Looking for Squares

At a Glance
Grouping:
small groups
Launch
  Draw a unit square on a 5-dot-by-5-dot grid and label its area.
  Challenge students to find as many squares with different areas as they can.
  Have groups of two or three work on the problem and follow-up.
Explore
  Help students who have trouble finding tilted squares.
  Remind students who find the same square more than once to check the areas.
Summarize
  Have students share the squares they found until all eight are displayed.
  Talk about the side lengths of the squares and the connection to square roots.
 
Problem 2.1 Follow-Up
1. Find the area of each triangle below.
2.

Describe the strategies you used to find the areas.
 

 

Looking for Squares

The smallest square you can draw by connecting the dots on a 5-dot-by-5-dot grid is a unit square, which has an area of 1 square unit. You can draw a 2-by-2 square by connecting the dots as shown. Since a 2-by-2 square contains 4 unit squares, it has an area of 4 square units.

In this problem, you will explore the other areas that are possible for squares drawn on a 5-dot-by-5-dot grid.

Problem 2.2  
On the 5-do-by-5-dot grids on Labsheet 2.2, draw squares of various sizes by connecting dots. Try to draw squares with as many different areas as possible. Label each square with its area.
 
   
Assignment Choices
ACE questions 4, 6, 7, 11, 15, and unassigned choices from earlier problems.

 
Answers to Problem 2.1 Follow-Up
1. a. 3 square units

b. 4 square units

 c. 2 square units
  d. 2 square units e. 3 1/2 square units f. 5 square units
2. See page 26i.    
Answer to Problem 2.2
See page 26i.
CONNECTED MATHEMATICS PROJECT - Looking For Squares - LESSON 2.2
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