The Number System Exponents Perfect Squares Factors GCF

The Number System

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

Exponents – 10 Write 122 in expanded form.

Exponents – 10 Answer 12 × 12

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

Exponents – 20 Answer 106

Exponents – 30 Evaluate 83.

Exponents – 30 Answer 512

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

Exponents – 40 Answer 123 = 1728

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

Exponents – 50 Answer 174 = 83521

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

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.

Perfect Squares – 20 True or false? “ 1, 4, and 20 are perfect squares. ”

Perfect Squares – 20 Answer False!

Perfect Squares – 30 List ALL the perfect squares between 0 and 30.

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

Perfect Squares – 40 List ALL the perfect squares between 30 and 100.

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

Perfect Squares – 50 List all the perfect squares between 100 and 200.

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

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

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

Factors – 20 Define “factor”.

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

Factors – 30 List ALL the factors of 24.

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

Factors – 40 List ALL the factors of 56.

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

Factors – 50 Which of these numbers have an ODD number of factors? Why is this? • 16 • 13 • 25 • 49 • 11

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

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

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

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

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

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

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

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

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

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

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

Mystery – 10 33 ÷ 11 × 12 ÷ 2

Mystery – 10 Answer 18

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?

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

Mystery – 30 9(3 + 2) – 3(8 – 7)

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

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

Mystery – 40 Answer YES to all. • 1260 is even, therefore it IS divisible by 2. • 1 + 2 + 6 + 0 = 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. • 1 + 2 + 6 + 0 = 9. The sum of the digits (9) is divisible by 9, therefore 1260 IS divisible by 9.

Mystery – 50 (15 – 10)2 + (15 – 5)2

Mystery – 50 Answer (15 – 10)2 + (15 – 5)2 (5) 2 + (10) 2 25 + 100 125