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 Hiding Ladybug (applet) Students create a path that enables the ladybug to hide under a leaf.

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

To plan the path the ladybug should take to hide under the leaf, click on the direction buttons. The commands will appear on the screen below the picture of the ladybug. Click on the Play button to see if the path works. To clear a step, click on the step in the plan and then click on the Clear Step button. To insert a step, click on the step in the plan and then click on another direction button. Other features can be accessed from the following buttons:

 Play Forward Pause (left button) and resume (right button) Backward Stop and erase the path (does not erase the plan) 45 degree right turn Shows or hides the leaf 45 degree left turn Moves the leaf 90 degree right turn Clears the selected step 90 degree left turn Clears all steps

Challenge

• Can you create a plan for a path using fewer steps?
• Can you create a plan for the shortest possible path?

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.

Take Time to Reflect

• What gross-motor experiences could teachers give students that would help them plan paths for the ladybug?
• How can conversations about the paths help students learn to predict the outcome of their plans?
• What mathematical ideas can be built on what the students learn in this activity?

Also See:

• 4.3  Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes

• 4.3.2  Making Rectangles