Transcript Gr04_Ch_15 - Etiwanda E

Chapter 15
Decimals: Addition and Subtraction
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15
Decimals: Addition and Subtraction
Lesson 15-1
Round Decimals
Lesson 15-2
Estimate Decimal Sums and
Differences
Lesson 15-3
Problem-Solving Strategy: Work
Backward
Lesson 15-4
Add Decimals
Lesson 15-5
Problem-Solving Investigation:
Choose a Strategy
Lesson 15-6
Subtract Decimals
15-1
Round Decimals
Five-Minute Check (over Chapter 14)
Main Idea and Vocabulary
California Standards
Example 1: Round Decimals
Example 2: Round Decimals
Example 3: Round Decimals
15-1
Round Decimals
• I will round decimals.
• decimal
• decimal point
15-1
Round Decimals
Standard 4NS2.2 Round two-place decimals to
one decimal or the nearest whole number and
judge the reasonableness of the rounded
answer.
15-1
Round Decimals
About 2.93 million people live in San Diego County,
California. How many people live in San Diego
County when rounded to the nearest whole
number?
15-1
Round Decimals
One Way: Use a Number Line
2.93 is between 2 and 3.
It is closer to 3.
So, round 2.93 to 3.
15-1
Round Decimals
Another Way: Use Rounding Rules
Use the same process that you use with
rounding whole numbers.
2.93
15-1
Round Decimals
Answer: To the nearest whole number,
2.93 rounds to 3. About 3 million
people live in San Diego County,
California.
15-1
Round Decimals
Round 4.65 to the nearest whole number.
A. 3
B. 4
C. 5
D. 6
15-1
Round Decimals
Round 46.45 to the nearest whole number.
Use the rounding rules.
46.45
Answer: To the nearest whole number,
46.45 rounds to 46.
15-1
Round Decimals
Round 87.38 to the nearest whole number.
A. 89
B. 88
C. 87
D. 86
15-1
Round Decimals
A golfer had an average score of 72.84 in one
season. Round this score to the nearest tenth.
Use the rounding rules.
72.84
Answer: To the nearest tenth, 72.84 rounds to 72.8.
15-1
Round Decimals
Round 92.37 to the nearest tenth.
A. 92.2
B. 92.3
C. 92.4
D. 92.5
15-2
Estimate Decimal Sums and Differences
Five-Minute Check (over Lesson 15-1)
Main Idea and Vocabulary
California Standards
Key Concept: Estimate Decimal Sums
Key Concept: Estimate Decimal Differences
Example 1: Estimate Sums
Example 2: Estimate Differences
15-2
Estimate Decimal Sums and Differences
• I will use rounding to estimate sums and
differences.
• estimate
15-2
Estimate Decimal Sums and Differences
Standard 4NS2.1 Estimate and compute the sum
or difference of whole numbers and positive
decimals to two places.
15-2
Estimate Decimal Sums and Differences
15-2
Estimate Decimal Sums and Differences
15-2
Estimate Decimal Sums and Differences
Belkis rides her bike 4.6 miles on Saturday and
6.25 miles on Sunday. About how many miles
does she ride her bike altogether on both days?
You need to estimate 4.6 + 6.25. Round each addend
to the nearest whole number. Then add.
4.6
+
5
6.25
+ 6
Round 4.6 to 5.
Round 6.25 to 6.
11
Answer: So, Belkis rode her bike about 11 miles.
15-2
Estimate Decimal Sums and Differences
Adriano ran 2.3 miles on Friday and 3.45 miles
on Saturday. About how many miles did he run
altogether on both days?
A. 3
B. 4
C. 5
D. 6
15-2
Estimate Decimal Sums and Differences
Jairo has $38.55. If he buys a CD that costs
$16.99, about how much money will he have left?
You need to estimate $38.55 – $16.99. Round each
decimal to the nearest whole number. Then subtract.
15-2
Estimate Decimal Sums and Differences
–
$38.55
$16.99
–
–
Round
$39 $38.55 to $39.
$17 $16.99 to $17.
Round
$39
$17
$22
Answer: So, Jairo will have about $22 left.
15-2
Estimate Decimal Sums and Differences
Sonia has $42.67. If she buys a pair of shoes for
$24.99, about how much money will she have left?
A. $18
B. $19
C. $20
D. $21
15-3
Problem-Solving Strategy: Work Backward
Five-Minute Check (over Lesson 15-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
15-3
Problem-Solving Strategy: Work Backward
• I will solve problems by working backward.
15-3
Problem-Solving Strategy: Work Backward
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information, and
observing patterns.
15-3
Problem-Solving Strategy: Work Backward
Standard 4NS3.1 Demonstrate an
understanding of, and the ability to use,
standard algorithms for the addition and
subtraction of multidigit numbers.
15-3
Problem-Solving Strategy: Work Backward
Rey has lacrosse practice in the evenings. He
gets home from school and eats a snack for
15 minutes. Then he spends 1 hour doing his
homework. It takes him 15 minutes to get to
practice. Practice is at 5 P.M. What time does
Rey get home from school?
15-3
Problem-Solving Strategy: Work Backward
Understand
What facts do you know?
• Rey eats a snack for 15 minutes.
• He works on homework for 1 hour.
• It takes 15 minutes to get to practice at 5 P.M.
What do you need to find?
• What time Rey gets home from school.
15-3
Problem-Solving Strategy: Work Backward
Plan
Work backward to solve the problem.
15-3
Problem-Solving Strategy: Work Backward
Solve
Start with the end result. Then work backward
one step at a time.
5 P.M. – 15 minutes = 4:45 P.M.
practice
starts
time to get
to practice
4:45 P.M. – 1 hour = 3:45 P.M.
time spent on
homework
15-3
Problem-Solving Strategy: Work Backward
Solve
3:45 P.M. – 15 minutes = 3:30 P.M.
time spent
eating
Answer: So, Rey gets home from school at 3:30 P.M.
15-3
Problem-Solving Strategy: Work Backward
Check
Look back at the problem.
15 + 1 hour + 15 minutes = 1 hour and 30 minutes
If he gets home at 3:30 P.M., one hour and 30 minutes
later would be 5 P.M.
The answer is correct.
15-4
Add Decimals
Five-Minute Check (over Lesson 15-3)
Main Idea
California Standards
Example 1: Add Decimals
Example 2: Add Decimals
Addition of Decimals
15-4
Add Decimals
• I will add decimals.
15-4
Add Decimals
Standard 4NS2.1 Estimate and compute the sum
or difference of whole numbers and positive
decimals to two places.
Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.
15-4
Add Decimals
Odina slept 8.3 hours on Monday night and
7.66 hours on Tuesday night. How many hours
did she sleep on the two nights combined?
Estimate 8.3 + 7.66
8 + 8 = 16
Step 1 Line up the decimal points.
+
Write
a 0 in the
8.30
hundredths
7.66 place
as a placeholder.
15-4
Add Decimals
Step 2 Add.
+
Add8.30
the digits in each
place 7.66
value. Then bring
down the15.96
decimal point.
Answer: So, Odina slept a total of 15.96 hours.
15-4
Add Decimals
Check for Reasonableness
Since 15.96 is close to the estimate of 16, the
answer is reasonable.
15-4
Add Decimals
Meredith studied for 2.4 hours on Tuesday night
and 1.83 hours on Wednesday night. How many
hours did she spend studying on the two nights
combined?
A. 3.23 hours
B. 4.23 hours
C. 4.33 hours
D. 5.23 hours
15-4
Add Decimals
Kate spent $1.25 for a juice box and $1.79 for
yogurt. How much did she spend in all?
You need to find $1.25 + $1.79.
Estimate $1 + $2 = $3
Step 1 Line up the decimal points.
+
$1.25
$1.79
15-4
Add Decimals
Step 2 Add.
1 1
+
$1.25in each place value.
Add the digits
Regroup$1.79
if necessary.
04$3.
Answer: So, Kate spent $3.04.
15-4
Add Decimals
Check for Reasonableness
The sum of $3.04 is close to the estimate of 3,
so the answer is reasonable.
15-4
Add Decimals
Jerome spent $2.55 on a sandwich and $1.75 on
a bottle of juice. How much did he spend in all?
A. $3.20
B. $4.20
C. $4.30
D. $4.75
15-5
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 15-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
15-5
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
15-5
Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
15-5
Problem-Solving Investigation: Choose a Strategy
Standard 4SDAP1.1 Formulate survey questions;
systematically collect and represent data on a
number line; and coordinate graphs, tables, and
charts.
15-5
Problem-Solving Investigation: Choose a Strategy
JENNIFER: My friends and I have
pets. We all have different kinds
of pets. Among the three of us, we
have a lizard, a cat, a gerbil, and
a snake. I do not have a cat.
Rondell’s pet is not a gerbil or a
snake. Lorena’s two pets are not
lizards. My pet does not begin with
the letters s or g.
YOUR MISSION: Find with person owns
each pet.
15-5
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• You know the clues for each person’s pet.
What do you need to find?
• You need to find which person owns
each pet.
15-5
Problem-Solving Investigation: Choose a Strategy
Plan
Make a table to show what you know. Then use
logical reasoning to find which person owns
each pet.
15-5
Problem-Solving Investigation: Choose a Strategy
Solve
Make a table. Write a yes or no for each fact
that you are given. Once you write yes in the
table, you can write no in the rest of the boxes
in that row and column.
15-5
Problem-Solving Investigation: Choose a Strategy
Solve
Answer: So, Jennifer owns a lizard. Lorena
owns a gerbil and a snake. Rondell
owns a cat.
15-5
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. The solution matches
the facts given in the problem. So, the answer is
correct.
15-6
Subtract Decimals
Five-Minute Check (over Lesson 15-5)
Main Idea
California Standards
Example 1: Subtract Decimals
Example 2: Subtract Decimals
Subtraction of Decimals
15-6
Subtract Decimals
• I will subtract decimals.
15-6
Subtract Decimals
Standard 4NS2.1 Estimate and compute the
sum or difference of whole numbers and
positive decimals to two places.
Standard 4MR2.1 Use estimation to verify
reasonableness of calculated results.
15-6
Subtract Decimals
A fruit stand sells a bag of grapes for $1.70 and
a bunch of bananas for $1.19. What is the
difference in price?
Estimate $1.70 – $1.19
$1.7 – $1.2 = $0.50
Step 1 Line up the decimal points.
–
$1.70
$1.19
15-6
Subtract Decimals
Step 2 Subtract. Regroup if needed.
6
–
10
$1.70
$1.19
51$0.Place the decimal point.
Answer: So, the difference in price is $0.51.
15-6
Subtract Decimals
Check for Reasonableness
Since the answer of $0.51 is close to the estimate of
$0.50, the answer is reasonable.
15-6
Subtract Decimals
Find the difference between 2.25 and 1.4.
A. 1.85
B. 0.85
C. 0.05
D. 0.80
15-6
Subtract Decimals
Arati is 52.5 inches tall and her sister is
48.8 inches tall. How much taller is Arati
than her sister?
Estimate 52.5 – 48.8
53 – 49 = 4
Step 1 Line up the decimal points.
–
52.5
48.8
15-6
Subtract Decimals
Step 2 Subtract.
11
41
15
–
7
3.
Subtract
52.5 the digits in each
place
48.8 value. Regroup if
necessary.
Answer: So, Arati is 3.7 inches taller than her sister.
15-6
Subtract Decimals
Check for Reasonableness
The answer 3.7 is close to the estimate of 4. So, the
answer is reasonable.
15-6
Subtract Decimals
Find the difference between 78.2 and 55.1.
A. 231
B. 2.31
C. 23.1
D. 0.231
15
Decimals: Addition and Subtraction
Five-Minute Checks
Math Tool Chest
Image Bank
Addition of Decimals
Subtraction of Decimals
15
Decimals: Addition and Subtraction
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following four slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
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in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
15
Decimals: Addition and Subtraction
15
Decimals: Addition and Subtraction
15
Decimals: Addition and Subtraction
15
Decimals: Addition and Subtraction
15
Decimals: Addition and Subtraction
Lesson 15-1 (over Chapter 14)
Lesson 15-2 (over Lesson 15-1)
Lesson 15-3 (over Lesson 15-2)
Lesson 15-4 (over Lesson 15-3)
Lesson 15-5 (over Lesson 15-4)
Lesson 15-6 (over Lesson 15-5)
15
Decimals: Addition and Subtraction
(over Chapter 14)
Compare. Write <, >, or =.
6
73
10
A. <
B. >
C. =
15
Decimals: Addition and Subtraction
(over Chapter 14)
Compare. Write <, >, or =.
5.6
A. <
B. >
C. =
5
15
Decimals: Addition and Subtraction
(over Chapter 14)
Compare. Write <, >, or =.
1
2
2.1
10
A. <
B. >
C. =
15
Decimals: Addition and Subtraction
(over Chapter 14)
Compare. Write <, >, or =.
4.7
A. <
B. >
C. =
4.07
15
Decimals: Addition and Subtraction
(over Chapter 14)
Use a number line to order from greatest to least.
11 1 , 11.9, 11 38 , 11.25
100
2
38
1
A. 11.9, 11.25, 11 , 11
100
2
B. 11
1
38
, 11.9, 11.25, 11
100
2
C. 11.9, 11
38
1
, 11
, 11.25
100
2
38
1
D. 11
, 11.9, 11 , 11.25
100
2
15
Decimals: Addition and Subtraction
(over Chapter 14)
Use a number line to order from greatest to least.
4
3 , 4.62, 3.2, 4 5
5
10
4
5
A. 3.2, 3 , 4 , 4.62
5 10
B. 4
5
4
, 4.62, 3 , 3.2
10
5
C. 4.62, 4
4
5
, 3.2, 3
5
10
5
4
D. 4.62, 4 , 3 , 3.2
10 5
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 1.43 to the nearest whole number.
A. 1.5
B. 1
C. 2
D. 0
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 26.72 to the nearest whole number.
A. 26
B. 20
C. 27
D. 30
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 53.54 to the nearest whole number.
A. 53
B. 50
C. 53.5
D. 54
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 67.15 to the nearest whole number.
A. 67
B. 70
C. 60
D. 68
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 3.16 to the nearest tenth.
A. 3.1
B. 3
C. 0
D. 3.2
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 9.35 to the nearest tenth.
A. 9.3
B. 9
C. 9.4
D. 10
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 48.51 to the nearest tenth.
A. 49
B. 48.5
C. 48
D. 48.1
15
Decimals: Addition and Subtraction
(over Lesson 15-1)
Round 92.64 to the nearest tenth.
A. 92.7
B. 93
C. 92.1
D. 92.6
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
1.5
+ 3.4
A. 4
B. 4.5
C. 5
D. 4.9
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
37.61
+ 12.84
A. 49
B. 50.5
C. 50
D. 51
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
28.90
– 8.27
A. 21
B. 38
C. 22
D. 20.8
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
66.3 – 19.51
A. 47.7
B. 45
C. 46
D. 46.8
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
2.18 + 17.4
A. 19
B. 19.6
C. 20
D. 15.2
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
22.78 + 29.82
A. 52
B. 53
C. 52.6
D. 51
15
Decimals: Addition and Subtraction
(over Lesson 15-2)
Estimate. Round to the nearest whole number.
$52.25 – $44.77
A. $8.00
B. $7.50
C. $12.52
D. $7.00
15
Decimals: Addition and Subtraction
(over Lesson 15-3)
Solve. Use the work backward strategy. A number
is added to 2. Next, the sum is divided by 3. Then,
1 is subtracted from the quotient. The result is 3.
What is the number?
A. 2
B. 7
C. 10
D. 12
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
0.8
+ 0.4
A. 0.12
B. 12
C. 1.2
D. 1.4
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
8.20
+ 1.46
A. 9.6
B. 10.66
C. 9.12
D. 9.66
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
4.35
+ 9.47
A. 12.72
B. 13.82
C. 11.82
D. 13.72
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
$6.07
+ $6.89
A. $13.96
B. $12.86
C. $12.96
D. $12.97
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
24.38
+ 33.92
A. 58.30
B. 68.30
C. 58.29
D. 57.20
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
45.23
+ 39.68
A. 85.90
B. 74.81
C. 75.91
D. 84.91
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
$62.50 + $19.52
A. $71.02
B. $82.02
C. $82.12
D. $81.02
15
Decimals: Addition and Subtraction
(over Lesson 15-4)
Add. Use estimation to check for reasonableness.
5.3 + 2.47 + 1.15
A. 8.82
B. 3.05
C. 8.92
D. 4.15
15
Decimals: Addition and Subtraction
(over Lesson 15-5)
Use any problem-solving strategy to solve. Finn,
Malik, and Kwag are all wearing different colored
shirts. Their shirts are red, blue, or green. Malik’s
shirt is not blue. Finn’s shirt color doesn’t start
with an r or a g. Kwag’s shirt is green. What color
shirt is each boy wearing?
A. Finn: red; Malik: blue; Kwag: green
B. Finn: blue; Malik: green; Kwag: red
C. Finn: yellow; Malik: red; Kwag: green
D. Finn: blue; Malik: red; Kwag: green
This slide is intentionally blank.