Draw Polygons & Compound Figures with a Given Area using Pro-Bot

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

This, again, is an assignment that I designed for our Grade 3 students. It relates to the Common Core Math Standards: Geometric measurement: understand the concepts of area. For 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.

Area of a Figure

The area of a figure is the number of squares required to cover it completely, and is specified in square units. Here's an article from math.com that gives a quick overview of the topic.

How do you calculate the area of a given figure? You add the number of squares needed to cover the entire figure. Say you are given a square with sides 3 cm each. You need 9 squares of sides 1 cm x 1 cm to cover it completely. The area of the square is 3 x 3 = 9 sq.cm. Similarly, a 5 cm x 6 cm rectangle has an area of 30 sq.cm.

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

Let's look at an example. Given an area of 9 sq.cm, how many polygons can we draw? We can draw multiple polygons, all with the exact same area of 9 sq.cm. In the figure below, you can see:

• a square 3 cm x 3 cm,
• couple of polygons with an area of 9 sq.cm.

Can you think of more polygons with an area of 9 sq.cm?

Let's now look at a scenario that shows the practical application of the concept of area. And then program the Pro-Bot to draw a few polygons with a given area.

Programming Assignment

You work for an architectural firm, and have been asked to design a single story house with a floor area of 100 square meters (roughly 1076 sq.ft.) You are to draw and present various designs for the floor plan.

1. How many different ways can you draw the floor plan with an area of 100 sq.m.? Provide at least 2 to 3 different designs and make a rough drawing of the figures that you come up with.

2. Classify the figures that you came up with into the various classes of polygons based on the number of sides.

3. Program the Pro-Bot to draw them on graph paper. Use 1 sq.cm. to represent 1 sq.m. in your figures.

4. Assume that the plot of land available for the construction, is a rectangle that is 15 m long and 8 m wide. Can you provide a design(s) to build a 100 sq.m. building in this plot? Program your Pro-Bot to draw the design. 
5. You can program the Pro-Bot to draw other figures with the 100 sq.m. area. Or explore other figures with different areas.

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 perimeter. For 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.

Programming Assignment

Old McDonald lives on a farm and has lots of animals. He would like to build a new set of fences to keep his cows safe.

1. If Old McDonald has 36 meters of fencing available, how many different ways can he build an enclosed area for his cows? Make a rough drawing of the figures that you come up with and then program the Pro-Bot to draw them on graph paper. Use 1 cm to represent 1 m in your figures.
2. Classify the figures that you came up with into the various classes of polygons based on the number of sides.
3. Write programs for Pro-Bot to draw at least 3 of the figures that you came up with.
4. Suppose Old McDonald has only 35 meters of fencing available, but wants to build a square or rectangular fence using all of that fencing material. Would it be possible for him to build it? Why or why not? 
5. You can program the Pro-Bot to draw other figures with the 36 cm perimeter. Or explore other figures with different perimeters.