In this investigation, students are building their ideas about the properties of classes of shapes, formulating conjectures about geometric relationships, exploring how geometry and measurement are related, and investigating the shapes with equal area. An understanding of congruence and similarity will develop as students explore shapes that in some way look alike. The triangles are similar. As they describe shapes, they should hear, understand, and use mathematical terms such as parallel, perpendicular, face, edge, vertex, angle, trapezoid, prism, and so forth, to communicate geometric ideas with greater precision. For example, as students develop a more sophisticated understanding of how geometric shapes can be the same or different, the everyday meaning of same is no longer sufficient, and they begin to need words such as congruent and similar to explain their thinking.
Students can first navigate on grids by using landmarks.
In this activity, students are using grids and developing fundamental ideas and strategies for navigating them, an important component of discrete mathematics. A map for exploring questions about navigation Students at this level also should learn how to use two numbers to name points on a coordinate grid and should realize that a pair of numbers corresponds to a particular point on the grid. Using coordinates, they can specify paths between locations and examine the symmetry, congruence, and similarity of shapes drawn on the grid. They can also explore methods for measuring the distance between locations on the grid. As students' ideas about the number system expand to include negative numbers, they can work in all four quadrants of the Cartesian plane.