Monday, September 28, 2015

Draw Polygons with a Given Perimeter using Pro-Bot

Can you program the Pro-Bot to draw polygons & compound figures with a given perimeter?

This is an assignment that I designed for our Grade 3 students. It relates to the Common Core Math Standards: Geometric measurement: recognize perimeterFor this exercise, I highly recommend using graph paper, as it provides a helpful medium for the kids to work out the math problems. Provide at least one sheet per child to work out the problem and then additional sheets as required for the groups to draw the figures using Pro-Bot. Here is a link to a graph paper with 1 cm grid in PDF format; you can make copies for the students to draw on using the Pro-Bot.

Perimeter of a Figure

A perimeter is a path that surrounds a two-dimensional shape. The term may be used for either the path or its length. It can be thought of as the length of the outline of a shape. (Wiki)

How do you calculate the perimeter of a given figure? You add the length of all the sides of that figure that form its outline. Say you are given a square with sides 3 cm each. The perimeter of the square is 3 + 3 + 3 + 3 = 12 cm. Similarly, a 5 cm x 6 cm rectangle. has a perimeter of 5 + 6 + 5 + 6 = 22 cm.

Can we do the reverse too? Given the perimeter, can we come up with the design for a figure with that perimeter?

Let's look at an example. Given a perimeter of 12 cm, how many polygons can we draw? We can draw multiple polygons, all with the exact same perimeter of 12 cm. In the figure below, you can see:
• a square 3 cm x 3 cm,
• a rectangle 5 cm x 1 cm,
• a rectangle 4 cm x 2 cm,
• a hexagon with sides 3 cm, 1 cm, 1 cm, 1 cm, 4 cm, 2 cm

Can you think of more polygons with a perimeter of 12 cm? Let's now look at a scenario that shows the practical application of the concept of perimeters. And then program the Pro-Bot to draw a few polygons with a given perimeter.