6th Grade Review

Whole Number Operations

1. 4137 + 739

2. 567 +139

3. 5602 +8835

4. 65391 + 87

5. 941372 + 128343

1. 4,876

2. 706

3. 14,437

4. 65,478

5. 1,069,715

Whole Number Operations

1. 345

- 278

57

2. 9864

- 671

9193

3. 149856

- 51743

97113

4. 7548362

- 969457

6678905

Can you find the

mistake?

Whole Number Operations

1. 65 x 32

2. 345 x 123

3. 265 x 524

Be Sure To Show All Your Work!!

Solutions To Multiplication Problems:

1. 2,0802. 42,4353. 138,860

Whole Number Operations

1. 9954 ÷ 63

2. 2571 3

3. 48026 ÷ 37

€

÷

1. 1582. 8573. 1298

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.

Power Examples

Your Turn to Try a Few Powers

Real World Apps with Powers

Lesson 1EQ: How do I solve

numerical expressions?

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

Vocabulary

Expression – a collection of numbers and operations

11 – 14 ÷ 2 + 6

PEMDAS

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

11 – 14 ÷ 2 + 6Order of Operations – the rules we follow when simplifying a numerical expression

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?

Simplify the expression.

Using the Order of Operations

3 + 15 ÷ 5

3 + 15 ÷ 5

3 + 3

6

Divide.

Add.

Simplify the expression.

Using the Order of Operations

44 – 14 ÷ 2 · 4 + 6

44 – 14 ÷ 2 · 4 + 6

44 – 7 · 4 + 6

44 – 28 + 6

16 + 6

22

Divide and multiply fromleft to right.

Subtract and add fromleft to right.

Simplify the expression.

Using the Order of Operations

3 + 23 · 5

3 + 23 · 5

3 + 8 · 5

3 + 40

43

Evaluate the power.

Multiply.

Add.

Using the Order of Operations

Simplify the expression.

28 – 21 ÷ 3 · 4 + 5

28 – 21 ÷ 3 · 4 + 5

28 – 7 · 4 + 5

28 – 28 + 5

0 + 5

5

Divide and multiply fromleft to right.

Subtract and add fromleft to right.

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

Helpful Hint

Simplify the expression.

Using the Order of Operations with Grouping Symbols

42 – (3 · 4) ÷ 6

42 – (3 · 4) ÷ 6

42 – 12 ÷ 6

42 – 2

40

Perform the operation inside the parentheses.

Divide.

Subtract.

Using the Order of Operations with Grouping Symbols

[(26 – 4 · 5) + 6]2

[(26 – 4 · 5) + 6]2

[(26 – 20) + 6]2

[6 + 6]2

122

144

The parentheses are inside the brackets, so perform the operationsinside the parenthesesfirst.

Simplify the expression.

Try this one on your own!

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 x 9 ÷ 3 – 7

3 + 54 ÷ 3 – 7

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

3 + 18 - 7

Try another!

150 ÷ (6 +3 x 8) - 5

Step 1: Parentheses

150 ÷ (6 +3 x 8) – 5

Step 2: Division150 ÷ 30 – 5

Step 3: Subtraction5 – 5

Challenge!

Classify each statement as true or false. If the statement is false, insert parentheses to make it true.

false1. 4 5 + 6 = 44( )

2. 24 – 4 2 = 40( ) false

3. 25 ÷ 5 + 6 3 = 23

4. 14 – 22 ÷ 2 = 12

true

true

ApplicationSandy 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

(5 + 3 · 3) · 4

(5 + 9) · 4

14 · 4

56 Sandy ran 56 miles last month.

Perform the operations in parentheses first.

Add.

Multiply.

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

(3 · 4 · 7) + 30

(12 · 7) + 30

84 + 30

114

Perform the operations in parentheses first.

Jill will know 114 words at the end of 7 weeks.

Multiply.

Add.

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

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

58

35

5

116

1,024

EQ: How can I perform operations with fractions?

Fraction Action Vocabulary

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

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

Fraction Action Vocabulary

Adding Fractions

1. 1/5 + 2/5

2. 7/12 + 1/12

3. 3/26 + 5/26

With Like Denominators!

Adding Fractions

1. 2/3 + 1/5

2. 1/15 + 4/21

3. 2/9 + 3/12

With Different Denominators!

Steps:1. Find the LCD

2. Rename the fractions to have the same LCD

3. Add the numerators

4. Simplify the fraction

Subtracting Fractions

1. 3/5 - 2/5

2. 7/10 – 2/10

3. 21/24 – 15/24

With Like Denominators!

Subtracting Fractions

1. 2/3 – 4/12

2. 4/6 – 1/15

3. 2/12 – 1/8

With Different Denominators!

Steps:1. Find the LCD

2. Rename the fractions to have the same LCD

3. Subtract the numerators

4. Simplify the fraction

Multiplying Fractions

1. 2/9 x 3/12

2. ½ x 4/8

3. 1/6 x 5/8

Steps:1. Multiply the numerators

2. Multiply the denominators

3. Simplify the fraction

Dividing Fractions

1. 2/10 ÷ 2/12

2. 1/8 ÷ 2/10

3. 1/6 ÷ 3/15

Steps:1. Keep it, change it, flip it!

2. Multiply the numerators

3. Multiply the denominators

4. Simplify the fraction

Fraction Action Vocabulary

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

Changing Improper Fractions to Mixed Numbers

1. 55/9

2. 39/4

3. 77/12

Steps:1. Divide

2. Remember…First come, first serve

Changing Mixed Numbers to Improper Fractions

1.

2.

3.

9

53

Steps:

1. Multiply the whole number by the denominator

2. Add the result to the numerator (that will be your new numerator)

3. The denominator stays the same

2

16

3

25

Operations with Mixed Numbers

1.

2.

9

33*

8

26

Steps:

1. Convert both mixed numbers to an improper fraction

2. Follow the necessary steps for the given operation

3. Simplify6

43

12

77

Equivalent Fractions

1. 3/8 = 375/10002. 18/54 = 23/693. 6/10 = 6000/1000

1. True2. True3. False

Homework: handout

EQ: How do I perform operations with decimals?

Decimals A way to represent fractions EX:

1. 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

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

Place Value Game

FunBrain - Place Value Puzzler

Ordering Order from least to greatest3.84, 4.4, 4.83, 3.48, 4.38

Order from greatest to least5.71, 5.8, 5.68, 5.79, 5.6

Comparing Decimals:Use <, >, or = to complete the following.

1. 6.5 ____ 6.45

2. 12.4312 _____ 12.43112

3. .6 ____.61

Rounding – “4 or less let it rest 5 or more let it score”1. Round to the nearest one

17.6

2. Nearest thousandth

12.5503

3. Nearest hundredth

2.2959

Decimal Operation ChantDo 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 Just make sure to line up the

decimal points so that all the decimal points are on a vertical line

HINT:

Try some!

156.7 + 23.14 =

57.123 – 14.25 =

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!

45.68 x 3.5=

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 Decimals

Then, divide like normal

Try these!

16.9 ÷ 6.5

55.318 ÷ 3.4

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

Percent: A ratio that compares a number to

100 Out of 100 Part/whole

Ratio: A comparison of two numbers Part Part

What is the ratio of pink

circles to white

circles?

Proportion: An equation that shows two ratios

are equal

25

15

5

3

56

49

8

7

Convert to a fraction and a percent…

1. .25

2. .003

Convert to a percent and decimal…

1. 3/4

2. 23/50

Convert to a fraction and a decimal…

1. 25%

2. 104%

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

Sales Tax & Tip Example

Discount Example

Mark-up Example

Practice with discounts, mark-ups, & tax.

EQ: How can I evaluate algebraic expressions?

Card activity

Variable --An unknown quantity

Expression -- A collection of numbers,

variables, and symbols NO equal sign!!

10 (x+3) + 2

Simplify -- To reduce to the most basic form Make it simple!

1. 3 + 5 (3*5)

2. 60

12

Find the variable, replace itSimplify the expression

Now your all doneJust remember to…

PLUG IT IN! PLUG IT IN!

Learning Partner Class Work

Lesson 6 Area & Perimeter

EQ: How can I solve mathematical problems that involve finding the area and perimeter of various shapes?

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 circle’s circumference to its diameter is represented by (3.14 or 22/7).

€

Π

Triangle Area Formula

Example

Parallelogram Area Formula

Example

Trapezoid Area Formula

Example

Circumference Formula

Example

Your Turn…

Your Turn