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 this 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 task is to give the ladybug directions so that it draws a rectangle. Click on the direction buttons to plan a path for the ladybug to draw a rectangle. Click the "Play" button to see if the plan works. Try making a rectangle that is long and thin. Make a rectangle that is short and almost square. Make the largest rectangle you can.

[How to Use the Interactive Figure]

[Stand-alone applet]

Getting Started in the Classroom

Although most students can readily draw a rectangle, writing directions for the computer or giving directions to someone else to make this shape is more difficult for them. Students must think about and analyze what determines a rectangle and the movements that must be made to draw one. In communicating their intuitive knowledge to others, students must make their thinking explicit. To prepare for this kind of communication, students might "walk around" rectangles in their classroom. As a group, they could discuss the motions they made, for example, "We walked five steps and turned right, nine steps and turned right, and then did the whole thing again!" Partners could then give directions to each other to "walk out" rectangles of different sizes, first predicting how the rectangles might look, such as long and thin or short and almost square.

What Students Learn in Ladybug Rectangles

Working in a computer environment allows students to quickly execute the plans they make to see if they have created the desired rectangles. As they experiment, students begin to understand the relationship of the lengths of the sides to the shape of a rectangle. And they will develop a sense of the amount of turn in a right angle.

With computer objects, students can often do more than they can with real objects. They can make on-screen records of their navigational paths, create scripts so that procedures can be repeated, focus on relationships between different representations of a path, and make multiple attempts quickly and efficiently. Using computer objects, students can make connections among related mathematical areas and concepts, such as geometry, spatial sense, problem solving, and measurement.

An interesting extension of this task is to design a path to make a shape that is not a rectangle or a square. Note that the commands for moving forward and turning allow only a few predetermined distances and angle measures, which will limit the variety of figures students can make.