To help students visualize abstract concepts Introduce a new topic; students then can discover the...
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![Page 1: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/1.jpg)
![Page 2: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/2.jpg)
To help students visualize abstract concepts
Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher
Reinforce a topic for a struggling student
![Page 3: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/3.jpg)
Positive Tiles Negative Tiles 1 1
1 1
1 1
x x
x X
x X x x
X
X²
1 1
X
X²
![Page 4: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/4.jpg)
Addition and Subtractions of Integers Distributive Property Combining Like Terms Solving Equations Multiplying Binominals Factoring Polynomials
![Page 5: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/5.jpg)
3 + ( -5 ) = ? Additions means “ Combine”
Use the zero property to
cancel/take away a pair of blue and red tiles
Left with 2 “-1 tiles” Answer = -2
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1
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1
![Page 6: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/6.jpg)
5 – (-2) = ?Start with 5
“take away” Answer = 7
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1
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1
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1Now you can take away 2 “-1 tiles”
Add a zero pair in order to be able to take away 2 “-1 tiles”
![Page 7: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/7.jpg)
3 (2x + 1) is equivalent to 6x + 33 (2x + 1) {using repeated addition) Rearrange
the tilesX X
1
XX
XX
1
1
X
X
X
X
X
X
1
1
1 +
+
![Page 8: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/8.jpg)
(x² - 2x -3) – (2x² + x – 2) = ?
X²
X
X
1
1
1
Subtraction would be represented by “adding the opposite of each term in parenthesis”
X²X²
X
1
1
Cross out all zero pairs, what you have left over is your answer
Answer = -x² – 3x – 1
+
![Page 9: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/9.jpg)
2x -2 = 4
X
X
1 1 = 1 111
![Page 10: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/10.jpg)
2x -2 = 4Add two tiles to the left to make a zero pair
* To keep scale balanced - do the same to both sides *
X
X
1 1 = 1 111
1 1 1 1
![Page 11: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/11.jpg)
2x -2 = 4Arrange the tiles into groups
Answer: X = 3
1
1
X =X
1
1 1
1
![Page 12: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/12.jpg)
(x + 3) (x + 2)
X 1 11
1
X
1
L W
![Page 13: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/13.jpg)
(x + 3) (x + 2)
X 1 11
1
X
1
X² X X X
X
X
1 1 1
1 1 1
Answer = x² + 5x + 6
Fill in the space so that lines between tiles are continuous
![Page 14: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/14.jpg)
2x² + 5x + 3
X² X² X
X
X X
X 1 1 1
First fill in the “x² tiles” and “1 tiles” Then arrange the “x tiles” to match
![Page 15: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/15.jpg)
2x² + 5x + 3
1 11
1
XX
X
x + 1
2x + 3
Answer = (2x +3) ( x + 1)
![Page 16: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/16.jpg)
Teaching the rules of Algebra Tiles Multiplying a Polynomial by a Binomial More difficult using negative number for:
Distributing Factoring Multiplying two binomials(It is possible but students might struggle)
![Page 17: To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55141420550346ec488b520e/html5/thumbnails/17.jpg)
Visualizing an abstract concept
Students generating rules Practice with basic problems then have
students find patterns to then apply to more challenging problems
Another tool in the tool box