6th Grade Review

1
6th Grade Review
2
Racing Review Of the very basics!
3
Whole Number Operations
Race!
Addition

• 1. 4137
• 739

2. 567 139
3. 5602 8835
4. 65391 87
5. 941372 128343
4
Solutions

1. 4,876
2. 706
3. 14,437
4. 65,478
5. 1,069,715

5
Whole Number Operations
Subtraction
Right or Wrong?
Can you find the mistake?

• 345
• - 278
• 57

2. 9864 - 671 9193
3. 149856 - 51743 97113

• 4. 7548362
• 969457
• 6678905

6
Whole Number Operations
Multiplication

1. 65 x 32
2. 345 x 123
3. 265 x 524

Be Sure To Show All Your Work!!
7
Solutions To Multiplication Problems

1. 2,080
2. 42,435
3. 138,860

8
Whole Number Operations
Division
RACE!

• 9954 63
• 2571 3
• 48026 37

9
1. 1582. 8573. 1298
Solutions
10
Powers
A POWER is a way of writing repeated
multiplication. The BASE of a power is the
factor, and the EXPONENT of a power is the number
of times the factor is used.
11
Power Examples
12
Your Turn to Try a Few Powers
13
Real World Apps with Powers
14
Lesson 1EQ How do I solve numerical
expressions?
15
Launch

• Draw a real world example of an event that must
  be done in a certain order

Order is important!
16
Vocabulary
EXAMPLE
Term
11 14 2 6

• Expression a collection of numbers and
  operations

17
PEMDAS
Vocabulary
EXAMPLE
11 14 2 6
Order of Operations the rules we follow
when simplifying a numerical expression

• P - parentheses
• E - exponents
• M - multiply
• D - divide
• A add
• S - subtract

18
Order of Operations
Ben Susie
3 4 x 2 7 x 2 14 3 4 x 2 3 8 11
Which student evaluated the arithmetic expression
correctly?
Susie!
19
Using the Order of Operations
Example 1
Simplify the expression.
3 15 5
Divide.
3 15 5
3 3
Add.
6
20
Using the Order of Operations
Example 2
Simplify the expression.
44 14 2 4 6
44 14 2 4 6
Divide and multiply from left to right.
44 7 4 6
44 28 6
Subtract and add from left to right.
16 6
22
21
Using the Order of Operations
Example 3
Simplify the expression.
3 23 5
Evaluate the power.
3 23 5
Multiply.
3 8 5
3 40
Add.
43
22
Using the Order of Operations
Example 4
Simplify the expression.
28 21 3 4 5
28 21 3 4 5
Divide and multiply from left to right.
28 7 4 5
Subtract and add from left to right.
28 28 5
0 5
5
23
Grouping Symbols

( )

24
Using the Order of Operations with Grouping
Symbols
Example 5
Simplify the expression.
42 (3 4) 6
Perform the operation inside the parentheses.
42 (3 4) 6
42 12 6
Divide.
42 2
Subtract.
40
25
Using the Order of Operations with Grouping
Symbols
Example 6
Simplify the expression.
(26 4 5) 62
The parentheses are inside the brackets, so
perform the operations inside the
parentheses first.
(26 4 5) 62
(26 20) 62
6 62
122
144
26
Try this one on your own!
Example 7

• 3 6 x (54) 3 - 7

Step 1 Parentheses 3 6 x (54) 3 7 Step
2 Multiply and Divide in order from left to
right 3 6 x 9 3 7 3 54 3 7 Step
3 Add and Subtract in order from left to
right 3 18 - 7
Solution 14
27
Try another!
Example 8

• 150 (6 3 x 8) - 5

• Step 1 Parentheses
• 150 (6 3 x 8) 5
• Step 2 Division
• 150 30 5
• Step 3 Subtraction
• 5 5

Solution 0
28
Challenge! Classify each statement as true or
false. If the statement is false, insert
parentheses to make it true.
(
)
false
1. 4 ? 5 6 44
2. 24 4 ? 2 40
(
)
false
3. 25 5 6 ? 3 23
true
4. 14 22 2 12
true
29
Application
Sandy runs 4 miles per day. She ran 5 days during
the first week of the month. She ran only 3 days
each week for the next 3 weeks. Simplify the
expression (5 3 3) 4 to find how many miles
she ran last month.
Week Days
Week 1 5
Week 2 3
Week 3 3
Week 4 3
Perform the operations in parentheses first.
(5 3 3) 4
(5 9) 4
Add.
14 4
Multiply.
56
Sandy ran 56 miles last month.
30
Application
Jill is learning vocabulary words for a test.
From the list, she already knew 30 words. She is
learning 4 new words a day for 3 days each week.
Evaluate how many words will she know at the end
of seven weeks.
Day Words
Initially 30
Day 1 4
Day 2 4
Day 3 4
Perform the operations in parentheses first.
(3 4 7) 30
(12 7) 30
Multiply.
Add.
84 30
Jill will know 114 words at the end of 7 weeks.
114
31
Application
Denzel paid a basic fee of 35 per month plus 2
for each phone call beyond his basic plan. Write
an expression and simplify to find how much
Denzel paid for a month with 8 calls beyond the
basic plan.
51
32
Ticket out the door
Simplify each expression. 1. 27 56 7 2. 9
7 5 3. (28 8) 4 4. 136 102 5 5. (9
5)3 (7 1)2 4
35
58
5
116
1,024
33
Lesson 2

• EQ How can I perform operations with fractions?

34
Fraction Action Vocabulary
Math Dictionary

Example
Fraction A number that names a part of a whole and has a numerator and denominator
Simplest form When the numerator and denominator have no common factor other than 1
Numerator The top portion of a fraction
Denominator The bottom portion of a fraction
35
Math Dictionary
Fraction Action Vocabulary
Example
Least Common Denominator The least common multiple (LCM) of the denominators of two or more fractions
Greatest Common Factor The largest number that factors evenly into two or more larger numbers
36
Adding Fractions

• 1. 1/5 2/5
• 2. 7/12 1/12
• 3. 3/26 5/26

With Like Denominators!
37
Adding Fractions
With Different Denominators!

• 1. 2/3 1/5
• 2. 1/15 4/21
• 3. 2/9 3/12

• Steps
• Find the LCD
• Rename the fractions to have the same LCD
• Add the numerators
• Simplify the fraction

38
Subtracting Fractions

• 1. 3/5 - 2/5
• 2. 7/10 2/10
• 3. 21/24 15/24

With Like Denominators!
39
Subtracting Fractions
With Different Denominators!

• 1. 2/3 4/12
• 2. 4/6 1/15
• 3. 2/12 1/8

• Steps
• Find the LCD
• Rename the fractions to have the same LCD
• Subtract the numerators
• Simplify the fraction

40
(No Transcript)
41
Multiplying Fractions

• 1. 2/9 x 3/12
• 2. ½ x 4/8
• 3. 1/6 x 5/8

• Steps
• Multiply the numerators
• Multiply the denominators
• Simplify the fraction

42
Dividing Fractions

• Steps
• Keep it, change it, flip it!
• Multiply the numerators
• Multiply the denominators
• Simplify the fraction

• 1. 2/10 2/12
• 2. 1/8 2/10
• 3. 1/6 3/15

Keep it, Change it, Flip it!
43
Lesson 3
More with fractions
44
Fraction Action Vocabulary
Math Dictionary

Example
Equivalent fractions Fractions that name the same number or are of equal value
Proper fraction Numerator is smaller than the denominator
Improper fraction When the numerator is larger than the numerator
Mixed Number A whole number and a fraction
45
Changing Improper Fractions to Mixed Numbers

• 1. 55/9
• 2. 39/4
• 3. 77/12

• Steps
• Divide
• RememberFirst come, first serve

Divide!
46
Changing Mixed Numbers to Improper Fractions

• Steps
• Multiply the whole number by the denominator
• Add the result to the numerator (that will be
  your new numerator)
• The denominator stays the same

• 1.
• 2.
• 3.

Check Mark Method
47
Operations with Mixed Numbers

• 1.
• 2.

• Steps
• Convert both mixed numbers to an improper
  fraction
• Follow the necessary steps for the given
  operation
• Simplify

48
Equivalent Fractions
True or False?

1. 3/8 375/1000
2. 18/54 23/69
3. 6/10 6000/1000

49
Solutions

1. True
2. True
3. False

50
Fraction BINGO
Homework handout
51
Lesson 4

• EQ How do I perform operations with decimals?

52
Decimals
Math Dictionary

• A way to represent fractions
• EX

• Look at the last decimal placethat place value
  is the denominator of the fraction
• 2. The numbers to the right of the decimal are
  the numerator

53
Place Value
Math Dictionary

• The value of a digit based on its position in a
  number

54
EXAMPLE
55
Place Value Game

• FunBrain - Place Value Puzzler

56
Ordering

• Order from least to greatest
• 3.84, 4.4, 4.83, 3.48, 4.38
• Order from greatest to least
• 5.71, 5.8, 5.68, 5.79, 5.6

57
Comparing DecimalsUse lt, gt, or to complete
the following.

• 1. 6.5 ____ 6.45
• 12.4312 _____ 12.43112
• .6 ____.61

58
Rounding 4 or less let it rest 5 or more let
it score

• Round to the nearest one
• 17.6
• Nearest thousandth
• 12.5503
• Nearest hundredth
• 2.2959

59
Decimal Operation Chant

• Do you know your decimals?
• Do you know your decimals?
• Add or Subtract, line it up, line it up!
• Add or Subtract, line it up, line it up!
• Multiply, Count it out, count it out!
• Multiply, Count it out, count it out!
• Division, step it out!
• Division, step it out!
• Now you know your decimals!
• Now you know your decimals!

60
Adding and Subtracting Decimals

• Just make sure to line up the decimal points so
  that all the decimal points are on a vertical line

Draw a line through the points!
HINT
61
Try some!

• 156.7 23.14
• 57.123 14.25

62
Multiplying Decimals

• Multiply the numbers like normal
• Move the decimal to the right the exact number of
  place values in the numbers being multiplied

63
Try One!

• 45.68 x 3.5

64
Dividing Decimals

• Stranger Story
• The stranger moves toward the door, so you move
  the same amount back
• The stranger gets to the door!
• GET AWAY! Go to the ROOF!

65
Dividing Decimals

• Then, divide like normal

66
Try these!

• 16.9 6.5
• 55.318 3.4

67
Handout
68
Lesson 4

• EQ How are percents, ratios, and proportions
  related?

69
Percent
Math Dictionary

• A ratio that compares a number to 100
• Out of 100
• Part/whole

25
30
95
73
70
Ratio
Math Dictionary

• A comparison of two numbers
• Part
• Part

What is the ratio of pink circles to white
circles?
71
Proportion
Math Dictionary

• An equation that shows two ratios are equal

Examples
72
Convert to a fraction and a percent
Conversions

• 1. .25
• 2. .003

73
Convert to a percent and decimal
Conversions

• 1. 3/4
• 2. 23/50

74
Convert to a fraction and a decimal
Conversions

• 1. 25
• 2. 104

75
Sales Tax, Discount Mark-Up Vocabulary

• Discount the amount taken off the price, this
  is a savings
• Sales Tax Tip amounts added to the price of a
  purchase that are calculated by using a percent
  of the purchase price.
• Sale Price the price of an item before a
  discount or mark-up is applied
• Mark-up- the increase from the wholesale price to
  the retail price
• Wholesale price the price the manufacturer
  charges the store who will sell its item
• Retail price - the price the store you buy the
  item from charges

76
Sales Tax Tip Example
77
Discount Example
78
Mark-up Example
79
Practice with discounts, mark-ups, tax.
80
Skittles Activity
81
Lesson 5

• EQ How can I evaluate algebraic expressions?

Card activity
82
(No Transcript)
83
Variable --
Math Dictionary

• An unknown quantity

x
k
z
y
m
84
Expression --
Math Dictionary

• A collection of numbers, variables, and symbols
• NO equal sign!!

Example
10 (x3) 2
85
Simplify --
Math Dictionary

• To reduce to the most basic form
• Make it simple!

1. 3 5 (35)

Examples
86
Plug it in, Plug it in!

• Find the variable, replace it
• Simplify the expression
• Now your all done
• Just remember to
• PLUG IT IN! PLUG IT IN!

87
Learning Partner Class Work
Handout
88
Lesson 6 Area Perimeter
EQ How can I solve mathematical problems that
involve finding the area and perimeter of various
shapes?
89
Vocabulary

• Perimeter the distance around a figure
• Area the amount of space inside a figure
• Circumference the distance around a circle.
  The ratio of the circles circumference to its
  diameter is represented by (3.14 or 22/7).

90
Triangle Area Formula
91
Example
92
Parallelogram Area Formula
93
Example
94
Trapezoid Area Formula
95
Example
96
Circumference Formula
97
Example
98
Your Turn
99
Your Turn