Transcript Gr04_Ch_02 - Etiwanda E

Chapter 2
Addition and Subtraction
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2
Addition and Subtraction
Lesson 2-1
Algebra: Addition Properties and
Subtraction Rules
Lesson 2-2
Estimate Sums and Differences
Lesson 2-3
Problem-Solving Strategy: Estimate
or Exact Answer
Lesson 2-4
Add Numbers
Lesson 2-5
Subtract Numbers
Lesson 2-6
Problem-Solving Investigation:
Choose a Strategy
Lesson 2-7
Subtract Across Zeros
2-1
Algebra: Addition Properties and Subtraction Rules
Five-Minute Check (over Chapter 1)
Main Idea and Vocabulary
California Standards
Key Concepts: Addition Properties
Key Concepts: Subtraction Rules
Example 1: Use Addition Properties
Example 2: Use Addition Properties to Add
Example 3: Use Subtraction Rules
2-1
Algebra: Addition Properties and Subtraction Rules
• I will use addition properties and subtraction rules
to add and subtract.
• Commutative Property of Addition
• Associative Property of Addition
• Identity Property of Addition
2-1
Algebra: Addition Properties and Subtraction Rules
Standard 4AF1.0 Students use and interpret
variables, mathematical symbols, and properties to
write and simplify expressions and sentences.
2-1
Algebra: Addition Properties and Subtraction Rules
2-1
Algebra: Addition Properties and Subtraction Rules
2-1
Algebra: Addition Properties and Subtraction Rules
Identify the property shown by 9 + 6 = 6 + 9.
The same numbers are being added on each side
of the equal sign, but they are in a different order.
This is the Commutative Property of Addition
because the order in which numbers are added
does not change the sum.
Answer: Commutative Property of Addition
2-1
Algebra: Addition Properties and Subtraction Rules
Identify the property shown by
(2 + 3) + 4 = 2 + (3 + 4).
A. Associative Property of Addition
B. Commutative Property of Addition
C. Identity Property of Addition
D. Associative Property of Multiplication
2-1
Algebra: Addition Properties and Subtraction Rules
Find (18 + 26) + 12.
You can use the Associative Property to add mentally.
(26 + 18) + 12
Commutative Property of Addition
26 + (18 + 12)
Associative Property of Addition
26 + 30
Add 18 and 12.
56
Add 26 and 30.
Answer: 56
2-1
Algebra: Addition Properties and Subtraction Rules
Find (13 + 31) + 17.
A. 30
B. 44
C. 61
D. 52
2-1
Algebra: Addition Properties and Subtraction Rules
Find the missing number in 5 –
= 5.
When you subtract 0 from 5, the result is 5.
5–0=5
Answer: So, the missing number is 0.
2-1
Algebra: Addition Properties and Subtraction Rules
Find the missing number in 7 –
A. 7
B. 0
C. 1
D. 2
= 7.
2-2
Estimate Sums and Differences
Five-Minute Check (over Lesson 2-1)
Main Idea and Vocabulary
California Standards
Example 1: Estimate Sums
Example 2: Estimate Sums
Example 3: Estimate Differences
Example 4: Estimate Differences
2-2
Estimate Sums and Differences
• I will estimate sums and differences of numbers.
• estimate
2-2
Estimate Sums and Differences
Standard 4NS3.1 Demonstrate an
understanding of, and the ability to use,
standard algorithms for the subtraction
of multidigit numbers.
2-2
Estimate Sums and Differences
Sam wanted to buy a bicycle for $239 and a helmet
for $37. About how much money will Sam need to
buy the bicycle and helmet? Round to the tens
place.
Round each amount to the nearest tens place.
Then add.
$239
+ $37
$240
+ $40
$280
Answer: So, Sam needs to save about $280.
2-2
Estimate Sums and Differences
Olivia wants to buy a desk for $217 and a chair to
go with it for $56. About how much money does
Olivia need to buy the desk and chair? Round to
the nearest tens place.
A. $260
B. $270
C. $275
D. $280
2-2
Estimate Sums and Differences
Estimate 6,243 + 942. Round to the hundreds place.
Round to the nearest hundreds place. Then add.
6,243
+ 942
6,200
+ 900
7,100
Answer: So, 6,243 + 942 is about 7,100.
2-2
Estimate Sums and Differences
Estimate 6,837 + 821. Round to the hundreds place.
A. 7,800
B. 7,700
C. 7,600
D. 7,500
2-2
Estimate Sums and Differences
Estimate $57.61 – $28.45. Round to the tens place.
Round each dollar amount to the nearest ten dollars
then subtract.
$57.61
– $28.45
$60.00
– $30.00
$30.00
Answer: So, $57.61 – $28.45 is about $30.00.
2-2
Estimate Sums and Differences
Estimate $25.72 – $17.55. Round to the tens place.
A. $40.00
B. $10.00
C. $20.00
D. $30.00
2-2
Estimate Sums and Differences
The table shows the world’s tallest mountains.
About how much taller is Mt. Everest than
Lhoste? Round to the thousands place.
2-2
Estimate Sums and Differences
Round each height to the nearest thousand.
Then subtract.
29,028
– 27,923
29,000
– 28,000
1,000
Answer: So, Mt. Everest is about 1,000 feet taller
than Lhoste.
2-2
Estimate Sums and Differences
Estimate 74,218 – 51,933. Round to the thousands
place.
A. 22,000
B. 23,000
C. 22,700
D. 23,700
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Five-Minute Check (over Lesson 2-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
2-3
Problem-Solving Strategy: Estimate or Exact Answer
• I will determine when to estimate or find an
exact answer.
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Standard 4NS1.4 Decide when a rounded
solution is called for and explain why such a solution
may be appropriate.
Standard 4MR2.5 Indicate the relative advantages
of exact and approximate solutions to problems
and give answers to a specified degree of accuracy.
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Keith and his brother are going to build a tree
house. They will need $12 for nails, $95 for
tools, and $46 for wood. About how much
money do they need to build the tree house?
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Understand
What facts do you know?
• Nails cost $12.
• Tools cost $95.
• Wood costs $46.
What do you need to find?
• Find about how much money they need to build
the tree house.
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Plan
Since the question asks about how much money
is needed, you can estimate the sum.
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Solve
Round each amount to each greatest place
value. Then add.
$12
$95
+ $46
$10
$100
+ $50
$160
Answer: So, about $160 is needed to build the
tree house.
2-3
Problem-Solving Strategy: Estimate or Exact Answer
Check
Look back at the problem.
Suppose the question asked
for an exact answer.
Since $153 is close to $160,
an estimate of $160 is correct.
$
$
+$
$153
2-4
Add Numbers
Five-Minute Check (over Lesson 2-3)
Main Idea
California Standards
Example 1: Add Whole Numbers
Example 2: Add Multi-Digit Numbers
2-4
Add Numbers
• I will add numbers, including multidigit numbers.
2-4
Add Numbers
Standard 4NS3.1 Demonstrate an
understanding of, and the ability to use,
standard algorithms for the addition and
subtraction of multidigit numbers.
2-4
Add Numbers
Add 4,568 + 2,429.
Estimate
4,568
+ 2,429
4,600
+ 2,400
7,000
2-4
Add Numbers
Step 1 Add ones.
1
4,568
+ 2,429
7
Step 2 Add tens.
1
4,568
+ 2,429
97
2-4
Add Numbers
Step 3 Add hundreds.
1
4,568
+ 2,429
9 97
2-4
Add Numbers
Step 4 Add thousands.
1
4,568
+ 2,429
6,997
Answer: So, 4,568 + 2,429 = 6,997.
Check for Reasonableness
The estimate was 7,000. Since 6,997 is close to the
estimate, the answer is reasonable.
2-4
Add Numbers
Add 3,792 + 5,249.
A. 9,041
B. 8,931
C. 9,000
D. 9,040
2-4
Add Numbers
The three largest farms
in Springfield are listed
in the table. What is the
total size of the three
farms?
Estimate
12,250
8,732
+ 997
12,300
8,700
+ 1,000
22,000
2-4
Add Numbers
Step 1 Add ones.
12,250
8,732
+ 997
9
Step 2 Add tens.
1
12,250
8,732
+ 997
79
2-4
Add Numbers
Step 3 Add hundreds.
1 1
12,250
8,732
+ 997
979
Step 4 Add thousands.
11 1
12,250
8,732
+ 997
1,979
2-4
Add Numbers
Step 5 Add ten thousands.
11 1
12,250
8,732
+ 997
21,979
Answer: The total size of the three farms is
21,979 acres.
Check for Reasonableness
The estimate was 22,000. Since 21,979 is close to the
estimate, the answer is reasonable.
2-4
Add Numbers
Add 33,473 + 4,522 + 722.
A. 38,771
B. 37,117
C. 38,717
D. 37,617
2-5
Subtract Numbers
Five-Minute Check (over Lesson 2-4)
Main Idea
California Standards
Example 1: Subtract Whole Numbers
Example 2: Subtract Money
Subtract Numbers
2-5
Subtract Numbers
• I will subtract multidigit numbers.
2-5
Subtract Numbers
Standard 4NS3.1 Demonstrate an
understanding of, and the ability to use,
standard algorithms for the addition and
subtraction of multidigit numbers.
2-5
Subtract Numbers
The Hernandez family flies 9,635 miles to visit
some cousins. Next year, they fly 3,867 miles to
visit their grandmother. How much farther did they
travel to see their cousins?
Estimate
9,635
– 3,867
9,600
– 3,900
5,700
2-5
Subtract Numbers
Step 1 Subtract ones.
2 15
9,635
– 3,867
8
Step 2 Subtract tens.
12
5 2 15
9,635
– 3,867
68
2-5
Subtract Numbers
Step 3 Subtract hundreds.
15 12
8 5 2 15
9,635
– 3,867
768
Step 4 Subtract thousands.
15 12
8 5 2 15
9,635
– 3,867
5,768
2-5
Subtract Numbers
Answer: So, the Hernandez family traveled
5,768 miles further to see their cousins.
Check
You can use addition to check your subtraction.
9,635
– 3,867
5,768
3,867
+ 5,768
9,635
The answer is correct and close to the estimate.
2-5
Subtract Numbers
Subtract 8,249 – 2,871.
A. 6,487
B. 5,378
C. 6,789
D. 5,738
2-5
Subtract Numbers
Elija had $96.47 in his checking account. He wrote
a check for $67.99 to buy a skateboard. How much
money did he have left?
Subtracting money is similar to subtracting whole
numbers.
Estimate
$96.47
– $67.99
$96
– $68
$28
2-5
Subtract Numbers
Step 1 Subtract pennies.
3 17
$96.47
– $67.99
8
Step 2 Subtract dimes.
13
5 3 17
$96.47
– $67.99
48
2-5
Subtract Numbers
Step 3 Subtract dollars.
15 13
8 5 3 17
$96.47
– $67.99
8.48
Step 4 Subtract ten dollars.
15 13
8 5 3 17
$96.47
– $67.99
$28.48
Answer: Elija had $28.48 left.
2-5
Subtract Numbers
Check
$96.47
– $67.99
$28.48
$67.99
+ $28.48
$96.47
The answer is correct and close to the estimate.
2-5
Subtract Numbers
Selena had $45.50 when she went to the store.
She bought shoes for $36.99. How much does
she have left?
A. $10.51
B. $9.50
C. $8.51
D. $8.49
2-6
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 2-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
2-6
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
2-6
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.
2-6
Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.
2-6
Problem-Solving Investigation: Choose a Strategy
MARCO: I am downloading music. So
far, I have downloaded 4 albums.
Each album has 14 songs.
YOUR MISSION: Find how many songs
Marco has downloaded.
2-6
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Marco has downloaded 4 albums.
• Each album has 14 songs.
What do you need to find?
• Find how many songs Marco has
downloaded.
2-6
Problem-Solving Investigation: Choose a Strategy
Plan
You can organize the information in a table and
use repeated addition to find how many songs
Marco has downloaded.
2-6
Problem-Solving Investigation: Choose a Strategy
Solve
Start with 14, the number of songs on the first
album. Then continue to add 14 for each
additional album.
14
+ 14
28
2-6
Problem-Solving Investigation: Choose a Strategy
Solve
1
28
+ 14
42
42
+ 14
56
Answer: So, he downloaded a total of 56 songs.
2-6
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem.
56 – 14 = 42, 42 – 14 = 28, 28 – 14 = 14,
and 14 – 14 = 0.
The answer is correct.
2-7
Subtract Across Zeros
Five-Minute Check (over Lesson 2-6)
Main Idea
California Standards
Example 1: Subtract Across Zeros
Example 2: Subtract Across Zeros
2-7
Subtract Across Zeros
• I will subtract multidigit numbers, when some
digits are zero.
2-7
Subtract Across Zeros
Standard 4NS3.1 Demonstrate an
understanding of, and the ability to use,
standard algorithms for the addition and
subtraction of multidigit numbers.
2-7
Subtract Across Zeros
Refer to the table. How
much larger is Jupiter
than Earth?
Step 1 Subtract ones.
9
1 10 10
142,200
– 12,756
4
2-7
Subtract Across Zeros
Step 2 Subtract tens.
9
1 10 10
142,200
– 12,756
44
Step 3 Subtract hundreds.
11 9
1 1 10 10
142,200
– 12,756
444
2-7
Subtract Across Zeros
Step 4 Subtract thousands.
11 11 9
3 1 1 10 10
142,200
– 12,756
9,444
Step 5 Subtract ten thousands.
11 11 9
3 1 1 10 10
142,200
– 12,756
29,444
2-7
Subtract Across Zeros
Step 6 Subtract hundred thousands.
11 11 9
3 1 1 10 10
142,200
– 12,756
129,444
Answer: So, Jupiter is 129,444 km larger than Earth.
Check
You can use addition to check your subtraction.
12,756 + 129,444 = 142,200. So, the answer is correct.
2-7
Subtract Across Zeros
Subtract 132,788 – 64,329.
A. 68,599
B. 68,459
C. 67,461
D. 67,459
2-7
Subtract Across Zeros
Marciel gave the store clerk $50.00 for her
purchase. She received $13.56 in change.
How much did she spend?
Step 1 Subtract pennies.
9 9
4 10 10 10
$50.00
– $13.56
4
2-7
Subtract Across Zeros
Step 2 Subtract dimes.
9 9
4 10 10 10
$50.00
– $13.56
44
Step 3 Subtract ones.
9 9
4 10 10 10
$50.00
– $13.56
6.44
2-7
Subtract Across Zeros
Step 4 Subtract tens.
9 9
4 10 10 10
$50.00
– $13.56
$36.44
Answer: So, Marciel spent $36.44.
2-7
Subtract Across Zeros
Seki bought some headphones at the mall. If he
took $35.00 with him and has $13.74 left, how
much did the headphones cost?
A. $21.26
B. $22.76
C. $22.27
D. $21.76
2
Addition and Subtraction
Five-Minute Checks
Math Tool Chest
Image Bank
Subtract Numbers
2
Addition and Subtraction
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2
Addition and Subtraction
2
Addition and Subtraction
2
Addition and Subtraction
2
Addition and Subtraction
2
Addition and Subtraction
Lesson 2-1
(over Chapter 1)
Lesson 2-2
(over Lesson 2-1)
Lesson 2-3
(over Lesson 2-2)
Lesson 2-4
(over Lesson 2-3)
Lesson 2-5
(over Lesson 2-4)
Lesson 2-6
(over Lesson 2-5)
Lesson 2-7
(over Lesson 2-6)
2
Addition and Subtraction
(over Chapter 1)
Use any strategy to solve. Tell which strategy you
used. Lee Ann’s family travels 60 miles in one hour.
Roberto’s family travels 40 miles in one hour. How
many hours would it take for Lee Ann’s family to
travel as far as Roberto’s family travels in 6 hours?
A. Roberto’s family travels 200 miles in 6 hours;
it will take Lee Ann’s family 4 hours to travel
200 miles.
B. Roberto’s family travels 2,400 miles in 6 hours;
it will take Lee Ann’s family 4 hours to travel
2,400 miles.
2
Addition and Subtraction
(over Chapter 1)
C. Roberto’s family travels 240 miles in 6 hours;
it will take Lee Ann’s family 4 hours to travel
240 miles.
D. Roberto’s family travels 280 miles in 6 hours;
it will take Lee Ann’s family 5 hours to travel
280 miles.
2
Addition and Subtraction
(over Chapter 1)
Answer:
C. Roberto’s family travels 240 miles in 6 hours;
it will take Lee Ann’s family 4 hours to travel
240 miles.
2
Addition and Subtraction
(over Lesson 2-1)
Copy and complete the number sentence. Write the
property or rule shown.
7 + __ = 7
A. 0; Associative Property
B. 0; Identity Property
C. 7; Identity Property
D. 1; Commutative Property
2
Addition and Subtraction
(over Lesson 2-1)
Copy and complete the number sentence. Write the
property or rule shown.
(9 + 2) + 7 = 9 + (__ + 7)
A. 9; Associative Property
B. 2; Commutative Property
C. 2; Associative Property
D. 7; Associative Property
2
Addition and Subtraction
(over Lesson 2-1)
Copy and complete the number sentence. Write the
property or rule shown.
4 – __ = 0
A. 4; Subtraction Rule
B. 0; Identity Property
C. 0; Subtraction Rule
D. 4; Identity Property
2
Addition and Subtraction
(over Lesson 2-1)
Copy and complete the number sentence. Write the
property or rule shown.
385 + 22 = 22 + __
A. 385; Associative Property
B. 385; Identity Property
C. 22; Commutative Property
D. 385; Commutative Property
2
Addition and Subtraction
(over Lesson 2-2)
Estimate $4.69 + $5.19.
A. $9.00
B. $11.00
C. $10.00
D. $9.50
2
Addition and Subtraction
(over Lesson 2-2)
Estimate $20.59 – $17.19.
A. $3.00
B. $38.00
C. $5.00
D. $4.00
2
Addition and Subtraction
(over Lesson 2-2)
Estimate 2,466 – 1,377.
A. 2,000
B. 1,100
C. 1,400
D. 3,000
2
Addition and Subtraction
(over Lesson 2-2)
Estimate 19,556 + 14,789.
A. 34,000
B. 5,000
C. 35,000
D. 33,000
2
Addition and Subtraction
(over Lesson 2-2)
Estimate 555 + 798.
A. 1,400
B. 1,350
C. 1,300
D. 1,200
2
Addition and Subtraction
(over Lesson 2-3)
Solve. Explain why you gave an estimate or an
exact answer. A turkey sandwich costs $3.75 and a
bottle of juice costs $1.45. If Tobin buys two
sandwiches and a bottle of juice, how much change
will he receive from $10.00?
A. $1.00; estimate because the question asks
about an estimated amount of change
B. $1.05; exact answer because the question
asks about an exact amount of change
2
Addition and Subtraction
(over Lesson 2-3)
C. $0; estimate because you always estimate
when using money
D. $2.05; exact answer because the question
asks about an exact amount of change
2
Addition and Subtraction
(over Lesson 2-3)
Answer:
B. $1.05; exact answer because the question
asks about an exact amount of change
2
Addition and Subtraction
(over Lesson 2-4)
Find 568 + 29. Check you work by estimating.
A. 578
B. 607
C. 597
D. 600
2
Addition and Subtraction
(over Lesson 2-4)
Find 478 + 245. Check you work by estimating.
A. 823
B. 734
C. 712
D. 723
2
Addition and Subtraction
(over Lesson 2-4)
Find 8,238 + 676. Check you work by estimating.
A. 8,804
B. 8,914
C. 8,924
D. 9,004
2
Addition and Subtraction
(over Lesson 2-4)
Find 4,765 + 3,482. Check you work by estimating.
A. 8,247
B. 8,337
C. 8,547
D. 8,257
2
Addition and Subtraction
(over Lesson 2-4)
Find 54,763 + 2,788. Check you work by estimating.
A. 56,551
B. 57,561
C. 56,651
D. 57,551
2
Addition and Subtraction
(over Lesson 2-5)
Solve. Nori bought a game for $14.95 and a CD
for $9.88. He gave the cashier $30.00. How much
change did he receive?
A. $6.27
B. $5.17
C. $15.17
D. $5.16
2
Addition and Subtraction
(over Lesson 2-5)
Solve. Nadia guessed that there were 9,546 beans
in a jar. Steve guessed that there were 5,969 beans.
How much larger was Nadia’s guess than Steve’s?
A. 4,423
B. 6,423
C. 4,577
D. 3,577
2
Addition and Subtraction
(over Lesson 2-6)
Use any of the following strategies to solve: draw a
picture, look for a pattern, make a table. Tiana writes
the following numbers in a row: 2, 7, 9, 14, 16. What
would be the next three numbers in her pattern?
A. 21, 23, 28
B. 18, 23, 25
C. 18, 20, 22
D. 21, 26, 31
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