Welcome to
+h
6 Grade
Ma+h
Day…..
1 – Multiplying Decimals by Whole Numbers
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
7 – Dividing decimals by Powers of 10
8 - Exploring Powers of 10
9 – 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….
Multiply 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 Work
Louisa 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……
Multiply decimals
by decimals.
Vocabulary
•
•
•
•
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
Wrap it Up
• Review
• Questions
• Station Work
Day 3
Bell 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?
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.
Vocabulary
•
•
•
•
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
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.
Vocabulary
•
•
•
•
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
Wrap it Up
• Review
• Questions
• Station Work
Day 5
Bell 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?
Justify your answer.
Vocabulary
•
•
•
•
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
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 = .048
13.4 x 10 = 134
3.6 x 100= 360
7742.3 x .001 = 7.7423
0.0063 x 1000 = 6.3
I Can……
Divide decimals
mentally by powers of
10.
Vocabulary
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
Wrap it Up
• Review
• Questions
• Station Work
Day 8
Bell 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?
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)
Vocabulary
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.
I Can……
Represent numbers
using exponents.
Using Exponents to
Represent Repeating Factors
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
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?
Vocabulary
•
•
•
•
•
•
•
•
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 and Assess
Please Take out your Study Guides
Wrap it Up
• Review
• Questions
• Station Work
Self Check # 1
A - 20
B - 12
C – 1,400
Self Check # 2
1 – 0.9
2 – 0.8
3 – 0.08
4 – 0.05
5 – 1.5
6 – 2.4
7 - 0.16
8 - 0.32
Self Check #3
A – 15.96
B – 0.206
C – 0.0518
D – 0.0128
E – 0.0533
F – 0.0798
Self Check # 4
10 – 14
11 – 34
12 – 49
13 – 41
14 – 4 million
Self Check # 5
A – 49 ÷ 7 = 7
B – 100 ÷ 25 = 4
C – 54 ÷ 9 = 6
D – 99 ÷ 11 = 9
Self Check # 6
1 – 1.7
2 – 1.4
3 – 1.4
4 – 0.45
Self Check # 7
1–4
2–3
3–3
4 – 0.4
5 – 0.7
6 - 0.5
Self Check # 8
A – 2,720
B – 59,800
C – 3,900,000
D – 1,390,000
E – 9.36
F - 0.00784
Self Check # 9
A – 0.06743
B – 3.142
C – 73 students
D – 15,800
E – 0.2
Self Check # 10
A – 74
B – 97
C – 100,00
D – 4.41
E – 2,187 gallons