1. Lesson 1

1.4. Discover

Mathematics 30-3 Module 3

Module 3: Algebra

 

Discover

 

There are many places where you will find linear relations. In the Math Lab you will investigate if the following relationships are linear relations.

 

Math Lab

 

Study the illustration of figures shown. Consider the width, area, and perimeter of each figure. Do you see a pattern?

 

This is an illustration of three T-shaped figures on a grid. Figure 1 has a top row of 3 squares with a second row of 1 square centred below the top row. Figure 2 has two rows of 6 squares with two rows of 2 squares centred below them. Figure 3 has three rows of 9 squares with three rows of 3 squares centred below them.

 

Use the illustration to answer the following questions.

  1. Use Grid Paper Template or your own graph paper to construct the next two figures, figure 4 and figure 5.
  2. Complete a table like the one shown. The first two rows have been completed for you.

    Figure

    Width

    Area

    Perimeter

    1

    3

    4

    10

    2

    6

    16

    20

    3

     

     

     

    4

     

     

     

    5

     

     

     
  3. Graph the data for all five figures using the variables listed. You can graph by hand, electronically by using a spreadsheet, or by using Grid Paper Template.
    1. perimeter versus figure number
    2. area versus figure number
    3. perimeter versus width
  1. You have now constructed three graphs. In which of these graphs do the points form a straight line? To quickly check for a straight line, try to line a straight edge up to the points.
  2. What pattern do you notice in the table you completed in question 2?
  3. Is the pattern from question 5 present for graphs that do not form a straight line?

course folder Save your responses in your course folder.

 

Share 1

 

Share your responses and discoveries from Math Lab with a classmate. Be sure to address questions 4 to 6 in your sharing discussion.

 

course folder Save a summary of your discussion in your course folder.

When graphing A versus B, B represents the horizontal axis and A represents the vertical axis.

 

This diagram shows an empty graph titled A Versus B. The vertical axis is labelled A and the horizontal axis is labelled B.