Download Chapter 1

SECTION 1.1
NATURAL NUMBERS (counting numbers) You Tube Video
1, 2, 3, 4, 5,…
1 2 3 4 5 6 7 8 9 10
WHOLE NUMBERS
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
0 1 2 3 4 5 6 7 8 9 10
123,456,789
Give the place value of the 3.
a) 12,351
b) 143
c) 300,000,000,000
Expanded form
607
3,502
597,506
d) 123,456
e) 56,730,987
In Words You Tube Video
607
3,502
252,030,005
587
597,506
Standard Form
Three hundred two
Four thousand, three
One hundred million, thirty-three thousand, five hundred eleven
Thirty-two million, twenty thousand, five
Two hundred thousand, four
ROUNDING WHOLE NUMBERS Rounding - YouTube
14,567
TENS
14,567
HUNDREDS
14,567
THOUSANDS
14,567
TEN THOUSANDS
14,567
14,570
14,600
15,000
20,000
14,560
14,500
14,000
10,000
14,550
14,400
13,000
0
STEPS FOR ROUNDING
Round 6,725 to the nearest hundred.
1. Find the hundreds place and underline it
6,725
2. Look at the digit to the right of the 4
6,725 This is the test digit.
3. a. If the test digit is 5 or more the 7 increases by one to 8.
b. If the test digit is 4 or less the 7 stays the same.
4. Every digit to the right of 7 becomes 0.
6,700 is 6,725 rounded to the nearest hundred.
ROUNDING
Circle the correct answer.
Round 48 to the nearest 10
5
95
15
25
35
0
10
20
90
100
Round 234 to the nearest 10
205
215
225
295
200
290
210
300
30
45
40
235
220
55
50
245
65
60
255
75
70
265
85
80
275
285
230
240
250
260
270
280
300
400
500
600
700
800
Round 385 to the nearest 100
0
900
100
1000
200
Round 450 to the nearest 100
Round 48 to the nearest 100
Round 968 to the nearest 100
Round 7486 to the nearest 100
Round 3486 to the nearest 1000
Round 13486 to the nearest 1000
SECTION 1.2
Properties of addition and multiplication You Tube Video
Commutative
Associative
Identity
Inverse
Distributive
Addition
Multiplication
Match the operations and the names of the properties by placing the correct number to the left of the letters A–E. (Not all properties on the right will
necessarily be used; some may be used more than once.)
___A) –3  (2 + 5) = –3  (5 + 2)
___B) 3  (2 + 5) = (3  2) + (3 5)
___C) 4 + (–3 + –1) + 2 = (4 + –3) +( –1 + 2)
___D) 5 + ( 8 + 0) = 5 + 8
___E) -4  1 = -4
___F) 6 + (4 + –4) = 6 + 0
___G) 32  23  1
___H) 3  (5 0) = (5  0)  3
___I) 3 + (2 + –5) = (3 + 2) + –5
1.
2.
3.
4.
5.
6.
7.
8.
9.
Associative property of multiplication
Additive identity property
Multiplicative inverse property
Additive inverse property
Commutative property of addition
Associative property of addition
Distributive property of  over +
Multiplicative identity property
Commutative property of multiplication
Adding Whole Numbers
You Tube Video
+
1
+ 3
4
The number in front tells you how many you have.
So, one apple plus three apples is four apples.
Remember this---the + means you can only count or remove your like terms, that is all.
A)
5
+
3
B) 4 X + 7 X
C) 3
+ 2
432+5,812
+ 2
Four different place values. What are they?
Standard Algorithm
Find 121 + 49 using an empty number line.
Expanded Form
Subtracting Whole Numbers You Tube Video
6,432 − 5,812
Standard Algorithm
Expanded Form
Find 145 - 49 using an empty number line.
145
Find 1000-899 using an empty number line by adding up from 899.
899
You Tube Video
Perimeter-- The distance around the outside of an object
What is the perimeter of a rectangular fenced region with a width of 45 feet and a length of 125 feet?
SECTION 1.3
Multiplication
You Tube Video
Multiplying by 1 digit.
𝒂) 𝟏𝟓𝟐 ∙ 𝟑
Multiplying by 2 or more digits.
𝒂) 𝟏𝟓𝟐 ∙ 𝟐𝟑
𝒃) 𝟐𝟓 ∙ 𝟕
𝒃) 𝟖𝟐𝟏 ∙ 𝟓𝟏
𝒄) 𝟏𝟓𝟎 ∙ 𝟕
𝒄) 𝟏𝟓𝟎 ∙ 𝟕𝟎𝟏
Area= the number of unit squares in an object. (laying tile) You Tube Video
Area = _____ Columns  ______ Rows =________
H
e
ig
ht
Area = Base  Height
Base
Find the area of a room that is 12 feet by 10 feet.
Multiplication – Applications You Tube Video
𝑓𝑎𝑐𝑡𝑜𝑟 ∙ 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝑝𝑟𝑜𝑑𝑢𝑐𝑡
Commutative property-Associative property--
𝑎∙𝑏 =𝑏∙𝑎
𝑎 ∙ (𝑏 ∙ 𝑐) = (𝑎 ∙ 𝑏) ∙ 𝑐
Part I: Multiplication can be represented as repeated addition.
𝟑∙𝟔
Three 6s
𝟔+𝟔+
𝟔∙𝟑
Six 3s
𝟑+𝟑+𝟑+𝟑+𝟑+𝟑
Fill in the shaded boxes:
𝟐∙𝟓
𝟒∙
Word problems:
There are 4 bears, and each bear has 3 pots of honey. How many pots of honey are there all together?
Julie collects spoons. If she has collected 3 spoons each week for 5 weeks, then how many spoons has she
collected altogether?
Jim spends $350 every month on association dues. How much did he spend in one year on association dues?
Dividing You Tube Video
6 251
12 253,021
Dividing You Tube Video
Repeated Subtraction:
Subtraction Subtraction
number 1
number 2
𝟔÷𝟑
𝟔−𝟑=𝟑
𝟑−𝟑= 𝟎

6
2 subtractions
3
=
2
2 groups of 3
Subtraction number 1
Subtraction number 2
Answer the questions using division and repeated subtraction:
Jim has 15 pizzas. If he gave 3 pizzas to each of his friends, then how many friends does he have?
Thomas has 10 toy cars. If he gives each of his friends three toy cars, then how many friends does he have and
how many toy cars will he have left over?
Partitive division or "Sharing Equally"
6

3
Divided by 3 groups
=
2 per group of 3
Answer the questions using division and "Sharing Equally":
Jim has 15 pizzas. If he has 5 friends, then how many pieces of pizza did each friend get?
Thomas has 10 toy cars. If he has 3 friends, then how many cars did Thomas give each of his friends and how
many did he have left over?
Division can be viewed as missing factors. Fill in the following:
a) _______ ∙ 10 = 40
b) 6𝑋_________ = 72
c) 𝑛 ∙ 5 = 70, 𝑛 = ___________
Jim collects toy cars. If he collects 5 cars a week, then how long did it take him to collect 55 cars?
SECTION 1.4
PRIMES AND COMPOSITES You Tube Video
12 = 6 X 2
12 = 4 X 3
12 = 1 X 12
Factors
Factors
12 is the product of 6 and 2. 12 is a multiple of 4. 12 is a multiple of 3.
12 can be divided by 6 and 2. 12 is divisible by 6 and 2.
Factors
Prime- A counting number other than 1 with only one and itself as factors.
Ex.
3 = 1 X 3
7=
3 = no other factors
1 X 7
5= 1 X 5
7 = no other factors
5 = no other factors
Composite- A counting number other than 1 that is not prime. Has a factor other than one and itself.
Ex.
4=
9=
24 =
4=
1
2
11
9=
3
4
5
6
7
8
9
10
12
13
14
15
16
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30
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32
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35
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100
TESTS FOR DIVISIBILITY You Tube Video
If a non-zero number can be divided by another number so that the remainder is 0, then we say:
The first number is DIVISIBLE by the second number.
2
Multiples of 2:
Ex. 6 is DIVISIBLE by 2
2 4 6 8 10 12 14 16 18 20 22
If a numbers last digit is a 0,2,4,6, or 8, then 2 divides that number.
Ex.
2 will divide 330 332 334 336 338 etc
If a numbers last two digits is divisible by 4, then 4 divides the number. Why?
Hint: 12524=12,500 + 24
If a numbers last three digits is divisible by 8, then 8 divides the number. Why?
Hint: 542,160=542,000 + 160
5
Multiples of 5:
5 10 15 20 25 30 35 40 45 50 55
If the number’s last digit is a 0 or 5, then 5 divides that number
Ex.
3
325
325’s last digit is a 5, therefore 5 will divide 325.
If 3 divides the sum of a numbers digits then
Ex.
3 divides that number.
The sum of 327’s digits is 3 + 2 + 7 = 12
3 will divide 12 , therefore 3 will divide 327.
Why does this work? Hint: 327 = 3(100) + 2(10) + 7 = 3(𝟗𝟗 + 1) + 2(𝟗 + 1) + 7
Try to show this for 258 using the rule and then by expansion of the number.
2
234
721
100002
5210
Sum
3
5
7
Finding factors of a number: You Tube Video
Find the factors of 12
Using Prime factorization:
Number of Factors.
Find the factors of 18
Find the factors of 24
PRIME FACTORIZATION You Tube Video
Every whole number greater than 1 is either a prime or can be expressed as the product of primes
uniquely.
Factor tree:
Ladder:
140
140
SECTION 1.5
Give Every Mom Or Dad Aspirin Or Sleep You Tube Video
Order of operations
1. Symbols of Grouping. (
2.
3.
4.
), [
], {
}, √
,
Exponents
Multiplication Or Division from LEFT TO RIGHT.
Addition Or Subtraction from LEFT TO RIGHT.
1
4  4  6  4  32  5
_________________
28  4  3 2  5
_________________
28  4  9  5
_________________
795
_________________
63  5
_________________
2
3
4
Try:

4  3 2  12

8 4 2
4  12
63
3  42  8
T
B