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 this last part, Ladybug Mazes, students plan a series of moves that take the ladybug through a maze.

Task

The objective of this task is to plan a path that moves the ladybug through the maze. Click on the direction buttons to help the ladybug plan the path it should take to move through the maze without crossing the walls. Click the "Play" button to see if your plan works. Try some of the other mazes.

[How to Use the Interactive Figure]

[Stand-alone applet]

Getting Started in the Classroom

As students develop proficiency in navigating with the ladybug, they can create navigational plans that will move the ladybug through a maze. This process enables them to apply strategies learned in the other activities. To assess students' understanding of direction and distance, as well as their problem-solving strategies, teachers might ask the following:

• Did you picture in your head how to get the ladybug through the maze?
• Which movements did you use the most?
• If you walked the same path here in the classroom, starting at your table, where would you end up?

What Students Learn in Ladybug Mazes

Creating a plan to move the ladybug through a maze offers different challenges that are more difficult than those in the previous activities. Students must make a plan that will turn the ladybug at the appropriate corners and keep it on the path without crossing the walls. Because the applet allows students to modify one step in their plan, to begin with a new set of directions, and to execute their plans step by step or in their entirety, students have some flexibility in how they can approach the task while they gain experience in estimating length and turn (angle) measures.

Take Time to Reflect

What mathematical ideas are being explored by students? How can dialogue among students help them reflect on their strategies and consider ways to create plans with less trial and error? By listening to discussions among students, what might a teacher learn about their understanding of movement in space? What misunderstandings might teachers anticipate?

Hiding Ladybug	Making Rectangles	Ladybug Mazes