## 4.3.2 Making Rectangles

Students plan the steps necessary for the ladybug to draw rectangles of different sizes.

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 |

**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.

**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.

**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?