1. Licensing information
This material is licensed under the Creative Commons Attribution-Share Alike license: (
Author: Kevin Hall

2. Please fill in this column on your own.
2).
Current Value
Instructions
Algebra Tiles
a).
Pick any number.
b).
Now add 3.
Please fill in this column on your own.
c).
Multiply that answer by 2.
d).
Subtract 6 from that answer.
e).
Divide that answer by 2.
What did you notice?

3. Here are my answers. 2). Current Value Instructions Algebra Tiles 5 8
Pick any number. 5 8
b).
Now add 3.
5 + 3 =
c).
Multiply that answer by 2.
8 • 2 = 16
d).
Subtract 6 from that answer.
16 – 6 = 10
e).
Divide that answer by 2. 10 = 5 2
Here are my answers.

4. This shows that the trick works when you start with 5.
2).
Current Value
Instructions
Algebra Tiles
a).
Pick any number. 5
This shows that the trick works when you start with 5.
But how can we know if it will work for ANY number? 8
b).
Now add 3.
5 + 3 =
c).
Multiply that answer by 2.
8 • 2 = 16
d).
Subtract 6 from that answer.
16 – 6 = 10
e).
Divide that answer by 2. 10 = 5 2

5. This represents x. 2). Current Value Instructions Algebra Tiles 5 8 16
Pick any number. x 5
This represents x. 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

6. …because x is a variable.
2).
Current Value
Instructions
Algebra Tiles
a).
Pick any number. x 5
It could be any length.
…because x is a variable. 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

7. It could be any length. 2). Current Value Instructions Algebra Tiles 5
Pick any number. 5 5
It could be any length. 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

8. It could be any length. 2). Current Value Instructions Algebra Tiles 5
Pick any number. 7 5
It could be any length. 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

9. It could be any length… 2). Current Value Instructions Algebra Tiles 5
Pick any number. 10 5
It could be any length… 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

10. It could be any length… 2). Current Value Instructions Algebra Tiles 5
Pick any number. 11 5
It could be any length… 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

11. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. x 5 x 1 1 1 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

12. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

13. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

14. 2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a).
Pick any number. 5 8
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5

15. Original number 2). Current Value Instructions Algebra Tiles 5 8 16 10
Pick any number. 5 8
b).
Now add 3.
Original number
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5
Final picture:

16. We proved that it works when you start with ANY number.
2).
Current Value
Instructions
Algebra Tiles
a).
Pick any number. 5 8
We proved that it works when you start with ANY number.
b).
Now add 3.
c).
Multiply that answer by 2. 16
d).
Subtract 6 from that answer. 10
e).
Divide that answer by 2. 5
Final picture:

17. 4).
Please write down these expressions and then draw each picture.
a).
4 + 2
b).
4 – 2
c).
3 • 2 or

18. Examples:
Watch & discuss these examples to help you with the next questions on the handout.
Ex. 1
Ex. 2
Ex. 3 8 x
3(x+1) 4 2 x 1 x 8 2
= 2 4
3(x+1)

19. 4).
Please write down these expressions and then draw each picture.
d). 6
e). 4x
f).
x + 4 2
g). x
h).
4x + 2
i).
4(x+2) 3
Why are these different?

20. Discuss this Example Your prediction? Why?
What would be the difference between the pictures of 5(x + 3) and 5x + 3 ?
Your prediction?
Why?
5(x + 3)
5x + 3

21. Please write down these expressions and then draw each picture.
4).
Please write down these expressions and then draw each picture.
4x + 6
Draw “4x + 6” first. 4x
j).
k).
+ 6 2 2
Now divide by 2.

22. Why NOT keep all 6 squares here? Why keep all 6 squares here?
4).
Please write down these expressions and then draw each picture.
j).
4x + 6
k). 4x
Why NOT keep all 6 squares here?
+ 6
Why keep all 6 squares here? 2 2