Unit 1: Number Theory

Rectangular Array: An arrangement of

objects in rows and columns that form a rectangle. All rows have the same number of objects and all columns have the same number of objects.

Lesson 1-2: Rectangular Arrays

Columns

Rows • • • • 

• • • • • • • • • •

Number Model: Rows * Columns =

Product

• • • • •

5 * 2 = 10

1 * 5 = 5

2 * 2 = 4

Practice: Draw all possible arrays for

the numbers below. Write the number model to match

the array.

8 12

• • • • • • • •

1 * 8 = 8

• •• •• •• •

4 * 2 = 8

• • • •• • • •2 * 4 = 8

••••••••••••

• •• •• •• •• •• •

6 * 2 = 12 

• • • • • • • •

8 * 1 = 8

••••••••••••1 * 12 = 12

• • • • • • • • • • • • 

2 * 6 = 12 

• • • • • • • • • • • • 3 * 4 =12

• • •• • •• • •• • •

4 * 3 = 1212 * 1 = 12

Classwork:1. Complete journal page 5

If time:2. Complete journal p. 6-7

3. Math Box 1-2 (p. 8)

4. Extra Credit

Journal Page 5 answersCorrect your work using a pen!

Factor * Factor = Product

2 * 5 = 10

Lesson 1-3: Factors

Number Factor PairsList (numerical

order)

15

12

9*Remember to use an organized approach to find all the factors of a number. Start with the number 1, find its factor pair, then continue in numerical order 2, 3, etc. until you hit a repeat!

1, 153, 51, 122, 63, 4

1, 93, 3

1, 2, 3, 4, 6, 12

1, 3, 9

1, 3, 5, 15

Classwork:1. Complete journal page 10

If time:

2. Math Box 1-3 (p. 11)

3. Extra Credit

Journal Page 10 answersCorrect your work using a pen!

Lesson 1-5: Divisibility RulesA whole number is divisible by a whole number if the remainder if

zero.4 ways to write a division problem

375 185

185/5 = 37

185 ÷ 5 = 37

185 5 = 37

Dividend QuotientDivisor

Divisibility Rules

Memorize Memorize

Number Rule Examples

One (1)All numbers are divisible by one.

Two (2)A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, 8).

Three (3)

A number is divisible by 3 if the sum of the digits adds up to a multiple of three.

Four (4)A number is divisible by 4 if it is even and can be divided by two twice.

Five (5) A number is divisible by 5 if it ends in a five or a zero.

Six (6)A number is divisible by 6 if it is a divisible by both 2 and 3.

Nine (9) A number is divisible by 9 if the sum of the digit adds up to a multiple of nine.

Ten (10) A number is divisible by 10 if it ends in a zero.

38, 104, 7,536

27, 603, 8,541

64, 132, 2, 016

95, 675, 3,500

72, 306, 1,548

36, 801, 6,732

70, 290 , 8,940

All whole numbers

Classwork:1. Complete journal page 14

If time:

2. Math Box 1-5 (p. 15)

3. Extra Credit

Journal Page 14 answersCorrect your work using a pen!

Lesson 1-5: Divisibility Continued

Using a calculator to test for divisibility

Reminder: A whole number(the dividend) is divisible by a whole number (the divisor) if the remainder in the division is zero. The result(the quotient)must be a whole number. If the remainder is not zero, then the number being divided is not divisible by the second number.

135 ÷ 5 = 27 R0

135 int ÷ 5 = 27

135 ÷ 4 = 33 R3

135 int ÷ 4 = 33.75

Classwork:1. Complete journal page 13

If time:

2. Math Box 1-5 (p. 15)

3. Extra Credit

Journal Page 13 answersCorrect your work using a pen!

Lesson 1-4: Factor CaptorAdd game

directions and game boards

Memorize

Lesson 1-6: Prime & Composite NumbersPrime Number: Has exactly 2 factors, one and itselfComposite Number: Has exactly 3 or more factors

The number 1 is not

prime or composite

Prime Numbers under 50

2, 3, 5, 7, 11,

13, 17, 19, 23, 29,

31, 37, 41, 43, 47

Classwork:1. Complete journal page 16

If time:

2. Journal page 18

3. Math Box 1-6 (p. 19)

4. Extra Credit

Journal Page 16 answersCorrect your work using a pen!

Lesson 1-7: Square Numbers Square Numbers are the product of a number

times itself.2

2

2

2

2

2

2

2

2

2

2

2

Exponential Notation

RepeatedMultiplication

SquareNumber

1 1 * 1 1

2 2 * 2 4

3 3 * 3 9

4 4 * 4 16

5 5 *5 25

6 6 *6 36

7 7 * 7 49

8 8 * 8 64

9 9 *9 81

10 10 * 10 100

11 11 * 11 121

12 12 * 12 144

Read these as either:

“four to the power of two” or “ four squared”

32

Base

Exponent

The exponent (2) tells how many times the base (3) is used as a factor.

Exponential Notation

Practice:28 =

2 =3

8 = 11 =

4 =

2

3

Powers Key^

Classwork:1.Complete journal page 20-21

If time:2. Math Box 1-7 (p. 22)

3. Extra Credit

Journal Page 20 - 21 answersCorrect your work using a pen!

Lesson 1-8: Unsquaring Numbers

* = 4

=2

81

When you unsquare a number, you have found the square root of the

number.

is the square root of 4

is the square root of 81

2 2 2

9 9

Practice: _is the square root of 16

8 is the square root of _

_is the square root of 36

7 is the square root of _

4

6

64

49

Classwork:1.Complete journal page 23

If time:2. Math Box 1-8 (p. 24)

3. Extra Credit

Journal Page 23 answersCorrect your work using a pen!

Unit 1: Review StationsStation 1: Square Numbers

Station 2: Arrays and Number Models

Station 3: Divisibility

Station 4: Prime and Composite Numbers

Station 5: Factors