MATHEMATICS

Grade 4

SPACE AND SHAPE, PATTERNS, DATA HANDLING

Module 13

investigate and compare two-dimensional shapes

Activity:

HANDS ON: PRACTICAL WORK.

You may work in pairs or in small groups. Use an old cornflake box (or other box) to make strips of cardboard. They must be wide enough for you to be able to punch a hole at both ends. Punch a hole at each end of each strip. Keep all your strips in an old envelope and bring them to the lesson. Also bring a packet of split pins to the lesson.

MAKING 2-DIMENSIONAL SHAPES: revision of properties and to test rigidity.

1. Each group/pair of learners must complete the following and record their findings on the dotted lines provided.

1.1 Triangles.

a) Make a three-sided figure by joining the ends of three strips of equal length by using split pins. Place your triangle on a table or on the floor and hold the corners. Is it possible to change the shape of the figure by pulling the corners (gently)?

b) Make another 3-sided shape with two strips of equal length and one strip of a different length. Pin it with the split pins. Again, place it on the table, hold the corners and try to change the shape by pulling one or more corners. Can the shape be changed?

c) Now make a 3-sided shape with three strips of different lengths. Pin it and place it on the table. Gently try to change its shape by pulling the corners. Can the shape be changed?

d) Pin two short strips of different lengths and make a square corner with them. Use them and one more strip to make a 3-sided shape with one square corner. (If you need to cut the third side to do this, do so.) Once you have pinned it, can the shape be changed?

1.2 Your group should now have four triangles, all of different shapes, but all with three sides. Use them to decorate the walls of your classroom. Make a neat, large label: TRIANGLES.

Any triangle has three straight sides and is rigid.

2. Quadrilaterals.

2.1 Use four strips of equal length to pin a 4-sided shape. Can it be moved to have square corners and be a square?

2.2 Can the corners be pulled so that they are not square corners, but the shape is still a 4-sided shape with all the sides equal in length?

2.3 Use two long strips and two short strips and see what different quadrilaterals you can make. See if each shape can be changed by gently pulling the corners. Your shapes should include the following shapes:

Figure 1

a) the _______________________

Figure 2

b) a parallelogram

Figure 3

c) the trapezium

Figure 4

d) the ____________________

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.

Shapes for cutting out

Figure 5

Figure 6

Not for cutting out

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

Figure 7

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

Concave shapes look like this:

Figure 8

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:

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

5. On the dotted paper below:

Example:

Figure 9

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:

Figure 10

5.3 Tessellate with a different triangle:

Figure 11

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:

Figure 12

5.5 Tessellate with squares:

Figure 13

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

Figure 14

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.

Figure 15

a)______ Explain your answer ____________

Figure 16

b)________ Explain your answer ________________

Figure 17

Figure 18

c)__________ Explain your answer ____________

Figure 19

Figure 20

d)__________ Explain your answer _____________

Assessment

Memorandum

ACTIVITY: comparing 2D shapes

(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.