Working With Algebra Tiles
(Grade 9 projects)
Members are: Shiekah Mohammed, ID: 1001943.
Sara Abdullah, ID: 1000741.
Sara Khalid, ID: 1001922.
Mariam Saeed, ID: 1001886.
Our Teacher is:
Ms. Inass Ibrahim.
Grade: nine fifty-three.
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Algebra tiles
Algebra Tiles Introduction: Students will investigate
the factorization of x2+bx+c and ax2+bx+c. It is the intent
of the project to develop the students’ insight into the
trinomial factorization process. Here x2+bx+c, where a, b,
and c denote constant values and the “x” term signifies the
unknown variable, often can be factored into the product of
two terms. Students will use algebra tiles to identify the
binomial factors. This sets the stage for the students to later
learn how to solve polynomial equations and explore
relationships between the trinomial x2 + bx + c and its
factored form (x + m)(x + n).
Learning Objectives:
Students will be able to:
Factor trinomials of the form x2 + bx + c into two binomial
factors.
Identify the relationships that exist between b, c, m, and n
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when x2 + bx + c is factored as (x + m)(x + n).
Generalize the process for factoring trinomials of the form:
x2 - bx + c , x2 - bx - c where b and c are positive integers.
Instructions:
1. In groups of four create a wiki/ blog
2. All group members try Algebra Tiles (Appendix I). 3.
Group members meet to accomplish Task1 Task2 Task3 4.
Post all steps of your work , your discussions and your
conclusion on your Wiki/ blog. 5. Visit four wikis/ blogs of
your friends, explore their results and comment on it.
Task 1: Navigate the web to search about the definition of the word "factor”
and the use of algebra tiles to factor trinomials.
Factor: A number may be made by multiplying two or more other
numbers together. The numbers that are multiplied together are called
factors of the final number. All numbers have a factor of one since one
multiplied by any number equals that number. All numbers can be
divided by themselves to produce the number one. Therefore, we
normally ignore one and the number itself as useful factors.
The number fifteen can be divided into two factors which are three and
five.
The number twelve could be divided into two factors which are 6 and
2. Six could be divided into two further factors of 2 and 3. Therefore
the factors of twelve are 2, 2, and 3.
If twelve was first divided into the factors 3 and 4, the four could be
divided into factors of 2 and 2. Therefore the factors of twelve are still
2, 2, and 3.
• There are several clues to help determine factors.
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• Any even number has a factor of two
• Any number ending in 5 has a factor of five
• Any number above 0 that ends with 0 (such as 10, 30, 1200) has
factors of two and five.
To determine factors see if one of the above rules apply (ends in 5, 0
or an even number). If none of the rules apply, there still may be
factors of 3 or 7 or some other number.
Access the Algebra Tiles (Appendix I) and work on the problems below.
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This is an Example of factoring trinomials by
using Algebra Tiles from this site
http://courses.wccnet.edu/~rwhatcher/VAT/Fa
Polynomials: X2+bx+c
ctoring/Factoring/Level One.html Factors:(x
+ m)(x + n)
Model the following quadratic trinomials using Algebra Tiles (Appendix
I), and then write the binomial factors to the right.
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X2+2X+1
(X+1)(X+1)
X2+3X+2
(X+2)(X+1)
X2+7X+6
(X+6)(X+1)
X2+5X+6
(X+3)(X+2)
X2+5X+4
(X+4)(X+1)
2X2+3X+1
(X+1)(2X+1)
2X2+7X+3
(X+3)(2X+1)
3X2+7X+2
(X+2)(3X+1)
4X2+8X+3
(2X+1)(2X+3)
Task 2: -
Design and present solid colored model on one of the above examples.
(Appendix II)
The example: 2x2+12x+6
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It’s a rectangle!
Generalize the process for factoring trinomials of the form: x2 + bx + c
where b and c are positive integers.
To factor polynomials of the form x2 + bx + c, begin with two pairs of parentheses
with x at the left of each.
Next, find two integers whose product is c and whose sum is b and place them at the
right of the parentheses.
Example 1: Factor x2 + 8 x +12
12 can be factored in a variety of ways:
The only
combination whose sum is also 8 is (2)(6), so
-------------------------------------------------------------------------------------------------Example 2: Factor x2 − 7 x − 18.
−18 can be factored in the following ways:
The only combination whose sum is also −7 is (2)(−9), so
Task 3: Generalize the process for factoring trinomials of the form: x2- bx + c ,
x2- bx - c where b and c are positive integers. Provide six examples on
the above two forms.( 3 examples on each form).
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x2- bx + c, The sine in the bracts
have to be (Minus)(Minus).
x2- bx -c, The sine in the bracts
have to be (Plus)(Minus) OR
(Minus)(Plus)
Ex1: 2t2-11t+15
2t2 > 2t . 1t
15> 5 . 3, 15 . 1
(t-3)(2t-5)
Ex4: 2x2-3x-9
2x2> 2x.1x 9> 3.3, 9.1
(x-3)(2x+3)
3q2
Ex2: 3q2-13q+6
> 3q . 1q 6> 1 . 6, 2 . 3
(3q-2)(q-3)
10w2>
Ex3: 3g2-7g+2
3q2 > 3g . 1g 2> 1 . 2
(3g-1)(g-2)
Ex5: 10w2-19w-15
5w.2w, 10w.1x 15>3.5, 15.1
(5w+3)(2x-5)
Ex6: 2x2 – x – 1
2x2> 2x.1x, 1> 1.1
(2x+1)(x-1)
OR
IF x2+bx+c the sins will be both positive.
IF x2+bx-c the sins will be positive and negative.
How to solve? We factor the last and the first numbers in the equation we
put the first number factors in the two bracts we opened (only pick two).
Then we put the last number factors (only two) & we try tell we find the
right answer, if you couldn’t find, change the sins place, if didn’t work, try
to change the first number factors if there were more than two. If there was
no answer however you tried we call it Prime.
References: 8
http://www.cliffsnotes.com/study_guide/Tri
nomials-of-the-Form-x2-bxc.topicArticleId-38949,articleId-38893.html
http://www.google.ae/imgres?imgurl=http:
//www.highhopes.com/L7541.JPG&imgrefu
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24&sig2=UgcuOfhlDW7mucoM9mUcIA&z
oom=1&um=1&itbs=1&tbnid=frhzYorUa
mjsZM:&tbnh=98&tbnw=130&prev=/imag
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680%26tbs%3Disch:1&ei=AByOTfK1MoGg
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http://nlvm.usu.edu/en/nav/frames_asid_18
9_g_4_t_2.html?open=activities&from=cate
gory_g_4_t_2.html
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