1. Created by Educational Technology Network. www.edtechnetwork.com 2009
The Number System

2. Exponents
Perfect Squares
Factors
GCF
Mystery 10 20 30 40 50

3. Exponents – 10
Write 122 in expanded form.

4. Exponents – 10 Answer
12 × 12

5. Write 10 × 10 × 10 × 10 × 10 × 10 as a power or in exponential form.
Exponents – 20
Write 10 × 10 × 10 × 10 × 10 × 10 as a power or in exponential form.

6. Exponents – 20 Answer
106

7. Exponents – 30
Evaluate 83.

8. Exponents – 30 Answer
512

9. Write 12 × 12 × 12 as a power or in exponential form. Then evaluate.
Exponents – 40
Write 12 × 12 × 12 as a power or in exponential form. Then evaluate.

10. Exponents – 40 Answer
123 = 1728

11. Exponents – 50
Write 17 × 17 × 17 × 17 as a power or in exponential form. Then evaluate.

12. Exponents – 50 Answer
174 = 83521

13. What is a “perfect square”?
Perfect Squares – 10
What is a “perfect square”?

14. Perfect Squares – 10 Answer
A “perfect square” is…
a number formed by squaring another number.
the product or result of a number multiplied by itself.

15. True or false? “1, 4, and 20 are perfect squares.”

16. Perfect Squares – 20 Answer
False!

17. List ALL the perfect squares between 0 and 30.

18. Perfect Squares – 30 Answer
1, 4, 9, 16, 25

19. List ALL the perfect squares between 30 and 100.

20. Perfect Squares – 40 Answer
36, 49, 64, 81, 100

21. List all the perfect squares between 100 and 200.

22. Perfect Squares – 50 Answer
121, 144, 169, 196

23. Factors – 10
If you had 16 tiles, how many rectangles could you build? What would their dimensions be?

24. Factors – 10 Answer You could build 3 rectangles: 16 tiles × 1 tile
2 tiles × 8 tiles
4 tiles × 4 tiles

25. Factors – 20
Define “factor”.

26. Factors – 20 Answer
A number that divides another number evenly. Example: 4 is a factor of 20 because 4 “goes in to” 20 evenly.
Numbers you can multiply to get another number.
factor × factor = product

27. Factors – 30
List ALL the factors of 24.

28. Factors – 30 Answer 1 24 2 12 3 8 4 6

29. Factors – 40
List ALL the factors of 56.

30. Factors – 40 Answer 1 56 2 28 4 14 7 8

31. Which of these numbers have an ODD number of factors? Why is this?16 13 25 49 11

32. Factors – 50 Answer
16, 25, 49 These numbers are all “perfect squares” and therefore have an odd number of factors.

33. Find the greatest common factor of 15 and 40.
GCF – 10
Find the greatest common factor of 15 and 40.

34. GCF – 10 Answer
15: 1, 3, 5, 15
40: 1, 2, 4, 5, 8, 40, 20, 10
Greatest common factor: 5

35. Find the greatest common factor of 36 and 56.
GCF – 20
Find the greatest common factor of 36 and 56.

36. GCF – 20 Answer
36: 1, 36, 2, 18, 3, 12, 4, 9 56: 1, 56, 2, 28, 4, 14, 7, 8 Greatest common factor: 4

37. Find the greatest common factor of 20 and 60.
GCF – 30
Find the greatest common factor of 20 and 60.

38. GCF – 30 Answer
20: 1, 20, 2, 10, 4, 5 60: 1, 60, 2, 30, 3, 20, 5, 12, 6, 10 Greatest common factor: 20

39. Find the greatest common factor of 70 and 80.
GCF – 40
Find the greatest common factor of 70 and 80.

40. GCF – 40 Answer
70: 1, 2, 5, 7, 10, 14, 35, 70 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Greatest common factor: 10

41. Find the greatest common factor of 143 and 110.
GCF – 50
Find the greatest common factor of 143 and 110.

42. GCF – 50 Answer
143: 1, 11, 13, : 1, 2, 5, 10, 11, 22, 55, 110 Greatest common factor: 11

43. Mystery – 10
33 ÷ 11 × 12 ÷ 2

44. Mystery – 10 Answer 18

45. Mystery – 20
A soccer camp is held at a complex that has 6 fields. The coaches would like each field to have the same number of players. Is this possible if 152 kids show up for camp?

46. Mystery – 20 Answer
No. 152 is not divisible by 6.

47. Mystery – 30
9(3 + 2) – 3(8 – 7)

48. Mystery – 30 Answer
9(3 + 2) – 3(8 – 7) 9(5) – 3(1) 45 – 3 42

49. Mystery – 40
Is the number 1260 divisible by 2, 3, 5, 6, 9, and 10? Explain.

50. Mystery – 40 Answer YES to all.
1260 is even, therefore it IS divisible by 2.
= 9. The sum of the digits (9) is divisible by 3, therefore 1260 IS divisible by 3.
1260 – The last two digits form 60, which is divisible by 4. Therefore, 1260 IS divisible by 4.
1260 ends in 0, therefore it is divisible by 5.
1260 is divisible by 2 and 3, therefore it is divisible by 6.
= 9. The sum of the digits (9) is divisible by 9, therefore 1260 IS divisible by 9.

51. Mystery – 50
(15 – 10)2 + (15 – 5)2

52. Mystery – 50 Answer
(15 – 10)2 + (15 – 5)2 (5) 2 + (10)