular hexagons; the sides may differ in length, but there must be six sides.)

3.2 Turn each quadrilateral into an 8-sided shape (octagon) by cutting off the corners. (They need not be regular octagons; the sides may differ in length, but there must be eight sides.) Cut out your octagons and paste them in the frame below.

S hapes for cutting out

N ot for cutting out

The convex pentagon – (the points are all “outwards”).

The convex pentagon – (the points are all “outwards”).

Concave shapes look like this:

The concave pentagon – there are still five sides but one point “goes inwards”.

4. Individual work: Use the grid paper on the rest of this page to make one of each of the following shapes and colour it in:

• triangle
• quadrilateral
• pentagon
• hexagon – 6 sides
• heptagon – 7 sides
• octagon

(They do not have to be regular; the sides may be of different lengths.)

5. On the dotted paper below:

• Draw a triangle by joining six dots.
• Imagine that your triangle is a floor tile. Try to cover the paper inside the frame with identical triangles to the one you have drawn. No spaces must be left and there must be no overlapping. You may, however, flip your triangle over.

Example:

Here a space has been left to show you a flip. Remember that when you do it, no spaces may be left.

My tessellation with triangles:

5.3 Tessellate with a different triangle:

5.4 Imagine that your rectangle is a floor tile. Try to cover the paper inside the frame with identical rectangles to the one you have drawn. No spaces must be left and there must be no overlapping. You may, however, flip your rectangle over.

My tessellation with rectangles :

5.5 Tessellate with squares:

5.6 Tessellate with other quadrilaterals, e.g. kites or parallelograms:

5.7 Use the grid paper on the next page to see what other polygons can be used to cover the floor without leaving spaces and without overlapping, e.g. regular pentagons; regular hexagons; regular octagons.

GRID PAPER (square blocks) for TESSELLATION

5.8 ARE THESE EXAMPLES OF TESSELLATION:

Write yes or no and then explain why you said that.

a)______ Explain your answer ____________

b)________ Explain your answer ________________

c)__________ Explain your answer ____________

d)__________ Explain your answer _____________

Assessment

Memorandum

ACTIVITY: comparing 2D shapes

• Triangles

(a) No

(b) No

(c) No

(d) No

1.2 Practical

1.3 3

1.4 straight

1.5 rigid

2. Quadrilaterals

2.1 yes

2.2 yes

2.3 (a) rectangle

(d) kite

2.4 yes

2.5 Add one diagonal (join one pair of opposite angles with a strip, cut the right length, and split pins.)

3.1 Practical: cutting and pasting

3.2 Practical: cutting and pasting

4.1 to 4.6 Own work on grid paper.

5.1 to 5.6 Own work on dotted paper.

5.7 Own tessellation on grid paper

5.8 (a) No; there are spaces between the hexagons but

Yes, if two shapes are allowed; the hexagons and diamonds cover the area.

(b) Yes; the shape covers the area

(c) No; in the first diagram there are spaces; in the second, there is over-lapping.

(d) and (e) Yes if two shapes are allowed. In this case the octagon and squares cover the area; octagons on their own cannot be placed to cover the area.