Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.
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Transcript of Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.
![Page 1: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/1.jpg)
Introduction to Algebra Tiles
Created by Nancy McAlindenNumeracy Lead TeacherN.B. District 14
![Page 2: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/2.jpg)
Remember how we modeled integers?
Legend
? ?+ -
![Page 3: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/3.jpg)
What is this worth?
Legend
+ -ZERO PAIRS
(-2)
![Page 4: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/4.jpg)
What is this worth?
Legend
+ -
+2
![Page 5: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/5.jpg)
Algebra Tiles work the same way!Legend
+ -
+3
![Page 6: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/6.jpg)
Algebra Tiles work the same way!Legend
+ -
-6
![Page 7: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/7.jpg)
Algebra Tiles work the same way!Legend
+ -
-2
![Page 8: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/8.jpg)
Model this question:
(-2) + (+3) = Legend
+ -
+1
zero pairs
![Page 9: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/9.jpg)
But…
Algebra Tiles can show MORE!
![Page 10: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/10.jpg)
Legend
+ -
These tiles help us model the unknown! The variable! The mystery number!
![Page 11: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/11.jpg)
Legend
+ -
These tiles represent x! (Or n) (or whatever letter you’re using for the variable or unknown amount.)
![Page 12: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/12.jpg)
Legend
+ -
One side represents a positive variable; the other side represents a negative.
![Page 13: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/13.jpg)
What does this show?Legend
+ -
+ -
3x
![Page 14: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/14.jpg)
What does this show?Legend
+ -
+ --9x
![Page 15: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/15.jpg)
What does this show?Legend
+ -
+ -
-2x
![Page 16: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/16.jpg)
What does this show?Legend
+ -
+ -
2x + 4
![Page 17: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/17.jpg)
What does this show?Legend
+ -
+ -
x - 6
![Page 18: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/18.jpg)
What does this show?Legend
+ -
+ -
-2x + 5
![Page 19: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/19.jpg)
What does this show?
x + 3
![Page 20: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/20.jpg)
But what is x worth?
We don’t know until:
1.) someone tells us the value of x
Or
2.) we have some information about the other side of the equation!
![Page 21: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/21.jpg)
3x = 9
This line represents the = sign, or the middle of the balance scale.
![Page 22: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/22.jpg)
If 3x = 9,
…what is one x worth?
![Page 23: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/23.jpg)
3x = 9
![Page 24: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/24.jpg)
3x = 9
x = 3
![Page 25: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/25.jpg)
Solve for x:
x + 2 = 6
![Page 26: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/26.jpg)
Solve for x: X + 2 = 6
We want a single x alone on one side and its value (the number of units or squares) on the other.
![Page 27: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/27.jpg)
Solve for x: x + 2 = 6
We can subtract the 2 units (or squares) from the leftIFwe also subtract 2 units from the right. This keeps the balance.
![Page 28: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/28.jpg)
Solve for x: x + 2 = 6x + 2 – 2 = 6 - 2
![Page 29: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/29.jpg)
Solve for x:
x = 4
![Page 30: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/30.jpg)
Solve for x: 2x + 4 = 8
![Page 31: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/31.jpg)
Solve for x: 2x + 4 = 8
We want a single x alone on one side and its value (the number of units or squares) on the other.
![Page 32: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/32.jpg)
Solve for x: 2x + 4 = 8
We can remove the 4 positive units from the left as long as we keep the balance and remove 4 positives from the right too.
2x + 4 - 4 = 8 - 4
![Page 33: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/33.jpg)
Solve for x: 2x + 4 = 8
Now we have 2 x on one sideand 4 on the other.
We want one x.
2x = 4
![Page 34: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/34.jpg)
Solve for x: 2x + 4 = 8
We can’t subtract an x from the leftbecause we don’t have an x to subtract from the right, but…
2x = 4
![Page 35: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/35.jpg)
Solve for x:
We can divide them and share fairly:
2x = 4
![Page 36: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/36.jpg)
Solve for x: 2x = 4
![Page 37: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/37.jpg)
Solve for x: 2x = 4___ = __ 2 2
![Page 38: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/38.jpg)
Solve for x: x = 2
![Page 39: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/39.jpg)
What about the big squares?
![Page 40: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/40.jpg)
They represent x2 and (-x2).
![Page 41: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/41.jpg)
We’ll use them in high school!
![Page 42: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/42.jpg)
Not all sets of algebra tiles are the same colours as the set we’ve seen here.
How can you tell which side is negative?
![Page 43: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/43.jpg)
The negative side is the colour that is the same for all sizes of tiles in the set:
White = negative
![Page 44: Introduction to Algebra Tiles Created by Nancy M c Alinden Numeracy Lead Teacher N.B. District 14.](https://reader036.fdocuments.net/reader036/viewer/2022062511/551787d65503460e6e8b5686/html5/thumbnails/44.jpg)
The negative side is the colour that is the same for all the tiles in the set:
Black = negative