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Transcript of Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other...
![Page 1: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/1.jpg)
Alge-Tiles
For all Alge-Tile work it is essential to remember that
RED means minus
And
Any other colour means plus.
![Page 2: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/2.jpg)
1
Variables
x2
-x2
x
-x-1
![Page 3: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/3.jpg)
ExampleRepresent the following trinomials using alge-tiles:
1. 2x2+3x+5
2. x2-2x-3
![Page 4: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/4.jpg)
Alge-Tile Uses
Algebra tiles can be used for (among other things):
Section 1. Identifying ‘like’ and ‘unlike’ terms
Section 2. Adding and Subtracting Integers
Section 3. Simplifying Expressions
Section 4. Multiplying in algebra
Section 5. Factorising trinomials
Section 6. Doing linear equations
![Page 5: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/5.jpg)
Section 1. Like Terms
Example 1. 4x+5
Can any of these be added ? Explain your answer
Example 2. 4x+5x
Can any of these be added ? Explain your answer
![Page 6: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/6.jpg)
Section 2. Adding and Subtracting Integers
Example 1. 4-7
Example 2. –3-6
![Page 7: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/7.jpg)
Section 3. Adding and Subtracting Trinomials
Example 1. 2x2+3x+5 + x2-5x-1
![Page 8: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/8.jpg)
Section 3. Adding and Subtracting Trinomials
Example 1. 2x2+3x+5 + x2-5x-1
Answer 3x2-2x+4
![Page 9: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/9.jpg)
Section 3. Adding and Subtracting Trinomials
Example 2. 2x2+3x+2 - ( x2-2x+1 )
-
A CONCRETE IDEA FOR CHANGING SIGNS.
![Page 10: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/10.jpg)
Section 3. Adding and Subtracting Trinomials
Example 2. 2x2+3x+2 - ( x2-2x+1 )
A CONCRETE IDEA FOR CHANGING SIGNS.
![Page 11: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/11.jpg)
Section 3. Adding and Subtracting Trinomials
Example 2. 2x2+3x+2 - ( x2-2x+1 )
A CONCRETE IDEA FOR CHANGING SIGNS.
Answer x2+5x+1
![Page 12: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/12.jpg)
Practice
Simplify the following:
1) 6-7
2) 3-2-4-1
3) 5x2+2x
4) 2x2+4x+2x2-x
5) 3x2-2x+4+x2-x-2
6) x2-3x-2-x2-2x+4
7) 2x2-2x-1-3x2-2x-2
8) x2+2x+1- 3x2-x
9) x2-x+3-2x2+2x+x2-2x-5
Simplify the following:
10)2-8-1
11)-5-1-4+1
12)x2+2
13)x2+5x+x2-2x
14)2x2-x+1 - (2x2-2x-5)
15)x2- 2x2-2x+4 - (x2+2x+3)
16)3x2-4x+2 - (x2+2)
17)x2+x-2 - 2(x2+2x-3)
18)-4x-3 - (2x2-2x-4)
![Page 13: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/13.jpg)
Multiplying & FactorisingGeneral Aim
•Whether multiplying or factorising, the general aim is to generate a rectangle and have no pieces left over.
•Also the small squares always go in the bottom right hand corner
![Page 14: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/14.jpg)
Section 4. Multiplying in algebra
Example 2. Multiply (x-1)(x-3)
Answer: x2-4x+3
![Page 15: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/15.jpg)
PracticeMultiply the following:
1) x(x+3)
2) 2(x-5)
3) 3x(x-1)
4) (x+4)(x+3)
5) (x-1)(x+2)
6) (x-4)(x-2)
7) (3x-1)(x-3)
8) (x-1)(x-1)
9) (2x+1)2
10) (x-2)2
![Page 16: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/16.jpg)
Factors and Area
- a geometrical approach
Review Multiplication Again
Section 5. Factorising Quadratic Trinomials
![Page 17: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/17.jpg)
Show (x+1)(x+3) by arranging the tiles in a rectangle.
x
x 3
1
+
+
Rearrange the tiles to show the expansion:
x 2 + 4x + 3How it works
Now Arrange them into a Now Arrange them into a RectangleRectangle
Remember the little guys go in the bottom right corner
![Page 18: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/18.jpg)
x 2 + 6x + 8
To factorise this expression form a rectangle with the pieces.
x + 4
x
+
2
( x + 4 )( x + 2 )
The factors are
Factorise x 2 + 6x + 8
Factorise x2+6x+8
![Page 19: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/19.jpg)
x + 3
x-
1
NOTE: REDS ARE NEGATIVE
NOW COMPLETE THE RECTANGLE WITH NEGATIVE SQUARES
Show (x+3)(x-1) by arranging the tiles in a rectangle.
Rearrange the tiles to show the expansion:
x2 + 3x -1x - 3 = x2 + 2x - 3(x+3)(x-1)
![Page 20: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/20.jpg)
Factorise x 2 - 4x + 3
x2 - 4x + 3x - 3
x - 1
The factors are ( x - 3 )( x - 1 )
Factorise x2-4x+3
![Page 21: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/21.jpg)
Factorise x 2 - x - 12
x2 - x -12
Factorise x2-x-12
Clearly there is no way to accommodate the 12 small guys in the bottom right hand corner. What do you do?
?You add in Zero in the form of +x and –x.
And Keep doing it to complete the rectangle.
![Page 22: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/22.jpg)
Factorise x 2 - x - 12
Factorise x2-x-12
The factors are ? ( x + 3 )( x - 4 )
x - 4
x + 3
![Page 23: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/23.jpg)
Section 6. Doing linear equations
Solve 2x + 2 = -8
=
![Page 24: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/24.jpg)
Section 6. Doing linear equations
Solve 2x + 2 = -8
=
![Page 25: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/25.jpg)
Section 6. Doing linear equations
Solve 2x + 2 = -8
=
=
=
![Page 26: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/26.jpg)
Section 6. Doing linear equations
Solve 2x + 2 = -8
=
=
Solution x = -5
![Page 27: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/27.jpg)
Section 6. Doing linear equations
=
Solve 4x – 3 = 9 + x
You can take away the same thing from both sides
![Page 28: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/28.jpg)
Section 6. Doing linear equations
=
Solve 4x – 3 = 9 + x
You can add the same quantity to both sides
![Page 29: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/29.jpg)
Section 6. Doing linear equations
=
Solve 4x – 3 = 9 + x
![Page 30: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/30.jpg)
Section 6. Doing linear equations
=
Solve 4x – 3 = 9 + x
=
=
![Page 31: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/31.jpg)
Section 6. Doing linear equations
=
Solve 4x – 3 = 9 + x
=
=
Solution x = 4
![Page 32: Alge-Tiles For all Alge-Tile work it is essential to remember that RED means minus And Any other colour means plus.](https://reader030.fdocuments.net/reader030/viewer/2022032606/56649eb65503460f94bbef65/html5/thumbnails/32.jpg)
PracticeSolve the following:
1) x+4 = 7
2) x-2 = 4
3) 3x-1 =11
4) 4x-2 = x-8
5) 5x+1 = 13-x
6) 2(x+3) = x-1
7) 2x-4 = 5x+8