Explore the Math Activity
Use the square tiles to make 5 rectangles with the dimension shown.
Length (cm)

Width (cm) 
Area (cmÂ²) 
Square? (yes/no) 
Side length of Square (cm) 
5 
3 



8 
2 



9 
1 



4 
3 



9 
4 



After constructing the shape, record the area of the shape.
Try to rearrange the tiles in each rectangle to make a square.
Which rectangles can you make into square? Record the results in your table.
Record the side length of each square in your table.
How is the area of each square related to its side length?
Complete the factor trees to determine the prime factors of 15 and 16.
15 16
3 X 5 2 X 8
2 X ____ X _____
2 X _____X ______ x ______
b) Write 15 and 16 as a product of prime factors.
15 = 3 x 5 16= ______ x _______ x ______ x _____
Complete the following table.
Number 
Perfect Square? (yes/ no) 
Prime Factors 
Number of times Each Prime Factor Appears 
15 



16 



9 



12 



36 



Look at the column titled Number of Times Each Prime Factor Appears.
What do all of the perfect squares have in common?
What do all of the nonperfect squares have in common?
A) How can square tiles help you to determine if a number is a perfect square?
B) How can prime factors help you to determine if a number is a perfect square?
