Home - Building & Designing with Shapes & Angles Map
In this Big Idea students explore the art and beauty of mathematics. Students explore the relationships between different shapes by creating patterns and tiles. Students are encouraged to see that creativity and imagination are both essential parts of mathematics.
Students will understand:
Regular shapes have all sides equal and all angles equal. Students are expected to be able to distinguish between regular and irregular shapes and to describe a polygon as either regular or irregular, eg a regular pentagon has five equal sides and five equal angles. It is important for students to have experiences with a variety of shapes in order to develop flexible mental images. Students need to be able to recognise shapes presented in different orientations. Students should be given the opportunity to attempt to create tessellating designs with a selection of different shapes, including shapes that do not tessellate.
Two-Dimensional Space
In this activity, students explore which shapes tile and which shapes do not. By focusing on how shapes fit together, students begin to attend to angles as much as to sides. - See page 51
Questions for reflection:
In the previous activity, students explored tiling a plane. In this activity, we focus on special shapes that when tiled produce the shape of the base unit. These shapes are called rep-tiles. These rep-tiles are interesting to mathematicians, and they provide students a creative idea to explore. - See page 56
Questions for reflection:
In this investigation, students explore shapes made out of equilateral triangles, which are known as polyiamonds. Students will investigate the following questions: How many different shapes can you make using a set number of equilateral triangles? Will the shapes you make tile a plane? - See Page 218
Questions for reflection:
In this sequence of activities students explore two-dimensional representations of three-dimensional objects and investigate the isometric angle. Students are surrounded by two-dimensional representations of three-dimensional objects but do not explore how these are constructed or the special angle which is commonly used in engineering drawings to give an impression of depth.
Three-dimensional space
Students will explore examples of three-dimensional objects represented in two-dimensions from their surroundings and also in artworks. Using the thinking routine “I See, I think, I wonder” to structure and document their thinking, students will have opportunities to name and notice common features of these representations and identify possible patterns between the images.
Questions for reflection:
Students create two-dimensional representations of objects of their own design using the Splat tool for Isometric drawings. The "Splat" tool is a small plastic tool which makes the construction of two-dimensional representations easy when combined with the online video tutorials which show how to place and move the "Splat" to create the required lines and angles for isometric drawings.
"Fusing together maths and creativity to boost spatial reasoning. The Splat combines isometric elements for rapid visualisation and product design."
Begin with a brief introduction to the tool showing how it can be used to create two-dimensional representations of rectangular prisms, cylinders, cones and spheres. Armed with this knowledge and by accessing the Online Guides to expand their knowledge, students create increasingly complicated representations by combining shapes. This is a great opportunity for collaborative learning and allows students to share their expertise. Students will enjoy the opportunity to share their drawings with the class or a wider audience.
Questions for reflection:
Visit the home of Splat at NutsNBolts Design for Guides
Look fors:
Are students experimenting with shapes? - When student first use the ‘Splat’ and follow the instructions in the online videos, they follow the steps very rigidly. The shapes they construct are defined by the dimensions of the ‘Splat’. As students have time to explore they will realise that they can be more creative and use the ‘Splat’ to bring their ideas to life.
Students will investigate the angles used in two-dimensional representations of three-dimensional objects, particularly ones where the object comprises many right angles. Students identify the main lines and angles within the image and then use their compass to measure these angles. Students then compare how these angles compare to those they have created using Splat and use Splat to find and name angles in other artworks and images.
Questions for reflection:
Look fors:
Noticing the Isometric Angle - This is something that students might not at first notice, but it is one of those things that once you see, you can’t not see it. Many diagrams, particularly technical drawings of three-dimensional objects make use of the isometric angle i.e. an angle of 30 degrees above the horizontal plane. If students don’t notice you chould show them this and then encourage them to “look again” to see if they can find this special angle at work. It can help to reveal that this angle is also found on one of the set squares in a standard geometry set.
Which angles matter? - Students will tend to initially measure the angles within the image, the angle between the sides of a table for example. Students who have an understanding of the use of the isometric angle will look to measure angles which give the impression of depth; the angle of projection from the horizontal.
How are students measuring angles? - This is a good opportunity to observe how students make use of their protractor and if necessary provide some targeted instruction.
