Download Using Algebra Tiles to Complete the Square

Page 1 of 2
ACTIVITY 5.5
Developing Concepts
Using Algebra Tiles
to Complete the Square
QUESTION Given b, what is the value of c that makes x 2 + bx + c
EXPLORING THE CONCEPT
GROUP ACTIVITY
Work with a partner.
MATERIALS
algebra tiles
Group Activity for use with Lesson 5.5
a perfect square trinomial?
1 Use algebra tiles to model
the expression x2 + 6x.
You will need one x 2-tile
and six x-tiles.
2 Arrange the tiles in a square.
Your arrangement will be
incomplete in one corner.
You want the length and width
of your “square” to be equal.
3 Determine the number of 1-tiles
needed to complete the square.
By adding nine 1-tiles,
you can see that
x 2 + 6x + 9 = (x + 3)2.
Square
Completing the
en
Expression writt
Number of 1-tiles e
re
et
ua
pl
sq
m
a
co
as
to
ed
ed
ne
Expression
the square
?
?
2 2x ?
x
?
?
2
?
x 2 4x 2 6x 9 (x 3)
x
9
?
x 2 6x ?
?
?
x 2 8x ?
?
?
2 10x x
DRAWING CONCLUSIONS
1. Copy and complete the table at the left by
following the steps above.
2. Look for patterns in the last column of
your table. Consider the general statement
x2 + bx + c = (x + d)2.
a. How is d related to b in each case?
b. How is c related to d in each case?
c. How can you obtain the numbers in the
second column of the table directly from
the coefficients of x in the expressions
from the first column?
5.5 Concept Activity
281