1. Alge-Tiles
an Overview

2. x
Set 1 1 x2
Set 2 xy y2 y

3. x
– x
= 0 –1 1 x2
– x2 xy y2
–y2
– xy y
– y

4. Adding Integers
(+ 5) (+ 7) +
= 12

5. Adding Integers
(– 5) + (– 7) +
= – 12

6. Adding Integers
(– 5)
= + 3

7. Subtracting Integers
(– 2) – (– 4) – +
= 2

8. Subtracting Integers
(– 4) – (+ 6) – +
= – 10

9. Multiplying Integers 6
(2)(3) –6
(2)(–3)
(–2)(–3) 6

10. Algebraic Expressions
x2 + 2x + 4
x2 – 3x – 2
2x2 – x + 2

11. Adding Polynomials
(4x + 5) + (2x – 3) +
= 6x + 2

12. Subtracting Polynomials
(5x + 2) – (3x – 4) – +
= 2x + 6

13. Multiplying Polynomials
3(x + 2)
x + 2 3
Guiding tiles

14. Multiplying Polynomials
3(x + 2)
3x + 6

15. Multiplying Polynomials
x(x – 3)
x – 3 x
Guiding tiles

16. Multiplying Polynomials
x(x – 3)
x2 – 3x

17. Multiplying Polynomials
(x + 2)(x + 3)
x + 2
x + 3
Guiding tiles

18. Multiplying Polynomials
(x + 2)(x + 3)
x2 + 5x + 6

19. Multiplying Polynomials
(x – 2)(x + 2)
x – 2
x + 2

20. Multiplying Polynomials
(x – 2)(x + 2)

21. Multiplying Polynomials
(x – 2)(x + 2)
x2 – 4

22. Factoring Polynomials
x2 + 6x + 8
x + 4
x + 2
Form a rectangle
x2 + 6x + 8 = (x + 2)(x + 4)

23. Solving Equations: solve for x

24. Solving Equations: solve for x

25. Solving Equations: solve for x

26. Solving Equations: solve for x

27. Solving Equations: solve for x

28. Solving Equations: solve for x
3x – 1 = x – 5

29. Solving Equations: solve for x
3x – 1 = x – 5

30. Solving Equations: solve for x
3x – 1 = x – 5
x = –2

31. Both sides have seven white tiles.
Check
Substitute
for
3x – 1 = x – 5
x = –2
Both sides have seven white tiles.