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4.3.2 Making Rectangles



Left 90   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.

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[Stand-alone 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: 

Entire Pattern    
Play 
Pause   
Pause (left button) and resume (right button) 
Stop   
Stop and erase the path (does not erase the plan)  
Show Leaf 
Shows or hides the leaf  
Move Leaf 
Moves the leaf  
Move Forward 
Forward  
 Move Back 
Backward 
  Right 45 
45 degree right turn  
left 45 
45 degree left turn  
Right 90 
90 degree right turn  
Left 90 
90 degree left turn 

Clear Step

 
Clears the selected step 
Clear All   
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 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?

Also See: 

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

     



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