OpenStax-CNX module: m30563 1 Investigate and compare 2-dimensional shapes * Siyavula Uploaders This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 1 MATHEMATICS 2 Grade 4 3 SPACE AND SHAPE, PATTERNS, DATA HANDLING 4 Module 13 5 investigate and compare two-dimensional shapes Activity: To investigate and compare two-dimensional shapes by making them and drawing them on a grid [LO 3.3] To make two-dimensional shapes with a focus on tessellation [LO 3.5] HANDS ON: PRACTICAL WORK. You may work in pairs or in small groups. Use an old cornake 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 ndings on the dotted lines provided. 1.1 Triangles. a) Make a three-sided gure by joining the ends of three strips of equal length by using split pins. Place your triangle on a table or on the oor and hold the corners. Is it possible to change the shape of the gure by pulling the corners (gently)? b) Make another 3-sided shape with two strips of equal length and one strip of a dierent 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 dierent lengths. Pin it and place it on the table. Gently try to change its shape by pulling the corners. Can the shape be changed? * Version 1.1: Jul 26, 2009 5:28 am -0500 http://creativecommons.org/licenses/by/3.0/
OpenStax-CNX module: m30563 2 d) Pin two short strips of dierent 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 dierent shapes, but all with three sides. Use them to decorate the walls of your classroom. Make a neat, large label: TRIANGLES. How many sides does any triangle have? Are the sides straight or curved? Is a triangle rigid, or can its shape be changed by pulling the corners? A shape that cannot be changed is said to be rigid. This is why triangles are used in the construction of the frame on which the roof of a house is built. A triangle is strong. Triangles may also be seen in the steel framework of bridges. 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 dierent 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
OpenStax-CNX module: m30563 3 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 dierent 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 o the corners. Cut out your hexagons and paste them in the frame below. (They need not be regular hexagons; the sides may dier in length, but there must be six sides.) 3.2 Turn each quadrilateral into an 8-sided shape (octagon) by cutting o the corners. (They need not be regular octagons; the sides may dier in length, but there must be eight sides.) Cut out your octagons and paste them in the frame below. Shapes for cutting out
OpenStax-CNX module: m30563 4 Figure 5
OpenStax-CNX module: m30563 5 Figure 6 Not for cutting out The convex pentagon (the points are all outwards).
OpenStax-CNX module: m30563 6 Figure 7 The convex pentagon (the points are all outwards). Concave shapes look like this:
OpenStax-CNX module: m30563 7 Figure 8 The concave pentagon there are still ve 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 dierent lengths.)
OpenStax-CNX module: m30563 8 5. On the dotted paper below: Table 1 Draw a triangle by joining six dots. Imagine that your triangle is a oor 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, ip your triangle over. Example:
OpenStax-CNX module: m30563 9 Figure 9
OpenStax-CNX module: m30563 10 Here a space has been left to show you a ip. Remember that when you do it, no spaces may be left. My tessellation with triangles: Figure 10 5.3 Tessellate with a dierent triangle:
OpenStax-CNX module: m30563 11 Figure 11 5.4 Imagine that your rectangle is a oor 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, ip your rectangle over. My tessellation with rectangles:
OpenStax-CNX module: m30563 12 Figure 12 5.5 Tessellate with squares:
OpenStax-CNX module: m30563 13 Figure 13 5.6 Tessellate with other quadrilaterals, e.g. kites or parallelograms:
OpenStax-CNX module: m30563 14 Figure 14 5.7 Use the grid paper on the next page to see what other polygons can be used to cover the oor without leaving spaces and without overlapping, e.g. regular pentagons; regular hexagons; regular octagons. GRID PAPER (square blocks) for TESSELLATION
OpenStax-CNX module: m30563 15 Table 2 5.8 ARE THESE EXAMPLES OF TESSELLATION: Write yes or no and then explain why you said that.
OpenStax-CNX module: m30563 16 Figure 15 a) Explain your answer Figure 16 b) Explain your answer
OpenStax-CNX module: m30563 17 Figure 17 Figure 18 c) Explain your answer
OpenStax-CNX module: m30563 18 Figure 19 Figure 20 d) Explain your answer 6 Assessment
OpenStax-CNX module: m30563 19 LO 3 Space and Shape (Geometry)The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions. We know this when the learner: 3.2 describes, sorts and compares two-dimensional shapes and three-dimensional objects from the environment according to geometrical properties including: shapes of faces; number of sides; at and curved surfaces, straight and curved sides. 3.3 investigates and compares (alone and/or as a member of a group or team) two-dimensional shapes and three dimensional objects studied in this grade according to the properties already studied, by: 3.3.1 making three-dimensional models using cut-out polygons (supplied); drawing shapes on grid paper; 3.4 recognises and describes lines of symmetry in two-dimensional shapes, including those in nature and its cultural art forms; 3.5 makes two-dimensional shapes, three-dimensional objects and patterns from geometric objects and shapes (e.g. tangrams) with a focus on tiling (tessellation) and line symmetry; 3.6 recognises and describes natural and cultural two-dimensional shapes, three-dimensional objects and patterns in terms of geometric properties; 3.7 describes changes in the view of an object held in dierent positions. Table 3 7 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
OpenStax-CNX module: m30563 20 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 rst 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.