Transcript Interactive Classroom - Lemoore Elementary School

Chapter 3
Adding and Subtracting Decimals
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3
Adding and Subtracting Decimals
Lesson 3-1
Representing Decimals
Lesson 3-2
Comparing and Ordering Whole
Numbers and Decimals
Lesson 3-3
Rounding Whole Numbers and
Decimals
Lesson 3-4
Problem-Solving Strategy: Use
Logical Reasoning
Lesson 3-5
Estimating Sums and Differences
Lesson 3-6
Problem-Solving Investigation:
Use Estimation
Lesson 3-7
Adding and Subtracting Decimals
3-1
Representing Decimals
Five-Minute Check (over Chapter 2)
Main Idea
California Standards
Example 1
Example 2
Example 3
Modeling Decimals
3-1
Representing Decimals
• I will represent decimals on a number line.
3-1
Representing Decimals
Standard 5NS1.5 Identify and represent
on a number line decimals, fractions, mixed
numbers, and positive and negative integers.
3-1
Representing Decimals
Graph 1.3 on a number line.
Since 1.3 is between 1 and 2, draw a number line from
1 to 2. Use increments of one tenth since 1.3 is written
to the tenths place value.
3-1
Representing Decimals
Which is the correct location for 1.9?
A
B
C
D
3-1
Representing Decimals
Graph 1.75 on a number line.
Since 1.75 is between 1.7 and 1.8, draw a number line
from 1.7 to 1.8. Use increments of one hundredth since
1.75 is written to the hundredths place value.
3-1
Representing Decimals
3-1
Representing Decimals
Which is the correct location of 1.21?
A
B
C
D
3-1
Representing Decimals
Which letter represents 4.44 on the number line?
P
Q
R
4.44 is greater than 4 and less than 5. The only
letter in the interval between 4 and 5 is S.
Answer: So, 4.4 is represented by S on the
number line.
S
3-1
Representing Decimals
Which letter represents –2.5 on the number line?
P
Q
R
S
3-2
Comparing and Ordering Whole Numbers and Decimals
Five-Minute Check (over Lesson 3-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
3-2
Comparing and Ordering Whole Numbers and Decimals
• I will compare and order whole numbers and
decimals.
• equivalent decimals
3-2
Comparing and Ordering Whole Numbers and Decimals
Reinforcement of Standard 4NS1.2 Order and
compare whole numbers and decimals to two
decimal places.
3-2
Comparing and Ordering Whole Numbers and Decimals
Use the table below. Use > or < to compare the area
of the Mediterranean Sea with the area of the South
China Sea.
3-2
Comparing and Ordering Whole Numbers and Decimals
One Way: Use place value.
South China Sea:
2,974,600
Mediterranean Sea: 2,509,960
Since 9 > 5,
2,974,600 > 2,509,960
Line up the digits
at the ones place.
Starting at the
left, find the first
place the digits
differ. Compare
the digits.
3-2
Comparing and Ordering Whole Numbers and Decimals
Another Way: Use a number line.
Graph and then compare the numbers.
Numbers to the right are greater than numbers
to the left. So, 2,974,600 > 2,509,960.
Answer: The South China Sea has a greater area
than the Mediterranean Sea.
3-2
Comparing and Ordering Whole Numbers and Decimals
Use the table below. Use > or < to compare the area
of the Sea of Okhotsk with the area of the Bering
Sea. Choose the correct answer.
A.
2,261,100 < 1,392,100
B.
2,515,900 > 1,392,100
C.
2,261,100 > 1,392,100
D.
2,974,100 > 2,261,100
3-2
Comparing and Ordering Whole Numbers and Decimals
Use the table below. Use > or < to compare the
scores of Takahura Nakai and Ross Powers.
3-2
Comparing and Ordering Whole Numbers and Decimals
Takahura Nakai:
40.7
First line up the decimal
points.
Ross Powers :
46.1
Then, starting at the left,
find the first place the
digits differ. Compare the
digits.
Since 0 < 6, 40.7 < 46.1.
Answer: So, Takahura Nakai’s score is less than Ross
Powers’ score.
3-2
Comparing and Ordering Whole Numbers and Decimals
Use the table below. Use > or < to compare the
scores of Giacomo Kratter and Danny Kass.
Choose the correct answer.
A.
42.5 < 42.0
B.
42.0 > 40.7
C.
46.1 > 42.5
D.
42.5 > 42.0
3-2
Comparing and Ordering Whole Numbers and Decimals
Order 18, 17.87, 18.9, 18.07 from greatest to least.
18
17.87
18.9
18.07
18.00
17.87
18.90
18.07
Answer: The order from greatest to least is,
18.9, 18.07, 18, and 17.87.
18.90
18.07
18.00
17.87
3-2
Comparing and Ordering Whole Numbers and Decimals
Which answer below puts the numbers 24, 23.56,
24.8, and 24.08 from least to greatest?
A.
23.56, 24.08, 24.8, 24
B.
23.56, 24, 24.08, 24.8
C.
23.56, 24, 24.8, 24.08
D.
24, 23.56, 24.8, 24.08
3-3
Rounding Whole Numbers and Decimals
Five-Minute Check (over Lesson 3-2)
Main Idea
California Standards
Key Concept: Round Decimals
Example 1
Example 2
Example 3
Example 4
3-3
Rounding Whole Numbers and Decimals
• I will round whole numbers and decimals.
3-3
Rounding Whole Numbers and Decimals
Standard 5NS1.1 Estimate, round, and manipulate
very large (e.g., millions) and very small (e.g.
thousandths) numbers.
3-3
Rounding Whole Numbers and Decimals
3-3
Rounding Whole Numbers and Decimals
Round 3,765,734 to the nearest hundred thousand.
3,765,734
3-3
Rounding Whole Numbers and Decimals
On the number line, 3,765,734 is closer to 3,800,000
than 3,700,000. To the nearest hundred thousand,
3,765,734 rounds to 3,800,000.
3-3
Rounding Whole Numbers and Decimals
Round 4,352,676 to the nearest million.
A.
4,300,000
B.
4,400,000
C.
4,000,000
D.
4,350,000
3-3
Rounding Whole Numbers and Decimals
Round 5.686 to the nearest whole number.
5.686
3-3
Rounding Whole Numbers and Decimals
On the number line, 5.6 is closer to 6.0 than to 5.0.
To the nearest whole number, 5.686 rounds to 6.
3-3
Rounding Whole Numbers and Decimals
Round 3.475 to the nearest whole number.
A. 3.4
B. 3.5
C. 3
D. 4
3-3
Rounding Whole Numbers and Decimals
Round 93.889 to the nearest hundredth.
93.889
3-3
Rounding Whole Numbers and Decimals
On the number line, 93.889 is closer to 93.89 than
to 93.88. To the nearest hundredth, 93.889 rounds
to 93.89.
3-3
Rounding Whole Numbers and Decimals
Round 45.632 to the nearest hundredth.
A. 45
B. 45.63
C. 45.6
D. 45.632
3-3
Rounding Whole Numbers and Decimals
In February 2006, the Dairy Institute of California
reported that California butter producers received
$0.014 cents less per pound of butter than
producers that sold their product on the Chicago
Mercantile Exchange. To the nearest cent, how
much less did California butter producers receive?
0.014
Answer: To the nearest cent, the California butter
producers received $0.01 less.
3-3
Rounding Whole Numbers and Decimals
Round $4.568 to the nearest cent.
A. $4.57
B. $4.56
C. $4.00
D. $5.00
3-4
Problem-Solving Strategy: Use Logical Reasoning
Five-Minute Check (over Lesson 3-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
3-4
Problem-Solving Strategy: Use Logical Reasoning
• I will solve problems by using logical reasoning.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Standard 5MR2.4 Express the solution clearly
and logically by using the appropriate
mathematical notation and terms and clear
language; support solutions with evidence in both
verbal and symbolic work.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Standard 5MG1.4 Differentiate between, and use
appropriate units of measures for, two- and threedimensional objects (i.e., find the perimeter, area,
volume).
3-4
Problem-Solving Strategy: Use Logical Reasoning
Mora, Sam, Aisha, and Jamal each have a
different colored notebook (blue, red, purple,
and green). Use the clues to determine which
person owns each notebook.
1.
Sam and the girl with the green notebook are
in the same class.
2.
The purple notebook is owned by a girl.
3.
Jamal and the person with the red notebook
eat lunch together.
4.
Mora is not in the same class as Sam.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Understand
What facts do you know?
• You know the four clues that are listed previously.
What do you need to find?
• Which person owns each notebook?
3-4
Problem-Solving Strategy: Use Logical Reasoning
Plan
Use logical reasoning to find which person owns
each notebook. Make a table to help sort out the
information.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Solve
Place an “X” in each box that cannot be true.
• Clue 3 shows that Jamal does not own the red
notebook.
• Clues 1 and 2 show that girls own the green and
purple notebooks and the boys own the blue and
red notebooks.
• Clue 4 shows that Mora is not in the same class as
Sam, so she does not own the green notebook.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Solve
Answer: So, Mora owns the purple notebook, Sam
owns the red notebook, Aisha owns the green
notebook, and Jamal owns the blue notebook.
3-4
Problem-Solving Strategy: Use Logical Reasoning
Check
Look back. Reread the clues to see if the answers
that you determined match the clues. Since all of
the answers match the clues, the answers are
reasonable.
3-5
Estimating Sums and Differences
Five-Minute Check (over Lesson 3-4)
Main Idea and Vocabulary
California Standards
Concept Summary: Estimation Methods
Example 1
Example 2
Example 3
Example 4
Example 5
3-5
Estimating Sums and Differences
• I will estimate sums and differences of decimals.
• clustering
• front-end estimation
3-5
Estimating Sums and Differences
Standard 5NS1.1 Estimate, round, and manipulate
very large (e.g., millions) and very small (e.g.
thousandths) numbers.
3-5
Estimating Sums and Differences
3-5
Estimating Sums and Differences
Using the graph below, estimate the total number of
passengers that travel through Hartsfield-Atlanta
and Dallas/Ft. Worth.
3-5
Estimating Sums and Differences
Round each number to the nearest ten for easier
adding.
41.596
+ 27.746
40
+ 30
41.596 rounds to 40.
27.746 rounds to 30.
70
Answer: About 70 million passengers travel through
these two airports.
3-5
Estimating Sums and Differences
Which choice is a correct estimate of the amount of
people who travel through Chicago O’Hare and Las
Vegas airports?
A.
about 40 million
B.
about 50 million
C.
about 60 million
D.
about 30 million
3-5
Estimating Sums and Differences
Using the graph below, estimate how many more
passengers travel through Hartsfield-Atlanta than
Dallas/Ft. Worth?
3-5
Estimating Sums and Differences
41.596
– 27.746
40
– 30
41.596 rounds to 40.
27.746 rounds to 30.
10
Answer: About 10 million more passengers travel
through Hartsfield-Atlanta.
3-5
Estimating Sums and Differences
Use the graph to choose which answer is about how
many more people travel through Hartsfield-Atlanta
than Los Angeles airports.
A.
about 20 million
B.
about 40 million
C.
about 50 million
D.
They are about
the same.
3-5
Estimating Sums and Differences
Estimate 4.89 + 5.16 + 5.02 using clustering.
The addends are clustered around 5. Round each
decimal to 5.
4.89
5.16
5
5
+ 5.02
+ 5
15
Answer: Using clustering, 4.89 + 5.16 + 5.02 is
about 15.
3-5
Estimating Sums and Differences
Use clustering to estimate 3.98 + 4.02 + 4.22.
Choose the correct answer.
A.
12.22
B.
12
C.
11
D.
11.22
3-5
Estimating Sums and Differences
Dao runs on the track team at Burbank Middle
School. One week he ran 4.626, 5.219, 4.992,
5.433, and 4.905 miles at practice. Use clustering
to determine the total amount of miles he ran for
the week.
3-5
Estimating Sums and Differences
The addends are clustered around 5. Round each
decimal to 5.
4.626
5
5.219
4.992
5.443
5
5
+ 4.905
+ 5
5
25
Answer: Dao ran about 25 miles during the week.
3-5
Estimating Sums and Differences
Shao rode his bike 15.002, 14.998, 14.757, 15.332,
and 15.011 miles last week. Use clustering to
determine the correct amount of miles Shao rode
his bike in a week.
A.
80
B.
75
C.
70
D.
72
3-5
Estimating Sums and Differences
Estimate 22.35 – 11.14 using front-end estimation.
22.35
20.00
– 11.14
– 10.00
Subtract the
leftmost digits.
10.00
Answer: Using front-end estimation,
22.35 – 11.14 is about 10.00.
3-5
Estimating Sums and Differences
Estimate 43.65 + 33.84 using front-end estimation.
Choose the best answer.
A.
77
B.
80
C.
60
D.
70
3-6
Problem-Solving Investigation: Use Estimation
Five-Minute Check (over Lesson 3-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
3-6
Problem-Solving Investigation: Use Estimation
• I will solve problems by estimating.
3-6
Problem-Solving Investigation: Use Estimation
Standard 5MR2.6 Make precise calculations and
check the validity of the results from the context of
the problem.
Standard 5NS1.1 Estimate, round, and manipulate
very large and very small numbers.
3-6
Problem-Solving Investigation: Use Estimation
PING: My family drove to North
Carolina for our vacation. We drove
356.8 miles the first day, 305.2
miles the second day, and 283.1
miles the third day. We are
following the same route to return
home.
YOUR MISSION: Find about how far
Ping’s family traveled.
3-6
Problem-Solving Investigation: Use Estimation
Understand
What facts do you know?
• You know that the family drove 356.8 miles,
305.2 miles, and 283.1 miles.
What do you need to find?
• You need to find about how far Ping’s family
traveled.
3-6
Problem-Solving Investigation: Use Estimation
Plan
Since you don’t need an exact answer, you can
estimate the number of miles traveled each day.
Add the total for the three days and double that to
account for the trip to North Carolina and then
back home.
3-6
Problem-Solving Investigation: Use Estimation
Solve
Day One
356.8
400
Day Two
305.2
300
Day Three
283.1
+ 300
1,000
Answer: The one-way trip was about 1,000 miles.
The return trip was another 1,000 miles,
for a total of 2,000 miles.
3-6
Problem-Solving Investigation: Use Estimation
Check
Use clustering. The miles are clustered around
300.
6 × 300 = 1,800
Since 1,800 ≈ 2,000, a total of 2,000 is
reasonable.
3-7
Adding and Subtracting Decimals
Five-Minute Check (over Lesson 3-6)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
Adding and Subtracting Decimals
3-7
Adding and Subtracting Decimals
• I will add and subtract decimals.
3-7
Adding and Subtracting Decimals
Standard 5NS2.1 Add, subtract, multiply, and
divide with decimals; add with negative integers;
subtract positive integers from negative integers; and
verify the reasonableness of results.
3-7
Adding and Subtracting Decimals
Find the sum of 98.5 and 6.3.
Estimate
98.5 + 6.3 ≈ 99 + 6 or 105
98.5
+ 6.3
Line up the decimal points
104.8
Add as with whole numbers.
Answer: So, 98.5 + 6.3 = 104.8.
Check for Reasonableness
104.8 ≈ 105 
3-7
Adding and Subtracting Decimals
Find the sum of 24.7 and 5.8.
A. 30.5
B. 31.2
C. 39.5
D. 31.5
3-7
Adding and Subtracting Decimals
Find 8.632 – 3.231.
Estimate
8.632 – 3.231 ≈ 9 – 3 or 6
8.632
– 3.231
Line up the decimal points
5.401
Subtract as with whole numbers.
Answer: So, 8.632 – 3.231 = 5.401.
Check for Reasonableness
5.401 ≈ 6 
3-7
Adding and Subtracting Decimals
Find 7.986 – 5.424.
A. 2.562
B. 2.256
C. 2.526
D. 2.565
3-7
Adding and Subtracting Decimals
Find 3 – 1.73.
Estimate
3 – 1.73 ≈ 3 – 2 or 1
3.00
– 1.73
Annex zeros so that both numbers have
the same place value.
1.27
Subtract as with whole numbers.
Answer: So, 3 –1.73 = 1.27.
Check for Reasonableness
1.219 ≈ 1 
3-7
Adding and Subtracting Decimals
Find 4 – 2.627.
A.
2.373
B.
1.373
C.
2.627
D.
1.627
3-7
Adding and Subtracting Decimals
Find 46 – 5.719.
Estimate
46.000
– 5.719
40.281
46 – 5.719 ≈ 46 – 6 or 40
Annex zeros so that both numbers have
the same place value.
Subtract as with whole numbers.
Answer: So, 46 – 5.719 = 40.281.
Check for Reasonableness
40.281 ≈ 40 
3-7
Adding and Subtracting Decimals
Find 57 – 4.628.
A.
53.628
B.
52.873
C.
52.372
D.
53.372
3-7
Adding and Subtracting Decimals
Every element found in the Periodic Table has an
atomic weight. The elements hydrogen and oxygen
have the following atomic weights, respectively,
1.01, and 15.99. What is the difference of the atomic
weights for hydrogen and oxygen?
3-7
Adding and Subtracting Decimals
Estimate
15.99 – 1.01 ≈ 16 – 1 or 15
15.99
Line up the decimal points.
– 1.01
14.98
Subtract as with whole numbers.
Answer: So, 15.99 – 1.01 = 14.98.
Check for Reasonableness
14.98 ≈ 15

3-7
Adding and Subtracting Decimals
The element chlorine has an atomic weight of
35.453, and helium has an atomic weight of 4.003.
How much more does chlorine weigh?
A.
31.45
B.
30.45
C.
31.54
D.
30.54
3
Adding and Subtracting Decimals
Five-Minute Checks
Modeling Decimals
Adding and Subtracting Decimals
3
Adding and Subtracting Decimals
Lesson 3-1
(over Chapter 2)
Lesson 3-2
(over Lesson 3-1)
Lesson 3-3
(over Lesson 3-2)
Lesson 3-4
(over Lesson 3-3)
Lesson 3-5
(over Lesson 3-4)
Lesson 3-6
(over Lesson 3-5)
Lesson 3-7
(over Lesson 3-6)
3
Adding and Subtracting Decimals
(over Chapter 2)
Write an integer to represent the data.
The stock market gained 16 points yesterday.
A.
an increase of 16
B.
16
C.
a decrease of 16
D.
–16
3
Adding and Subtracting Decimals
(over Chapter 2)
Write an integer to represent the data.
The reef is located 35 feet below sea level.
A.
35
B.
35 feet below
C.
35 feet above
D.
–35
3
Adding and Subtracting Decimals
(over Chapter 2)
Write an integer to represent the data.
The team gained 8 yards on the last play.
A. +8
B. moved up by 8
C. –8
D. moved back by 8
3
Adding and Subtracting Decimals
(over Chapter 2)
Write an integer to represent the data.
The cat lost 2 pounds last week.
A.
2
B.
raised by 2
C.
decreased by 2
D.
–2
3
Adding and Subtracting Decimals
(over Chapter 2)
Write an integer to represent the data.
Ms. Steinberg withdrew $80 from her
savings account.
A.
reduced by $80
B.
$80
C.
–$80
D.
lost $80
3
Adding and Subtracting Decimals
(over Lesson 3-1)
Graph 0.8 in the approximate position on a
number line.
A. A
B. B
C. C
3
Adding and Subtracting Decimals
(over Lesson 3-1)
Graph 3.2 in the approximate position on a
number line.
A. A
B. B
C. C
3
Adding and Subtracting Decimals
(over Lesson 3-1)
Graph –1.93 in the approximate position on a
number line.
A. A
B. B
C. C
3
Adding and Subtracting Decimals
(over Lesson 3-1)
Graph –4.1 in the approximate position on a
number line.
A. A
B. B
C. C
3
Adding and Subtracting Decimals
(over Lesson 3-2)
Use >, <, or = to compare 632,876
A.
>
B.
<
C.
=
632,678.
3
Adding and Subtracting Decimals
(over Lesson 3-2)
Use >, <, or = to compare 11,943,549
A.
>
B.
<
C.
=
11,754,106.
3
Adding and Subtracting Decimals
(over Lesson 3-2)
Use >, <, or = to compare 0.06
A.
>
B.
<
C.
=
0.1.
3
Adding and Subtracting Decimals
(over Lesson 3-2)
Use >, <, or = to compare 4.50
A.
>
B.
<
C.
=
4.5.
3
Adding and Subtracting Decimals
(over Lesson 3-2)
Use >, <, or = to compare 17.72
A.
>
B.
<
C.
=
17.63.
3
Adding and Subtracting Decimals
(over Lesson 3-3)
Round 3.275 to the nearest whole number.
A. 4
B. 3.3
C. 3.28
D. 3
3
Adding and Subtracting Decimals
(over Lesson 3-3)
Round 53.86 to the nearest tenth.
A. 53.8
B. 54
C. 53.9
D. 53
3
Adding and Subtracting Decimals
(over Lesson 3-3)
Round 6,594,428 to the nearest million.
A.
6,600,000
B.
7,000,000
C.
6,000,000
D.
6,500,000
3
Adding and Subtracting Decimals
(over Lesson 3-3)
Round 12,856,439 to the nearest thousand.
A.
12,000,000
B.
12,856,400
C.
12,900,000
D.
12,856,000
3
Adding and Subtracting Decimals
(over Lesson 3-4)
Glen and Fatou each drew two pictures of animals.
The animals they drew were a dog, cat, mouse, and
squirrel. Glen did not draw a dog. Fatou did not draw
a mouse. The person who drew the mouse did not
draw a cat. Which animals did each person draw?
A.
Glen drew a mouse and a dog; Fatou drew a
squirrel and a cat
B.
Glen drew a dog and a cat; Fatou drew a
mouse and a squirrel
3
Adding and Subtracting Decimals
(over Lesson 3-4)
Glen and Fatou each drew two pictures of animals.
The animals they drew were a dog, cat, mouse, and
squirrel. Glen did not draw a dog. Fatou did not draw
a mouse. The person who drew the mouse did not
draw a cat. Which animals did each person draw?
C. Glen drew a mouse and a squirrel; Fatou
drew a dog and a cat
D. Glen drew a dog and a cat; Fatou drew a
mouse and a squirrel
3
Adding and Subtracting Decimals
(over Lesson 3-4)
Glen and Fatou each drew two pictures of animals.
The animals they drew were a dog, cat, mouse, and
squirrel. Glen did not draw a dog. Fatou did not draw
a mouse. The person who drew the mouse did not
draw a cat. Which animals did each person draw?
C. Glen drew a mouse and a squirrel; Fatou
drew a dog and a cat
3
Adding and Subtracting Decimals
(over Lesson 3-5)
Basir’s basketball team scored the following points
in their first 4 basketball games: 42, 23, 28, and 46.
About how many points have they scored so far?
A.
150 points
B.
140 points
C.
130 points
D.
120 points
3
Adding and Subtracting Decimals
(over Lesson 3-5)
The two richest men in the world are worth $46.6
and $42.9 billion, respectively. Estimate their total
worth.
A.
$85 billion
B.
$87 billion
C.
$89 billion
D.
$90 billion
3
Adding and Subtracting Decimals
(over Lesson 3-5)
Use clustering to estimate the sum of $29.30, $33.62,
$28.75, and $31.46.
A.
$123.00
B.
$121.00
C.
$120.00
D.
$100.00
3
Adding and Subtracting Decimals
(over Lesson 3-5)
Use front-end estimation to estimate 862 – 357.
A.
500
B.
510
C.
550
D.
600
3
Adding and Subtracting Decimals
(over Lesson 3-6)
Determine whether you need an estimate or an
exact answer. Then solve. Jaya worked 6.5 hours
on Monday, 6 hours on Tuesday, 7.5 hours on
Wednesday, 5.5 hours on Thursday, and 6 hours
on Friday. About how many hours did she work
last week?
A.
estimate; 32.5 hours
B.
exact; 31.5 hours
C.
estimate; 30 hours
D.
exact; 33 hours
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