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6 th Grade Review. Racing Review. Race!. Whole Number Operations. Addition. 1 . 4137 + 739. 2 . 567 +139. 3 . 5602 +8835. 4 . 65391 + 87. 5 . 941372 + 128343. Solutions:. 4,876 706 14,437 65,478 1,069,715. Whole Number Operations. Subtraction. Right or Wrong?.

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6 th grade review

6th Grade Review



Whole number operations

Race!

Whole Number Operations

Addition

1. 4137

+ 739

2. 567

+139

3. 5602

+8835

4. 65391

+ 87

5. 941372

+ 128343


6 th grade review

Solutions:

  • 4,876

  • 706

  • 14,437

  • 65,478

  • 1,069,715


Whole number operations1
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


Whole number operations2
Whole Number Operations

Multiplication

Learning Partners

  • Create 3 multiplication problems (do not use more than 3 digits)

  • Switch with a neighbor

  • Check your partner’s work


Whole number operations3
Whole Number Operations

Division

RACE!

  • 9954 ÷ 63

  • 87 ÷ 3

  • 48026 ÷ 37

  • 73080 ÷ 20

  • 850 ÷ 5

6. 210 ÷ 7

7. 54 ÷ 6

8. 2571 ÷ 3

9. 2992 ÷ 4

10. 63 ÷ 9


1 158 2 29 3 1298 4 3654 5 170 6 30 7 9 8 857 9 748 10 7
1. 1582. 293. 12984. 36545. 1706. 307. 98. 8579. 74810. 7

Solutions



6 th grade review

Launch

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

Order is

important!


Vocabulary
Vocabulary

Term

EXAMPLE

Expression – a collection of numbers and operations

11 – 14 ÷ 2 + 6


Pemdas

P - parentheses

E - exponents

M - multiply

D - divide

A – add

S - subtract

Vocabulary

PEMDAS

EXAMPLE

11 – 14 ÷ 2 + 6

Order of Operations

– the rules we follow when simplifying a numerical expression


Order of operations
Order of Operations

Which student evaluated the arithmetic expression correctly?

Susie!


6 th grade review

Using the Order of Operations

Example 1

Simplify the expression.

3 + 15 ÷ 5

Divide.

3 + 15 ÷ 5

3 + 3

Add.

6


6 th grade review

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


6 th grade review

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


6 th grade review

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


6 th grade review

Helpful Hint

When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set.

Grouping Symbols

[ ]

( )

{ }


6 th grade review

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


6 th grade review

Using the Order of Operations with Grouping Symbols

Example 6

Simplify the expression.

A. 24 – (4 · 5) ÷ 4

Perform the operation inside the parentheses.

24 – (4 · 5) ÷ 4

24 –20 ÷ 4

Divide.

24 – 5

Subtract.

19


6 th grade review

Using the Order of Operations with Grouping Symbols

Example 7

Simplify the expression.

[(26 – 4 · 5) + 6]2

The parentheses are

inside the brackets, so

perform the operations

inside the parentheses

first.

[(26 –4 · 5) + 6]2

[(26 –20) + 6]2

[6 + 6]2

122

144


6 th grade review

Using the Order of Operations with Grouping Symbols

Example 8

Simplify the expression.

[(32 – 4 · 4) + 2]2

The parentheses are

inside the brackets, so

perform the operations

inside the parentheses

first.

[(32 –4 · 4) + 2]2

[(32 –16) + 2]2

[16 + 2]2

182

324


Try this one on your own
Try this one on your own!

Example 9

3 + 6 x (5+4) ÷ 3 - 7

Step 1: Parentheses

3 + 6 x (5+4) ÷ 3 – 7

Step 2: Multiply and Divide in order from left to right

3 + 6 x9 ÷ 3 – 7

3 + 54÷ 3 – 7

Step 3: Add and Subtract in order from left to right

3 + 18 - 7

Solution: 14


Try another
Try another!

Example 10

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


6 th grade review

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

true

3. 25÷ 5 + 6  3 = 23

4. 14 – 22 ÷ 2 = 12

true


6 th grade review

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.

Perform the operations in parentheses first.

(5 + 3 · 3) · 4

(5 + 9) · 4

Add.

Multiply.

14 · 4

56

Sandy ran 56 miles last month.


6 th grade review

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.

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


6 th grade review

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


6 th grade review

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


6 th grade review

Lesson 2

EQ: How can I perform operations with fractions?


Fraction action vocabulary
Fraction Action Vocabulary

Math Dictionary

Example


6 th grade review

Math Dictionary

Fraction Action Vocabulary

Example


Adding fractions
Adding Fractions

1. 1/5 + 2/5

2. 7/12 + 1/12

3. 3/26 + 5/26

With Like Denominators!


Adding fractions1
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


Subtracting fractions
Subtracting Fractions

1. 3/5 - 2/5

2. 7/10 – 2/10

3. 21/24 – 15/24

With Like Denominators!


Subtracting fractions1
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


Multiplying fractions
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


Dividing fractions
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!


6 th grade review

Lesson 3

More with fractions


Fraction action vocabulary1
Fraction Action Vocabulary

Math Dictionary

Example


Changing improper fractions to mixed numbers
Changing Improper Fractions to Mixed Numbers

  • Steps:

  • Divide

  • Remember…First come, first serve

1. 55/9

2. 39/4

3. 77/12

Divide!


Changing mixed numbers to improper fractions
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


Operations with mixed numbers
Operations with Mixed Numbers

1.

2.

  • Steps:

  • Convert both mixed numbers to an improper fraction

  • Follow the necessary steps for the given operation

  • Simplify


Equivalent fractions
Equivalent Fractions

True or False?

  • 3/8 = 375/1000

  • 18/54 = 23/69

  • 6/10 = 6000/1000


6 th grade review

Solutions:

  • True

  • True

  • False


6 th grade review

Fraction BINGO

Homework: handout


6 th grade review

Lesson 4

EQ: How do I perform operations with decimals?


Decimals
Decimals

Math Dictionary

  • A way to represent fractions

  • EX:

  • Look at the last decimal place…that place value is the denominator of the fraction

  • 2. The numbers to the right of the decimal are the numerator


Place value
Place Value

Math Dictionary

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



Place value game
Place Value Game

FunBrain - Place Value Puzzler


Ordering
Ordering

  • Order from least to greatest

    3.84, 4.4, 4.83, 3.48, 4.38

    5.71, 5.8, 5.68, 5.79, 5.6


Comparing decimals
Comparing Decimals

1. 6.5 ____ 6.45

  • 12.4312 _____ 12.43112

  • .6 ____.61


Rounding
Rounding

  • Round to the nearest one

    17.6

    • Nearest thousandth

      12.5503

    • Nearest hundredth

      2.2959


Decimal operation chant
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!


Adding and subtracting decimals
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:


Try some
Try some!

156.7 + 23.14 =

57.123 – 14.25 =


Multiplying decimals
Multiplying Decimals

  • Multiply the numbers like normal

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


Try one
Try One!

45.68 x 3.5=


Dividing decimals
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!


Dividing decimals1
Dividing Decimals

  • Then, divide like normal


Try these
Try these!

16.9 ÷ 6.5

55.318 ÷ 3.4



6 th grade review

Lesson 4

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


Percent
Percent:

Math Dictionary

  • A ratio that compares a number to 100

  • Out of 100

  • Part/whole

25%

30%

95%

73%


Ratio
Ratio:

Math Dictionary

  • A comparison of two numbers

  • Part

    Part

What is the ratio of pink circles to white circles?


Proportion
Proportion:

Math Dictionary

  • An equation that shows two ratios are equal

Examples


Convert to a fraction and a percent

Conversions

Convert to a fraction and a percent…

1. .25

2. .003


Convert to a percent and decimal

Conversions

Convert to a percent and decimal…

1. 3/4

2. 23/50


Convert to a fraction and a decimal

Conversions

Convert to a fraction and a decimal…

1. 25%

2. 104%



6 th grade review

Lesson 5

EQ: How can I evaluate algebraic expressions?

Card activity


Variable
Variable --

Math Dictionary

  • An unknown quantity

x

k

z

y

m


Expression
Expression --

Math Dictionary

  • A collection of numbers, variables, and symbols

  • NO equal sign!!

Example

10 (x+3) + 2


Simplify
Simplify --

Math Dictionary

  • To reduce to the most basic form

  • Make it simple!

  • 3 + 5 (3*5)

Examples


6 th grade review

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!