## Designing a Virtual Path

Pre-K-2
1

In this activity, students use their knowledge of number, measurement and geometry to design a "virtual path" which enables a ladybug to hide under a leaf. They also develop navigational skills by testing to see if their path is accurate and revising their solutions.

Initiating the Excursion

To introduce this excursion, students should experience classroom navigation activities by 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."

 move backward move forward 45 degree 90 degree

Once students understand the basic concepts of navigating paths, then you can provide a brief overview of the four directional buttons used to navigate the ladybug at the interactive applet. It is important for students to understand how clicking each of the buttons affects the direction of the ladybug. Remember to include movements for left, right, forward and backward. (See directional figures above). Students should also review strategies that can be used to help the ladybug turn corners. Ask them to predict how many corner-turns are required to equal a "big turn" (90 degrees). Demonstrate that two "small turns" (45 degrees) are required to equal a "big turn".

Distribute a Make My Path Activity Sheet to each student and have him/her identify the beginning of the path (ladybug) and ending (leaf).

Ask the students to describe how they could develop a simple path from the ladybug to the leaf. As they orally describe their paths, the students should state the movements using the following terms: move forward, move backward, turn right and turn left. You can provide the class with a set number of forward and/or backward movements that must be used when developing the solution. After a few practice paths created by the class, individual students then illustrate their own ladybug’s route on the Make My Path Activity Sheet Activity Sheet.

Developing the Excursion

After students have had the opportunity to illustrate their ladybug’s path using the Make My Path Activity Sheet, they should visit the Hiding Ladybug E-Example.

Working together, partners share the responsibility of "Mouse Driver" and "Reader/Recorder." The "Reader/Recorder" will read the directions from the activity sheet and record observations while guiding the activity. The "Mouse Driver" controls the action of the mouse and movement on the computer screen, partners should switch roles until all have moved the ladybug.

Once at the site, students should click on "stand-alone applet" and practice using each of the directional buttons.

Allow time for them to experiment with each button and describe to a partner or the teacher how each button functions.

After the exploration period, read the following narrative to the group.

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.

Closing

Now that the students have experimented with the ladybug applet, distribute another blank copy of the Make My Path Activity Sheet to each member of the class. The objective is to help the ladybug navigate a path to the leaf using a different route. Ask students to compare their first route with the second describing the similarities and differences.

Pose the Questions for Students, to wrap-up the lesson.

Extensions

1. An extension to this activity would be to challenge one student to create a ladybug path and then orally describe it a partner. The partner would then try to duplicate the path, and record his or her efforts on paper.
2. Move on to the next lesson, Making Triangles.

Questions for Students

1. Describe the path you created for the ladybug to reach the leaf.
2. How many different directions did you travel?
3. Did you find the shortest route to get the ladybug to the leaf? How do you know?
4. Can you find another way?
5. Can you find a shortcut?
6. What is the fewest number of turns you might use?
7. What is the most number of turns you might use?
8. Are there any 90-degree turns in our classroom?
9. Are there any 45-degree turns in our classroom?
10. Where are these turns located? What might you call these turns?

### Making Triangles

Pre-K-2
In this activity, students use 45- and 90-degree angles to create triangles, and develop an understanding of the relationship between angles and the shape of triangle. Students use their knowledge of number, measurement and geometry to design a "virtual path" using two different angles to help a ladybug reach its hiding place under a leaf.

### Making Rectangles

Pre-K-2
In this activity, students use their knowledge of number, measurement and geometry to plan the steps necessary for a ladybug to draw rectangles of different sizes. As they experiment, students begin to understand the relationship between the shape of a rectangle and the lengths of its sides. They also develop a sense of the amount of turn in a right angle.

Pre-K-2
In this activity, students plan a series of moves that will navigate a ladybug through a maze. Their plans turn the ladybug at the appropriate corners and keep it on a path without crossing the walls. This activity helps students gain experience in estimating length and angle measures.

### Learning Objectives

Students will:
• Name, describe and use orientation, direction and measurement concepts in planning paths.

### NCTM Standards and Expectations

• Describe, name, and interpret relative positions in space and apply ideas about relative position.
• Create mental images of geometric shapes using spatial memory and spatial visualization.

### Common Core State Standards – Mathematics

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.A.1
Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

-Kindergarten, Geometry

• CCSS.Math.Content.K.G.B.4
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).