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Chapter 2Addition and Subtraction
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Chapter 2Addition and Subtraction
Click the mouse or press the space bar to continue.
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
22Addition and Subtraction
Five-Minute Check (over Chapter 1)
Main Idea and Vocabulary
California Standards
Key Concepts: Addition Properties
Key Concepts: Subtraction Rules
Example 1
Example 2
Example 3
2-12-1 Algebra: Addition Properties and Subtraction Rules
2-12-1 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
2-12-1 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.
Here, the order of the numbers are reversed from one side of the equal sign to the other. This is the Commutative Property of Addition because the order in which numbers are added does not change the sum.
2-12-1 Algebra: Addition Properties and Subtraction Rules
Identify the property shown by 9 + 6 = 6 + 9.
Answer: Commutative Property of Addition
2-12-1 Algebra: Addition Properties and Subtraction Rules
A. Associative Property of Addition
B. Commutative Property of Addition
C. Identity Property of Addition
D. Associative Property of Multiplication
Identify the property shown by (2 + 3) + 4 = 2 + (3 + 4).
Find 18 + 26 + 12.
You can use the Associative Property to add mentally.
2-12-1 Algebra: Addition Properties and Subtraction Rules
(26 + 18) + 12
26 + (18 + 12)
26 + 30
56
Regroup to add 18 and 12 first.
Associative Property of Addition
Add 18 and 12.
Add 26 and 30.
Answer: 56
2-12-1 Algebra: Addition Properties and Subtraction Rules
A. 30
B. 44
C. 61
D. 52
Find 13 + 31 + 17.
5 – 0 = 5
When you subtract 0 from 5, the result is 5.
2-12-1 Algebra: Addition Properties and Subtraction Rules
So, the missing number is 0.
Answer: 0
Find the missing number in 5 – = 5.
2-12-1 Algebra: Addition Properties and Subtraction Rules
A. 7
B. 0
C. 1
D. 2
Find the missing number in 7 – = 7.
Five-Minute Check (over Lesson 2-1)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
2-22-2 Estimate Sums and Differences
2-22-2 Estimate Sums and Differences
• I will estimate sums and differences of numbers.
• estimate
2-22-2 Estimate Sums and Differences
Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the subtraction of multidigit numbers.
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.
Answer: So, Sam needs to save about $280.
2-22-2 Estimate Sums and Differences
$239+ $37
$240+ $40 $280
2-22-2 Estimate Sums and Differences
A. $260
B. $270
C. $275
D. $280
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.
Estimate 6,243 + 942. Round to the hundreds place.
Round to the nearest hundreds place. Then add.
Answer: So, 6,243 + 942 is about 7,100.
2-22-2 Estimate Sums and Differences
6,243+ 942
7,100
6,200+ 900
2-22-2 Estimate Sums and Differences
A. 7,800
B. 7,700
C. 7,600
D. 7,500
Estimate 6,837 + 821. Round to the hundreds place.
Estimate $57.61 – $28.45. Round to the tens place.
Round each dollar amount to the nearest ten dollars then subtract.
Answer: So, $57.61 – $28.45 is about $30.00.
2-22-2 Estimate Sums and Differences
$57.61– $28.45
$60.00– $30.00
$30.00
2-22-2 Estimate Sums and Differences
A. $40.00
B. $10.00
C. $20.00
D. $30.00
Estimate $25.72 – $17.55. Round to the tens place.
The table shows the world’s tallest mountains. About how much taller is Mt. Everest than Lhoste? Round to the thousands place.
Round each height to the nearest thousand. Then subtract.
2-22-2 Estimate Sums and Differences
Answer: So, Mt. Everest is about 1,000 feet taller than Lhoste.
2-22-2 Estimate Sums and Differences
29,028– 27,923
29,000– 28,000
1,000
2-22-2 Estimate Sums and Differences
A. 22,000
B. 23,000
C. 22,700
D. 23,700
Estimate 74,218 – 51,933. Round to the thousands place.
Five-Minute Check (over Lesson 2-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
• I will determine when to estimate or find an exact answer.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Standard 4MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.
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?
2-32-3 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.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Plan
Since the question asks about how much money is needed, you can estimate the sum.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Solve
Round each amount to each greatest place value. Then add.
Answer: So, about $160 is needed to build the tree house.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Check
Look back at the problem. Suppose the question asked for an exact answer.
2-32-3 Problem-Solving Strategy: Estimate or Exact Answer
Since $153 is close to $160, an estimate of $160 is correct.
Five-Minute Check (over Lesson 2-3)
Main Idea
California Standards
Example 1
Example 2
2-42-4 Add Numbers
2-42-4 Add Numbers
Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
Add 4,568 + 2,429.
2-42-4 Add Numbers
Estimate 4,568+ 2,429
4,600+ 2,400
7,000
7
Step 1 Add ones.
2-42-4 Add Numbers
Step 2 Add tens.
4,568+ 2,429
1
7
4,568+ 2,429
1
9
Step 4 Add thousands.
2-42-4 Add Numbers
Check for Reasonableness
The estimate was 7,000. Since 6,997 is close to the estimate, the answer is reasonable.
997
4,568+ 2,429
1
6,
The three largest farms in Springfield are listed in the table. What is the total size of the three farms?
2-42-4 Add Numbers
Estimate 12,2508,732+ 997
12,3008,700
+ 1,00022,000
9
Step 1 Add ones.
2-42-4 Add Numbers
Step 2 Add tens.
12,2508,732
+ 997
9
12,2508,732
+ 9977
1
979
12,2508,732
+ 997
11
Step 3 Add hundreds.
2-42-4 Add Numbers
Step 4 Add thousands.
79
12,2508,732
+ 997
1
9
1
1,
1
Step 5 Add ten thousands.
2-42-4 Add Numbers
Check for Reasonableness
The estimate was 22,000. Since 21,979 is close to the estimate, the answer is reasonable.
21,979
12,2508,732
+ 997
111
2-42-4 Add Numbers
A. 38,771
B. 37,117
C. 38,717
D. 37,617
Add 33,473 + 4,522 + 722.
Five-Minute Check (over Lesson 2-4)
Main Idea
California Standards
Example 1
Example 2
2-52-5 Subtract Numbers
Subtract Numbers
2-52-5 Subtract Numbers
Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
The Hernandez family flies 9,635 miles to visit some cousins. Next year, they fly 3,867 to visit their grandmother. How much farther did they travel to see their cousins?
2-52-5 Subtract Numbers
Estimate 9,635– 3,867
9,600– 3,900
5,700
8
9,635– 3,867
152
8
Step 1 Subtract ones.
2-52-5 Subtract Numbers
Step 2 Subtract tens.
9,635– 3,867
152
6
125
68
9,635– 3,867
15212
5
Step 3 Subtract hundreds.
2-52-5 Subtract Numbers
Step 4 Subtract thousands.
7
158
5,768
9,635– 3,867
15212
515
8
Check
2-52-5 Subtract Numbers
You can use addition to check your subtraction.
So, the answer is correct. The answer, 5,768, is also close to the estimate.
5,768
9,635– 3,867
9,635
3,867+ 5,768
Answer: So, the Hernandez family traveled 5,768 miles further to see their cousins.
2-52-5 Subtract Numbers
A. 6,487
B. 5,378
C. 6,789
D. 5,738
Subtract 8,249 – 2,871.
$28
$96– $68
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?
2-52-5 Subtract Numbers
Estimate $96.47– $67.99
Subtracting money is similar to subtracting whole numbers.
8
Step 1 Subtract pennies.
2-52-5 Subtract Numbers
Step 2 Subtract dimes.
$96.47– $67.99
173
8
$96.47– $67.99
173
4
135
Step 3 Subtract dollars.
2-52-5 Subtract Numbers
Step 4 Subtract ten dollars.
8.
13
48
$96.47– $67.99
173515
8
$2
13
8.48
$96.47– $67.99
173515
8
Check
2-52-5 Subtract Numbers
So, the answer is correct. The answer, $28.48, is also close to the estimate.
$28.48
$96.47– $67.99
$96.47
$67.99+ $28.48
2-52-5 Subtract Numbers
A. $10.51
B. $9.50
C. $8.51
D. $8.49
Selena had $45.50 when she went to the store. She bought shoes for $36.99. How much does she have left?
Five-Minute Check (over Lesson 2-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
2-62-6 Problem-Solving Investigation: Choose a Strategy
2-62-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
2-62-6 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.
2-62-6 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.
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.
2-62-6 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.
2-62-6 Problem-Solving Investigation: Choose a Strategy
Plan
Use the four-step plan to find how many songs Marco has downloaded. Use repeated addition to find the answer.
2-62-6 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.
2-62-6 Problem-Solving Investigation: Choose a Strategy
Solve
2-62-6 Problem-Solving Investigation: Choose a Strategy
Answer: So, he downloaded a total of 56 songs.
Check
Look back at the problem. 56 – 14 = 42, 42 – 14 = 28, 28 – 14 = 14, and 14 – 14 = 0.
The answer is correct.
2-62-6 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 2-6)
Main Idea
California Standards
Example 1
Example 2
2-72-7 Subtract Across Zeros
2-72-7 Subtract Across Zeros
• I will subtract multidigit numbers, when some digits are zero.
2-72-7 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.
Refer to the table. How much larger is Jupiter than Earth?
2-72-7 Subtract Across Zeros
Step 1 Subtract ones.
4
142,200– 12,756
101019
Step 2 Subtract tens.
Step 3 Subtract hundreds.
2-72-7 Subtract Across Zeros
4
142,200– 12,756
101019
4
44
142,200– 12,756
101019
4
111
444
142,200– 12,756
101019
111
Step 4 Subtract thousands.
2-72-7 Subtract Across Zeros
9,
11
Step 5 Subtract ten thousands.
3
29,444
142,200– 12,756
101019
11111
3
29,444
142,200– 12,756
101019
11111
3
Step 6 Subtract hundred thousands.
2-72-7 Subtract Across Zeros
Check
You can use addition to check your subtraction. 12,756 + 129,444 = 142,200. So, the answer is correct.
1
Answer: So, Jupiter is 129,444 km larger than Earth.
2-72-7 Subtract Across Zeros
A. 68,599
B. 68,459
C. 67,461
D. 67,459
Subtract 132,788 – 64,329.
Marciel gave the store clerk $50.00 for her purchase. She received $13.56 in change. How much did she spend?
2-72-7 Subtract Across Zeros
Step 1 Subtract pennies.
4
$50.00– $13.56
4 10 10 109 9
4
$50.00– $13.56
4 10 10 109 9
Step 2 Subtract dimes.
Step 3 Subtract ones.
2-72-7 Subtract Across Zeros
4
44
$50.00– $13.56
4 10 10 109 9
6.
Step 4 Subtract tens.
2-72-7 Subtract Across Zeros
Answer: So, Marciel spent $36.44.
6.44
$50.00– $13.56
4 10 10 109 9
$3
2-72-7 Subtract Across Zeros
A. $21.26
B. $22.76
C. $22.27
D. $21.76
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?
22Addition and Subtraction
Five-Minute Checks
Subtract Numbers
22Addition 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)
22Addition and Subtraction
(over Chapter 1)
A. Roberto’s family travels 200 miles in 6 hours; it will take Lee Ann’s family 4 hours to travel 200 miles.
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?
B. Roberto’s family travels 2,400 miles in 6 hours; it will take Lee Ann’s family 4 hours to travel 2400 miles.
22Addition and Subtraction
C. Roberto’s family travels 240 miles in 6 hours; it will take Lee Ann’s family 4 hours to travel 240 miles.
(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?
D. Roberto’s family travels 280 miles in 6 hours; it will take Lee Ann’s family 5 hours to travel 280 miles.
22Addition and Subtraction
C. Roberto’s family travels 240 miles in 6 hours; it will take Lee Ann’s family 4 hours to travel 240 miles.
(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?
22Addition and Subtraction
A. 0; Associative Property
B. 0; Identity Property
C. 7; Identity Property
D. 1; Commutative Property
(over Lesson 2-1)
7 + __ = 7
Copy and complete each number sentence. Write the property or rule shown.
22Addition and Subtraction
A. 9; Associative Property
B. 2; Commutative Property
C. 2; Associative Property
D. 7; Associative Property
(over Lesson 2-1)
Copy and complete each number sentence. Write the property or rule shown.
(9 + 2) + 7 = 9 + (__ + 7)
22Addition and Subtraction
A. 4; Subtraction Rule
B. 0; Identity Property
C. 0; Subtraction Rule
D. 4; Identity Property
(over Lesson 2-1)
Copy and complete each number sentence. Write the property or rule shown.
4 – __ = 0
22Addition and Subtraction
A. 385; Associative Property
B. 385; Identity Property
C. 22; Commutative Property
D. 385; Commutative Property
(over Lesson 2-1)
Copy and complete each number sentence. Write the property or rule shown.
385 + 22 = 22 + __
22Addition and Subtraction
A. $9.00
B. $11.00
C. $10.00
D. $9.50
(over Lesson 2-2)
Estimate each sum or difference.
$4.69 + $5.19
22Addition and Subtraction
A. $3.00
B. $38.00
C. $5.00
D. $4.00
(over Lesson 2-2)
Estimate each sum or difference.
$20.59 – $17.19
22Addition and Subtraction
A. 2,000
B. 1,000
C. 1,400
D. 3,000
(over Lesson 2-2)
Estimate each sum or difference.
2,466 – 1,377
22Addition and Subtraction
A. 34,000
B. 5,000
C. 35,000
D. 33,000
(over Lesson 2-2)
Estimate each sum or difference.
19,556 + 14,789
22Addition and Subtraction
A. 1,400
B. 1,350
C. 1,300
D. 1,200
(over Lesson 2-2)
Estimate each sum or difference.
555 + 798
22Addition and Subtraction
A. $1.00; estimate because the question asks about an estimated amount of change
(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?
B. $1.05; exact answer because the question asks about an exact amount of change
22Addition and Subtraction
C. $0; estimate because you always estimate when using money
(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?
D. $2.05; exact answer because the question asks about an exact amount of change
22Addition 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?
B. $1.05; exact answer because the question asks about an exact amount of change
22Addition and Subtraction
A. 1,283
B. 8,137
C. 8,247
D. 8,237
(over Lesson 2-4)
Find each sum. Check you work by estimating.
4,765 + 3,482
22Addition and Subtraction
A. 57,451
B. 51,975
C. 56,441
D. 57,551
(over Lesson 2-4)
Find each sum. Check you work by estimating.
54,763 + 2,788
22Addition and Subtraction
(over Lesson 2-4)
A. 113,354
B. 124,364
C. 114,364
D. 134,354
Find each sum. Check you work by estimating.
78,539 + 45,825
22Addition and Subtraction
A. 1,336,379
B. 1,335,379
C. 1,235,379
D. 1,336,378
(over Lesson 2-4)
Find each sum. Check you work by estimating.
890,456 + 445,923
22Addition and Subtraction
A. 415,586
B. 324,906
C. 315,686
D. 415,686
(over Lesson 2-4)
Find each sum. Check you work by estimating.
45,390 + 370,296
22Addition and Subtraction
A. $6.27
B. $5.17
C. $15.17
D. $5.16
(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?
22Addition and Subtraction
A. 4,423
B. 6,423
C. 4,577
D. 3,577
(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?
22Addition and Subtraction
A. 21, 23, 28
B. 18, 23, 25
C. 18, 20, 22
D. 21, 26, 31
(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?
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