Transcript Unit 1: Number Theory

Unit 1: Number
Theory
Lesson 1-2: Rectangular
Arrays
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.
C
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l
u
m
n
s
Rows
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2*2=4
5 * 2 = 10
Number Model:
Rows * Columns = Product
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1*5=5
Practice:
Draw all possible arrays for the numbers below.
Write the number model to match the
array.
8
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2*4=8
4*2=8
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1*8=8
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8*1=8
12
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1 * 12 = 12
2 * 6 = 12
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6 * 2 = 12
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12 * 1 •= 12
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3 * 4 =12
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4 * 3 = 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 answers
Correct your work using a pen!
Lesson 1-3: Factors
Factor * Factor =
Product
2 * 5 = 10
Number
Factor Pairs
15
1, 15
3, 5
12
1, 12
2, 6
3, 4
List (numerical order)
1, 3, 5, 15
1, 2, 3, 4, 6, 12
1, 9
1, 3, 9
3, 3
*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!
9
Classwork:
1. Complete journal page 10
If time:
2. Math Box 1-3 (p. 11)
3. Extra Credit
Journal Page 10 answers
Correct your work using a pen!
Lesson 1-5: Divisibility
Rules
A whole number is divisible by a whole
number if the remainder if zero.
4 ways to write a division problem
37
5 185
185/5 = 37
Dividend
Divisor
185 ÷ 5 = 37
Quotient
185
5 = 37
Memorize
Divisibility Rules
Number
One (1)
Rule
Memorize
Examples
All numbers are divisible by one.
All whole numbers
Two (2)
A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, 8).
38,
104,
7,536
Three (3)
A number is divisible by 3 if the sum of the digits adds up to a multiple of three.
27, 603,
8,541
Four (4)
A number is divisible by 4 if it is even and can be divided by two twice.
64, 132, 2, 016
Five (5)
Six (6)
Nine (9)
Ten (10)
A number is divisible by 5 if it ends in a five or a zero.
95,
675,
3,500
A number is divisible by 6 if it is a divisible by both 2 and 3.
72,
306,
1,548
A number is divisible by 9 if the sum of the digit adds up to a multiple of nine.
36,
801,
6,732
A number is divisible by 10 if it ends in a zero.
70,
290 ,
8,940
Classwork:
1. Complete journal page 14
If time:
2. Math Box 1-5 (p. 15)
3. Extra Credit
Journal Page 14 answers
Correct your work using a pen!
Lesson 1-5: Divisibility
Continued
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.
Using a calculator to test for divisibility
135 int ÷ 5 = 27 135 int ÷ 4 = 33.75
135 ÷ 5 = 27 R0 135 ÷ 4 = 33 R3
Classwork:
1. Complete journal page 13
If time:
2. Math Box 1-5 (p. 15)
3. Extra Credit
Journal Page 13 answers
Correct your work using a pen!
Lesson 1-4: Factor
Captor
Add game directions
and game boards
Lesson 1-6: Prime & Composite Numbers
Prime Number: Has exactly 2 factors, one and itself
Composite Number: Has exactly 3 or more factors
The number
1 is not
prime or
composite
Memorize
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 answers
Correct your work using a pen!
Lesson 1-7: Square
Numbers
Square Numbers are the product of a number times itself.
Exponential
Notation
Repeated
Multiplication
Square
Number
2
1*1
1
2
2
2*2
4
3
2
3*3
9
4
2
4*4
16
5 *5
25
6 *6
36
7*7
49
8*8
64
9 *9
81
10 * 10
100
11 * 11
121
12 * 12
144
1
2
5
6
2
2
7
8
9
10
2
2
2
2
11
12
2
Read these as either:
“four to the power of two” or “ four squared”
Exponential
Notation
The exponent (2) tells how many
times the base (3) is used as a factor.
3
2
Exponent
^
Powers Key
Base
Practice:
2
2
8 =
11 =
3
3
2 =
4 =
Classwork:
1. Complete journal page 20-21
If time:
2. Math Box 1-7 (p. 22)
3. Extra Credit
Journal Page 20 - 21 answers
Correct your work using a pen!
Lesson 1-8: Unsquaring Numbers
When you unsquare a number, you have
found the square root of the number.
2
*
2
9
2
4
=
81
=
2 is the square root of 4
9 is the square root of 81
Practice:
_4 is the square root of 16
8 is the square root of64
_
6
_is the square root of 36
_
49
7 is the square root of
Classwork:
1. Complete journal page 23
If time:
2. Math Box 1-8 (p. 24)
3. Extra Credit
Journal Page 23 answers
Correct your work using a pen!
Unit 1: Review Stations
Station 1: Square Numbers
Station 2: Arrays and Number Models
Station 3: Divisibility
Station 4: Prime and Composite Numbers
Station 5: Factors