The three-part ladybug example presents a rich computer environment in which students can use their knowledge of number, measurement, and geometry to solve interesting problems. Planning and visualizing, estimating and measuring, and testing and revising are components of the ladybug activities. These interactive figures can help students build ideas about navigation and location, as described in the Geometry Standard, and use these ideas to solve problems, as described in the Problem Solving Standard. In the first part, Hiding Ladybug, students create a path that enables the ladybug to hide under a leaf. In the second part, Making Rectangles, students plan the steps necessary for the ladybug to draw rectangles of different sizes. In the last part, Ladybug Mazes, students plan a series of moves that take the ladybug through a maze.

Task

The ladybug hears someone coming and wants to hide. Your task is to plan a path that will take the ladybug to a hiding place under the leaf. Click on the direction buttons to plan a path the ladybug could take to hide under the leaf. Click on the "Play" button to see if the path works. The ladybug leaves a trail, so you can see the connection between the mathematical movement commands and the resulting path.

[How to Use the Interactive Figure]

[Stand-alone applet]

Getting Started in the Classroom with Navigation Activities

Prior to engaging in this activity, students should experience classroom navigation activities—for instance, drawing simple pictures or diagrams to represent paths they might walk, such as a path from a table to the door and later from their classroom to the playground. They can write a set of directions for a classmate to move around the room, test the directions, and talk about the results and any modifications that should be made to their plan. Such activities help students make their ideas about navigation explicit. Through these experiences, students use mathematics in understanding space when they say, "Turn right" or "Go forward eight steps." Using computer activities such as Hiding Ladybug can support, extend, and connect the development of these mathematical ideas.

What Students Experience As They Carry Out Navigation Activities

In a computer environment, students can make on-screen records of their navigational paths. They can create plans, focus on relationships between different representations of paths, create scripts so that procedures can be repeated, and make multiple attempts quickly and efficiently. They can analyze the plans and change them so that they work. In performing these tasks, students are increasing their understandings of location and movement in space as they use various related mathematical concepts in geometry and measurement to solve different problems. Writing sequences of directions for computer environments encourages students to visualize spatial relationships and enables the teacher to see what they are thinking.

Hiding Ladybug	Making Rectangles	Ladybug Mazes