welcome to 6 +h grade ma+h. day….. 1 – multiplying decimals by whole numbers 2 – multiplying...

Welcome to 6+h Grade

Ma+h

Day…..1 – Multiplying Decimals by Whole Numbers2 – Multiplying Decimals by Decimals3 – Dividing Decimals by Whole Numbers4 - Dividing Decimals by Decimals5 – Exploring Multiplying and Dividing Decimals6 - Multiplying decimals by Powers of 107 – Dividing decimals by Powers of 108 - Exploring Powers of 109 – Exponents and Chapter Review

Chapter 1 Multiply and Divide

Decimals

Day 1

Bell Work

The Steven’s Family drove 258 miles a day

for 3 days. How many miles did the drive in

all?

Justify your answer.

If they continued to travel at this rate, how

many miles would they drive in a week?

I Can……

Estimate the product of

decimals and judge the

reasonableness of the

results.

Vocabulary• Estimate – a reasonable guess• Compatible number- numbers that are easily

multiplied or divided mentally.• Decimal - a representation of a real number

using the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.

• Round-Off Error – the difference between an approximation of a number used in computation and it’s exact value

Let’s Review

• Place Value

Estimate Products• Essential Understanding: To estimate the product of decimals, round to the nearest whole number or compatible number before multiplying.

Guided Practice: Complete Problems a, b, c on page 25

Self-Check # 1

Independent Practice: Complete Problems 7-8 on page 27

I Can….

Multiple decimals by whole numbers.

Multiply Decimals by Whole Numbers

• Essential Understanding: Use the basic rules of multiplication when multiplying a decimal by a whole number or other decimal. To place the decimal in the product, find the sum of decimals places in each factor.

Example: 3 x .02 = .06

Guided Practice: Complete Problems 1-8 on page 30

Self-Check # 2

Independent Practice: Complete Problems 9-17 on page 31

Wrap it Up

• Review

• Questions

• Station Work

Day 2

Bell WorkLouisa walked her dog 0.4 miles a day on

Tuesday, Wednesday, Thursday, and Friday.

Find the total distance she walked all week.

Justify your answer.

If Louisa continued to walk her dog at this rate how far would she walk in 4 weeks?

I Can……

Multiple decimals by decimals.

VocabularyNo New Vocabulary

• Estimate – a reasonable guess• Compatible number- numbers that are easily

multiplied or divided mentally.• Decimal - a representation of a real number using

the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.

• Round-Off Error – the difference between an approximation of a number used in computation and it’s exact value

Multiplying Decimals by Decimals

• Essential Understanding: Use the basic rules of multiplication when mulitpling a decimal by a whole number or other decimal. To place the decimal in the product, find the sum of decimals places in each factor.

Example: 1 .5 x 1.5 = 2.25

Guided Practice: Complete Problems a-f on pages 38-39

Self-Check # 3

Independent Practice: Complete Problems 2-10 even on page 39

Wrap it Up

• Review

• Questions

• Station Work

Day 3

Bell WorkJunnie walked for 2.5 hours at a speed of 2.3

miles per hour. Maurice walked for 1.8 hours

at a speed of 4.1 miles per hour. Who walked

farther?

Justify your answer.

(Hint: Distance = speed x time)How much farther did Junnie Walk?

I can…..

Estimate the quotient of

decimals and judge the

reasonableness of the

results.

VocabularyNo New Vocabulary

• Estimate – a reasonable guess• Compatible number- numbers that are easily

multiplied or divided mentally.• Decimal - a representation of a real number using

the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.

• Round-Off Error – the difference between an approximation of a number used in computation and it’s exact value

Let’s Review

• Long Division• Quick Check: Complete Problems 10-14 on page 24• Self Check # 4

Estimate Quotients• Essential Understanding: To estimate the quotient of decimals, round to the nearest compatible number before dividing.

Guided Practice: Complete Problems a-d on page 42

Self-Check # 5

Independent Practice: Complete Problems 2-4 on page 43

I Can….

Divide decimals by whole numbers.

Dividing Decimals by Whole Numbers

• Essential Understanding: Use the basic rules of division. To divide by decimals, change the divisor into a whole number by multiplying it by some power of 10. Then multiply the quotient by the same power of 10. Finally, bring the decimal up and divide as usual.

Guided Practice: Complete Problems 1-4 on page 48

Self-Check # 6

Independent Practice: Complete Problems a-f on pages 49-50

Wrap it Up

• Review

• Questions

• Station Work

Day 4

Bell Work

Ryan and his brother are sharing the cost

of a video game. The game cost $28.60.

How much does each brother have to pay?

Justify your answer.

If Ryan saves $20 for the game, how much money will he have left?

I Can……

Divide decimals by decimals.

VocabularyNo New Vocabulary

• Estimate – a reasonable guess• Compatible number- numbers that are easily

multiplied or divided mentally.• Decimal - a representation of a real number using

the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.

• Round-Off Error – the difference between an approximation of a number used in computation and it’s exact value

Dividing Decimals by Decimals

• Essential Understanding: Use the basic rules of division. To divide by decimals, change the divisor into a whole number by multiplying it by some power of 10. Then multiply the quotient by the same power of 10. Finally, bring the decimal up and divide as usual.

Guided Practice: Complete Problems 1-6 on pages 54-55

Self-Check # 7

Independent Practice: Complete Problems 19-25 on page 58

Wrap it Up

• Review

• Questions

• Station Work

Day 5

Bell WorkThe longest vehicle tunnel in the world is the

Laerdal Tunnel in Norway with a length of 15.2

miles long. How many vehicles could fit in the

tunnel, bumper to bumper, if the average

vehicle’s length is 0.004 mile?

Justify your answer.

VocabularyNo New Vocabulary

• Estimate – a reasonable guess• Compatible number- numbers that are easily

multiplied or divided mentally.• Decimal - a representation of a real number using

the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.

• Round-Off Error – the difference between an approximation of a number used in computation and it’s exact value

Explore

Lab Day

Wrap it Up

• Review

• Questions

• Station Work

Day 6

Bell Work

A necklace is being made with beads that

are 1.25 centimeters in diameter. The

necklace is 30 centimeters long. How many

beads are needed?

Justify your answer.How many beads are needed to make 20 necklaces?

I Can……

Multiply decimals mentally by powers

of 10.

Vocabulary• Base – the number used as a factor in a power .• Exponent – in a power, the number that tells

how many times the base is used as a factor.

• Powers – numbers expressed using exponents. • Power of 10 – numbers such as 10; 100; 1,000; 10,000 and so on.

Multiplying Decimals by Powers of 10

Essential Understanding: • To multiply a decimal by a power of 10 greater than 1, move the

decimal to the right one place for every zero in the power of 10.

Example: 1.8565 x 100 = 185.65

• To multiply a decimal by a power of 10 that is between 0 and 1, move the decimal to the left one place for every decimal place in the power of 10.

Example: 34.5 x 0.001 = 0.0345

Guided Practice: Complete Problems a-f on pages 66-67

Self-Check # 8

Independent Practice: Complete Problems 12-24 even on page 68

Wrap it Up

• Review

• Questions

• Station Work

Day 7

Bell Work

4.8x .01 =

13.4 x 10 =

3.6 x 100=

7742.3 x .001 =

0.0063 x 1000 =

.048

134

360

7.7423

6.3

I Can……

Divide decimals mentally by powers

of 10.

VocabularyNo New Vocabulary

• Base – the number used as a factor in a power

Exponent – in a power, the number that tells how

many times the base is used as a factor.

• Powers – numbers expressed using exponents.

• Power of 10 – numbers such as 10; 100; 1,000; 10,000

and so on.

Dividing Decimals by Powers of 10

Essential Understanding: To divide a decimal by a power of 10 greater than 1, move the decimal

the left one place for every zero in the power of ten.

Example: 421.2 ÷ 10 = 42.12 

To divide a decimal by a power of 10 that is between 0 and 1, move the decimal the right one place for every decimal place in the power of 10.

Example: 3.172 ÷ 0.01 = 317.2

Guided Practice: Complete Problems a-e on pages 70-71

Self-Check # 9

Independent Practice: Complete Problems 8-18 even on page 72

Wrap it Up

• Review

• Questions

• Station Work

Day 8

Bell WorkMrs. Ewen’s class has collected $578.92 in

pennies to donate to charity. A penny is equal to $0.01. How many pennies did the

students collect?Justify your answer.

If Mrs. Ewen’s class collected the same amount of money in dimes, how many dimes would they

have? (hint a dime is equal to $0.10)

VocabularyNo New Vocabulary

• Base – the number used as a factor in a power

Exponent – in a power, the number that tells how

many times the base is used as a factor.

• Powers – numbers expressed using exponents. • Power of 10 – numbers such as 10; 100; 1,000;

10,000 and so on.

I Can……

Represent numbers using exponents.

Using Exponents to Represent Repeating

FactorsEssential Understanding: • To write a product using an exponent: Count the number of

times the base is used is used as a factor.

Example:

5 x 5 x 5 x 5 = 54

Guided Practice: Complete Problems a-e on pages 62-63

Self-Check # 10

Independent Practice: Complete Problems 14-32 on page 64

Wrap it Up

• Review

• Questions

• Station Work

Day 9

Bell Work

Annie wants to buy 2 pairs of capris for

$34.99 each and 3 pairs of flip flops for

$7.99 each. Does she need to save $150, or

is $100 enough?

Justify your answer.How much change will she have left, after her purchase?

VocabularyNo New Vocabulary

• Estimate – a reasonable guess• Compatible number- numbers that are easily multiplied or divided

mentally.• Decimal - a representation of a real number using the base ten and

decimal notation, such as 201.4, 3.89, or 0.0006.• Round-Off Error – the difference between an approximation of a

number used in computation and it’s exact value• Base – the number used as a factor in a power .• Exponent – in a power, the number that tells how many times the

base is used as a factor.• Powers – numbers expressed using exponents. • Power of 10 – numbers such as 10; 100; 1,000; 10,000 and so on.

Review and Assess

Please Take out your Study Guides

Wrap it Up

• Review

• Questions

• Station Work

Self Check # 1A - 20B - 12C – 1,400

Self Check # 21 – 0.92 – 0.83 – 0.084 – 0.055 – 1.56 – 2.47 - 0.168 - 0.32

Self Check #3

A – 15.96 B – 0.206C – 0.0518D – 0.0128E – 0.0533F – 0.0798

Self Check # 4

10 – 1411 – 3412 – 4913 – 4114 – 4 million

Self Check # 5

A – 49 ÷ 7 = 7B – 100 ÷ 25 = 4C – 54 ÷ 9 = 6D – 99 ÷ 11 = 9

Self Check # 6

1 – 1.72 – 1.43 – 1.44 – 0.45

Self Check # 7

1 – 42 – 33 – 34 – 0.45 – 0.76 - 0.5

Self Check # 8

A – 2,720B – 59,800C – 3,900,000D – 1,390,000E – 9.36F - 0.00784

Self Check # 9

A – 0.06743B – 3.142C – 73 studentsD – 15,800E – 0.2

Self Check # 10

A – 74 B – 97 C – 100,00D – 4.41E – 2,187 gallons