1. Evaluate the following expressions: 52 43 -22
Do Now:
Evaluate the following expressions: 52 43
-22

2. Perfect Squares and Cubes Perfect Numbers
This is targeted to Algebra I students to help them identify perfect numbers. The term “perfect” will be new to some students. Most students have been exposed to perfect numbers that are whole numbers. They will need to differentiate between perfect squares and perfect cubes. They will need to learn about fractions, and negatives. In the future, they will use this skill to simplify radicals.
There are a variety of instructional strategies used in this presentation. The introductions of perfect squares and cubes is presented by giving examples and then giving the rule. The sections on fractions and negative numbers are presented by giving a rule and then several examples. After each section the quiz provides feedback to the student. The instruction in negative numbers and the repetition of rules throughout the presentation help to stimulate recall of prior knowledge. The use of sounds and clipart helps gain and keep the attention of the student.

3. Perfect Numbers
In this presentation you will learn what perfect numbers are and how to identify them. You will look at whole numbers, fractions, and negative numbers.
Learning objective

4. A Perfect Number is a number that has equal factors.
Definition
A Perfect Number is a number that has
equal factors.

5. Examples of perfect numbers
4 = 2x2 25 = 5x5 1= 1x1
64 = 8x8 81 = 9x9 36 = 6x6
The numbers in black are all perfect squares because they have 2 equal factors.

6. More Examples of Perfect Numbers
8 = 2x2x = 10x10x10
125 = 5x5x5
The numbers in black are perfect cubes because they have 3 equal factors.

7. TRY THESE !!!
Three of the following numbers are perfect squares. Two of the following numbers are perfect cubes? Find both of the perfect cubes before you go on. 27 49
144
125

8. No This is a Perfect Square.
This number has two equal factors.
Return

9. Yes This is a Perfect Cube.
This number has three equal factors.

10. Factor
A factor is a number that divides into another with no remainder.
2 is a factor of 6 because:
2 divides into 6 three times with no remainder
2 is not a factor of 7 because:
2 divides into 7 three times with a remainder of one

11. Special numbers
In addition to whole numbers, you will look at fractions and negative numbers. The Rule for perfect numbers still applies to fractions and negative numbers.
Remember – Numbers can be perfect squares or perfect cubes.

12. A Perfect Number is a number that has
Remember !!!
A Perfect Number is a number that has
equal factors.

13. Fractions that are perfect numbers
If both the numerator and denominator are perfect squares or if both are perfect cubes, then the fraction is perfect.
¼ = ½ x ½ 9/25 = 3/5 x 3/5
8/27 = 2/3 x 2/3 x 2/3
3/25 is not perfect because 3 is not perfect.
4/27 is not perfect because 4 is a perfect square and 27 is a perfect cube.

14. Which two fractions are perfect?
9/25
16/21
8/25 23 25
1/36

15. Good Job !!!
This number is
Perfect.
Return

16. Sorry
This number is not
Perfect.
Review the Rules
Back to the quiz

17. A Perfect Number is a number that has equal factors.
Remember !!
A Perfect Number is a number that has equal factors.
Note: If both the numerator and denominator are perfect squares or if both are perfect cubes, then the fraction is perfect.

18. Negative Numbers that are Perfect
Perfect cubes can be negative.
-8 is perfect because -8 = -2 x -2 x -2
Perfect squares cannot be negative.
-4 is not perfect because -4 does not have two equal factors.
(-2 x -2  -4 and 2 x 2  -4)

19. Which two are perfect?
-27
-25
-16
-1000

20. Good Job !!!
This number is
Perfect.
Return

21. Sorry
This number is not
Perfect.
Review the Rules
Back to the quiz

22. A Perfect Number is a number that has equal factors.
Remember !!
A Perfect Number is a number that has equal factors.
Perfect cubes can be negative.
Perfect squares cannot be negative.

23. Final Quiz
Click on numbers that are perfect. ( There are 6.) 11 17
49/81
- 9
400
- 8/27
1/7
100
End

24. Good job!!
This number is
Perfect!!!
Find
More

25. Sorry
This number is
Not Perfect!!
TRY AGAIN