
Making Rectangles (4.3.2)
Students plan the steps necessary for the ladybug to draw rectangles of different sizes. 
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.
[Standalone applet]
How to Use
the Interactive Figure
To plan a path
for the ladybug to draw a rectangle 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 

Pause (left
button) and resume (right button) 

Stop and
erase the path (does not erase the plan) 

Shows or
hides the leaf 

Moves the
leaf 

Forward


Backward 

45 degree
right turn 

45 degree
left turn 

90 degree
right turn 

90 degree
left turn 

Clears the
selected step 

Clears all
steps 
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 onscreen 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.
Take Time to Reflect
 What experiences should students have following this activity that can extend their thinking?
 On the basis of the plans students create, what might a teacher learn about the students' understanding of geometric shapes?
Also See:
 4.3 Learning Geometry and Measurement Concepts by Creating Paths and Navigating Mazes