The current teaching of Algebra is abstract and complex which makes its learning dull. In algebra classes, students memorized steps and rules without meaning and explanation. Algebra tiles can be used to develop concrete representations of abstract algebraic concepts. The concrete models help students become comfortable with using symbols to represent algebraic concepts. The webinar demonstrates the use of Algebraic tiles in developing students’ understanding of simplification of algebraic expression, equation, and factoring.

1. Let Play Algebra: Concrete to Abstract
Muhammad Yusuf
Pedagogy Expert

2. Manipulatives are concrete physical objects that students can
use in a hands-on approach to learning.
Manipulatives can be an important tool to help students
think and reason in a more meaningful way.
Manipulatives are able to facilitate the creation of a learning
environment that encourages engagement and enables
understanding.
Source: Cockett, A., & Kilgour, P. W. (2015). Mathematical manipulatives: Creating an
environment for understanding, efficiency, engagement, and enjoyment. TEACH
COLLECTION of Christian Education, 1/1, 47-54.
Let us Remind ourselves

3. Menu
Introduction of Algebra Tiles
Solving Equations
Simplification
Addition
Subtraction
Multiplication
Factoring
Making Perfect Square
How can we get Algebra tiles?

4. Algebra Tiles
X
X
X2 X
1
X 1 -X2 -X -1
Y2 Y XY -XY -Y2 -Y

5. Linear Equations
𝑥 + 7 = 4
=
𝑥 = −3

6. 𝑥 − 2 =5 𝑥 − 2 =5
= ⇒ 𝑥 − 2 + 2 =5+2
⇒ 𝑥 = 7

7. 3𝑥 + 4 = 10
3𝑥 + 4 = 10
=
=
⇒ 3𝑥 + 4 − 4 = 10 − 4
⇒ 3𝑥 = 6
⇒
3
3
𝑥 =
6
3
⇒ 𝑥 = 2

8. Solve the equation 5𝑥 + 3 = 4𝑥 + 5.
=

9. Solve the equation 5𝑥 + 3 = 4𝑥 + 5.
=
5𝑥 + 3 = 4𝑥 + 5
⇒ 5𝑥 + 3 − 3 = 4𝑥 + 5 − 3
⇒ 5𝑥 = 4𝑥 + 2
⇒ 5𝑥 − 4𝑥 = 4𝑥 − 4𝑥 + 2
⇒ 𝑥 = 2

10. Simplification

11. Let us re-arrange
4𝑥2
+ 3𝑥 − 7 − 2𝑥2
− 4𝑥 + 2
2𝑥2
− 𝑥 − 5

12. Let us re-arrange
4𝑥2
+ 3𝑥 − 7 − 2𝑥2
− 4𝑥 + 2
4𝑥2
−2𝑥2
+3𝑥−4𝑥 −7+2
= 2𝑥2
−𝑥 −5

13. 2𝑥2
+ 2𝑥𝑦 − 2𝑦2
− 4𝑥𝑦 + 3𝑥2
+ 3𝑦2
5𝑥2 − 2𝑥𝑦 + 𝑦2

14. Addition &
Subtraction

15. Add 4x, 5x
9X

16. Add 3x+4y, -4x+6
3𝑥 − 4𝑦, −4𝑥 + 6
3𝑥 − 4𝑥 − 4𝑦 + 6
−𝑥 − 4𝑦 + 6

17. Add 2𝑥2
− 2𝑥 + 4, 3𝑥2
+ 4𝑥 − 2
5𝑥2
+ 2𝑥 + 2

18. Subtract -3X from 5X
8X

19. Subtract 3x² - 6x -3 from 5 + x - 2x².
- 5x² + 7x + 2

20. Multiplication

21. (2x+3) (x+2)
2𝑥2
+ 3𝑥 + 4𝑥 + 6
2𝑥2 + 7𝑥 + 6

22. (3x-4)(x-1)
3𝑥2 − 4x − 3x + 4
3𝑥2 − 7x + 4

23. (2x + 3y) (x – 2y)
2𝑥2 + 3𝑥𝑦 − 4𝑥𝑦 − 6𝑦2
2𝑥2 − 𝑥𝑦 − 6𝑦2

24. The factorization of algebraic expressions

25. 3𝑥2
+ 6𝑥
Arrange tiles represents 3𝑥2 + 6𝑥
We will arrange the tiles into a complete rectangle
X X X
x+1+1
3𝑥(𝑥 + 2)

26. x² +5x +6
Arrange tiles represents x² +5x +6
We will arrange the tiles into a complete rectangle
X +1 +1 + 1
x+1+1
=(X + 3) (X + 2)
𝑥2 + 3𝑥 + 2𝑥 + 6

27. x² -7x +12
X -1 -1 -1 -1
X
-1
-1
-1
=(X-3) (X-4)
𝑥2
− 4𝑥 − 3𝑥 + 12

28. x² +2x -8
To make a
rectangle, we
can add in x and
–x tiles in pairs,
because the
cancel each
other out.
X +1 +1 +1 +1
X
-1
-1
=(X+3) (X-2)
𝑥2
+ 4𝑥 − 2𝑥 − 8

29. x² -5x -6
X -1 -1 -1 -1 -1 -1
X
1
=(X-6) (X+1)
𝑥2
− 6𝑥 + 𝑥 − 6

30. How can we find them?
Buy-online
Android Application
Make your own:
https://www.amazon.in/MATHWORLD-ALGEBRA-TILES-PLASTIC-
DIFFERENT/dp/B07JH2ZGQM/ref=sr_1_1?dchild=1&keywords=algebra+tiles&qid=1600371552&sr=8-1
https://play.google.com/store/apps/details?id=com.khunter83.Algebra_Tiles&hl=en
https://play.google.com/store/apps/details?id=air.ca.mathclips.algebratiles&hl=en

31. Now, it is your turns.