Module 5 Project

In this project you will work with dot paper to drawing straight and tilted squares and calculate their areas and side lengths.

 

It is difficult to visualize a line that is or long. You will be using 1-cm dot paper to draw squares with different areas and finding the lengths of line segments between dots on the grid. This project will give you a greater understanding of radicals and help you to see that are numbers as real and definite as 2 or 5.

 

Project Assessment

 

There are three parts to your assignment. All three parts must be handed in to your teacher.

 

Part 1	20 marks
Part 2	30 marks
Part 3	20 marks
Total Marks	70 marks

Are You Ready?

 

Refresh your memory of some skills needed for the project by completing the following section.

 

Assume the dots on the figure are exactly 1 cm apart.

 

1. Find the area of the square figure by
   
   
   1. counting the number of square centimetres enclosed by the figure
    
   2. calculating it from the formula A = (length of side)2
    
   Answers
   
   
2. Calculate the slope of segment AB. Recall that Answer

3. Find the length of segment AB by
   
   
   1. approximate measurement
    
   2. calculation
      
      
   Answers

If you successfully completed the Are You Ready? questions and feel comfortable with the concepts, move on to Part 1 of the project.

 

If you experienced difficulties with the questions, use the resources in the Refresher to review the prerequisite concepts before continuing through the lesson.

 

Refresher

 

Visit Pythagorean Theorem to find a definition, examples of how it is used, and a demonstration applet.

 

 

Go back to the Are You Ready? section, and try the questions again. If you are still having difficulty, contact your teacher.

Part 1

 

You may work with a partner or as a small group on this activity; however, each person must submit his or her own answers as part of the project submission.

 

You can choose to print out 1-cm Dot Paper and draw squares on grid paper, or you can use the Geoboard applet. To draw squares using the applet, drag either or both of the red dots. The area of the square created will be shown inside the square.

 

 

Using the applet or grid paper, draw squares that have the areas listed in Table 1. Give the exact length of each side of the square. (20 marks)

 

Remember to save your completed Table 1 to your course folder. You will submit it to your teacher for marks at the end of Lesson 3. At this time, you should read the Lesson 1 Summary.

Part 2

1. Determine the exact length of each of the segments shown on a 1-cm dot grid.
   
   
   
   Complete Table 2. Hint: You can use the Pythagorean theorem. (8 marks)

2. Determine the exact length of each of these segments.
   
   
   
   Complete Table 3. (8 marks)

3. You may work with a partner or as a small group on this activity; however, each person must submit his or her own answers. On a sheet of 1-cm dot paper, draw and label line segments that have the exact length shown in the following table. Be sure that both ends of each line segment are on a dot.
   
   

   Segment	Exact Side Length (cm)
   a
   b	2
   c
   d
   e	0.5
   f
   g	10

   Segment	Exact Side Length (cm)
   h
   i
   j	15
   k
   l
   m
   n

   
   
   You can use the Geo-lines applet to help you find the line segment length, but you must submit your answers on dot paper. You may use 1-cm Dot Paper to complete this project. (14 marks)

 

Remember to save your work from Part 2 to your course folder. You will submit it to your teacher for marks at the end of Lesson 3. At this time, you should read the Lesson 2 Summary.

Part 3

 

For the summary of the Module 5 Project, complete the following questions.

1. Draw a line segment that is in length. Now draw a line segment that is in length. How do the two line segments compare? (2 marks)
   
   
2. Draw a line segment that is in length. Now draw a line segment that is in length. How do the two line segments compare? (2 marks)
   
   
3. Write a paragraph or two that summarizes what you have learned in this project. Consider questions such as the following:
   
   
   • How has this activity increased your understanding of radicals?
     
   • If you worked with a partner or group, what advantages or disadvantages did you find in doing so?
   • What was the most valuable part of this project for you?
     
   • What did you find most difficult or frustrating in this activity?
     
   • Can you describe a moment when a new understanding or thought occurred to you?
     
   • What connections can you make between this project and your work in Lessons 1, 2, and 3?
     
     
   (16 marks)

Submit to your teacher the following completed documents for your assessment of the project.

• Part 1
• Part 2
• Part 3