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# Welcome to 6 + h Grade Ma + h - PowerPoint PPT Presentation

Welcome to 6 + h Grade Ma + h. Day…. 1 – Multiplying Decimals by Whole N umbers 2 – Multiplying Decimals by Decimals 3 – Dividing Decimals by Whole Numbers 4 - Dividing Decimals by Decimals 5 – Exploring Multiplying and Dividing Decimals 6 - Multiplying decimals by Powers of 10

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1 –Multiplying Decimalsby Whole Numbers

2 – Multiplying Decimalsby Decimals

3 – Dividing Decimals by Whole Numbers

4 - Dividing Decimals by Decimals

5 – Exploring Multiplying and Dividing Decimals

6 - Multiplying decimals by Powers of 10

7 – Dividing decimals by Powers of 10

8 - Exploring Powers of 10

9 – Exponents and Chapter Review

Multiply and Divide

Decimals

The Steven’s Family drove 258 miles a day for 3 days. How many miles did the drive in all?

• If they continued to travel at this rate, how many miles would they drive in a week?

Estimate the product of decimals and judge the reasonableness of the results.

• 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

• Place Value

• 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

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

• Review

• Questions

• Station Work

Louisa walked her dog 0.4 miles a day on Tuesday, Wednesday, Thursday, and Friday. Find the total distance she walked all week.

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

Multiple decimals

by decimals.

No 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

• Review

• Questions

• Station Work

Junnie 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?

(Hint: Distance = speed x time)

How much farther did Junnie Walk?

Estimate the quotient of decimals and judge the reasonableness of the results.

No 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

• Long Division

• Quick Check: Complete Problems 10-14 on page 24

• Self Check # 4

• 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

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

• Review

• Questions

• Station 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?

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

Divide decimals

by decimals.

No 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

• Review

• Questions

• Station Work

The 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?

No 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

Lab Day

• Review

• Questions

• Station 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?

How many beads are needed to make 20 necklaces?

Multiply decimals mentally by powers of 10.

• 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.

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

• Review

• Questions

• Station Work

.048

134

360

7.7423

6.3

4.8x .01 =

13.4 x 10 =

3.6 x 100=

7742.3 x .001 =

0.0063 x 1000 =

Divide decimals mentally by powers of 10.

No 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

• Review

• Questions

• Station Work

Mrs. 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?

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)

No 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.

Represent numbers using exponents.

Essential 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

• Review

• Questions

• Station 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?

How much change will she have left, after her purchase?

No 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

• Questions

• Station Work

A - 20

B - 12

C – 1,400

1 – 0.9

2 – 0.8

3 – 0.08

4 – 0.05

5 – 1.5

6 – 2.4

7 - 0.16

8 - 0.32

A – 15.96

B – 0.206

C – 0.0518

D – 0.0128

E – 0.0533

F – 0.0798

10 – 14

11 – 34

12 – 49

13 – 41

14 – 4 million

A – 49 ÷ 7 = 7

B – 100 ÷ 25 = 4

C – 54 ÷ 9 = 6

D – 99 ÷ 11 = 9

1 – 1.7

2 – 1.4

3 – 1.4

4 – 0.45

1 – 4

2 – 3

3 – 3

4 – 0.4

5 – 0.7

6 - 0.5

A – 2,720

B – 59,800

C – 3,900,000

D – 1,390,000

E – 9.36

F - 0.00784

A – 0.06743

B – 3.142

C – 73 students

D – 15,800

E – 0.2

A – 74

B – 97

C – 100,00

D – 4.41

E – 2,187 gallons