Develop Skills and Strategies
Lesson 3
Part 1: Introduction
CCSS
4.NBT.B.4
Add and Subtract Whole Numbers
In this lesson, you will use place-value understanding and basic facts to add
and subtract numbers. Take a look at this problem.
Katie has 3,437 stamps in her collection and Steve has 942 stamps in his
collection. How many stamps do Katie and Steve have in all?
Explore It
Use the math you already know to solve the problem.
What operation can you use to find the number of stamps Katie and Steve have
in all? What is the sum of the digits in the ones place? What is the sum of the digits in the tens place? What is the sum of the digits in the hundreds place? What is the sum of the digits in the thousands place? Which place value has a sum of more than 10? Explain how you can find the number of stamps Katie and Steve have in all.
16
L3: Add and Subtract Whole Numbers
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Part 1: Introduction
Lesson 3
Find Out More
There are many different ways to add numbers. For example, you can use base-ten
blocks, or place-value drawings. You can break numbers apart and add the parts.
When you add numbers in the thousands, some methods are more convenient
than others.
You can stack the numbers and line up place values. Here is one way to find the sum
on page 16. Add from right to left. Add the ones, add the tens, add the hundreds, and
then add the thousands.
3,437
1   942
9
70
1,300
1 3,000
7 ones 1 2 ones 5 9 ones
3 tens 1 4 tens 5 7 tens
4 hundreds 1 9 hundreds 5 13 hundreds or 1 thousand 1 3 hundreds
3 thousands
4,379
Katie and Steve have 4,379 stamps in all.
Reflect
1 Solve the problem above by adding left to right: thousands, hundreds, tens, ones.
Describe how the methods are alike and how they are different.
3,437
1   942
L3: Add and Subtract Whole Numbers
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17
Part 2: Modeled Instruction
Lesson 3
Read the problem below. Then explore different ways to add four-digit numbers.
At a fair, 4,657 ride tickets were sold on Saturday and 3,804 were sold on
Sunday. How many tickets were sold in all during those two days?
Model It
You can use place value to add. Add ones to ones, tens to tens, hundreds to
hundreds, thousands to thousands.
4,657
1 3,804
11
50
1,400
1 7,000
7 ones 1 4 ones 5 11 ones or 1 ten 1 1 one
5 tens 1 0 tens 5 5 tens
6 hundreds 1 8 hundreds 5 14 hundreds or 1 thousand 1 4 hundreds
4 thousands 1 3 thousands 5 7 thousands
8,461
Model It
You can record the sums by showing regrouping above the problem.
1
4,657
1 3,804
1
7 ones 1 4 ones 5 11 ones or 1 ten 1 1 one
1
4,657
1 3,804
61
1
1 ten 1 5 tens 1 0 tens 5 6 tens
1
4,657
1 3,804
461
1
6 hundreds 1 8 hundreds 5 14 hundreds or 1 thousand 1 4 hundreds
1
4,657
1 3,804
18
8,461
1 thousand 1 4 thousands 1 3 thousands 5 8 thousands
L3: Add and Subtract Whole Numbers
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Part 2: Guided Instruction
Lesson 3
Connect It
Now you will see how to solve the problem by showing all the steps at once.
2 Here is what the second model looks like showing all the steps at once.
1
1
4,657
1 3,804
8,461
The sum of the ones values is 11. Where do you see the 11 in the equation above?
3 The sum of the hundreds values is 1,400. Where do you see the 1,400 in the
equation above?
4 Why are there numbers above the tens place and above the thousands place?
5 Explain how to add two four-digit numbers if you need to regroup tens and
hundreds. Try It
Use what you just learned to solve this problem. Show your work two ways on a
separate sheet of paper.
6 A video game company sold 5,680 copies of its new game on the first day and
3,235 copies on the second day. In just two days, how many copies of the game
did the company sell? L3: Add and Subtract Whole Numbers
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19
Part 3: Modeled Instruction
Lesson 3
Read the problem below. Then explore different ways to subtract numbers.
Last week, Mr. Diaz flew 4,002 miles for work. This week, he flew 2,153 miles.
How many more miles did Mr. Diaz fly last week than this week?
Model It
You can use place value to subtract 4,002 2 2,153.
You can’t subtract 3 from 2, so you need to borrow and regroup to subtract the ones
digits. Write 4,002 in a place-value chart. You can’t borrow from the tens or hundreds
places, so borrow from the thousands place. Keep regrouping until you can subtract.
Thousands Hundreds Tens
4
0
0
Ones
2
3
10
0
2
4 thousands 5 3 thousands 1 10 hundreds
3
9
10
2
10 hundreds 5 9 hundreds 1 10 tens
3
9
9
10 1 2 5 12 10 tens 5 9 tens 1 10 ones
Now you can subtract.
Thousands Hundreds Tens
3
9
9
2
2
1
5
1
8
4
20
Ones
12
 3
 9
L3: Add and Subtract Whole Numbers
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Part 3: Guided Instruction
Lesson 3
Connect It
Now you will solve the problem from the previous page by showing regrouping
above the problem.
4,002
2 2,153
9
3 1010
3 10
4,002
2 2,153
99
3 101012
4,002
2 2,153
4,002
2 2,153
1,849
7 How is regrouping thousands shown in the problem above? 8 Why is the 10 crossed out in the hundreds column? 9 Explain the regrouping shown in the tens column. 10 Why are 12 ones shown in the ones column? 11 Explain how to subtract two four-digit numbers if you need to regroup in all
places. Try It
Use what you just learned to solve these problems. Show your work on a
separate sheet of paper.
12 There were 11,402 fans at the Hawks game and 9,617 fans at the Bulls game. How
many more fans attended the Hawks game than the Bulls game? 13 129,027 2 98,918 5 L3: Add and Subtract Whole Numbers
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Part 4: Guided Practice
Lesson 3
Study the model below. Then solve problems 14–16.
Student Model
The student regrouped
1 ten to make 10 ones.
Sallie earned $4,580 last month. Her bills for that month
totaled $3,178. How much money does Sallie have left after she
pays her bills?
Look at how you could show your work.
7 10
4,580
2 3,178
1,402
Pair/Share
What is another way
you could solve this
problem?
What operation can
you use to solve this
problem?
Solution: $1,402
14 The population of Turtle Valley is 407,989. The population of
Art Creek is 86,966. What is the total population of the two cities?
Show your work.
Pair/Share
How did you decide
which operation to use?
22
Solution: L3: Add and Subtract Whole Numbers
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Part 4: Guided Practice
15 On Friday, 13,728 tickets were sold for a play. On Saturday,
15,419 tickets were sold, and 12,399 tickets were sold on Sunday.
What was the total number of tickets sold for the play?
Lesson 3
Does this problem use
addition or subtraction?
Show your work.
Pair/Share
Solution: 16 The Pyramid of Khafra, in Egypt, is 448 feet tall. The Eiffel Tower,
in France, is 1,063 feet tall. How much taller is the Eiffel Tower
than the Pyramid of Khafra? Circle the letter of the correct answer.
How can you check
your answer?
Do you need to regroup
to solve this problem?
A 515 feet
B 615 feet
C 625 feet
D 1,511 feet
Cara chose D as the correct answer. How did she get that answer?
L3: Add and Subtract Whole Numbers
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Pair/Share
How can you tell if
Cara’s answer is
reasonable by looking
at the two given
heights?
23
Part 5: Common Core Practice
Lesson 3
Solve the problems.
1 Josh’s web site had 805,289 visitors. Diego’s site had 784,976 visitors. How many more
visitors did Josh’s site have than Diego’s?
A20,313
B21,313
C101,713
D181,713
2 Prince Edward Island in Canada is made up of three counties: Kings, Prince, and
Queens. In 2011, there were 17,990 people living in Kings. There were 44,348 people
living in Prince. How many people were living in Queens if the total number of people
living on Prince Edward Island was 140,204?
A62,338
B77,866
C122,134
D202,542
3 Tell whether each number sentence is True or False.
24
a.538 1 491 5 1,029
True
False
b.8,902 2 3,407 5 5,405
True
False
c.16,234 2 5,235 5 999
True
False
d.729 1 385 5 1,014
True
False
L3: Add and Subtract Whole Numbers
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Part 5: Common Core Practice
Lesson 3
4 Seventh- and eighth-grade students attend the junior high school. This year there are
122 more seventh graders than there were last year. Use this information to fill in the
data that are missing from the table.
7th Graders
Last Year
This Year
8th Graders
1,043
Total
2,185
1,027
5 A school raised $13,809 during its fall fundraiser and $20,786 during its winter
fundraiser. The goal for all fundraisers is $50,000. How much more money does the
school need to raise during the spring fundraiser to reach its goal?
Show your work.
Answer The school needs to raise during the spring fundraiser.
6 Effie’s store has 10,908 more comic books than Brody’s store. Brody’s store has
45,607 comic books. How many comic books do Effie’s and Brody’s stores have
altogether?
Show your work.
Answer The stores have comic books altogether.
Self Check Go back and see what you can check off on the Self Check on page 1.
L3: Add and Subtract Whole Numbers
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25
Develop Skills and Strategies
Lesson 3
(Student Book pages 16–25)
Add and Subtract Whole Numbers
Lesson Objectives
The Learning Progression
•Use the standard algorithm to add multi-digit
whole numbers.
In Grade 3, students fluently added and subtracted
2- and 3-digit numbers. In Grade 4, students are
expected to be proficient with adding and subtracting
numbers up to 999,999. In this lesson, students use the
strategies they have gained in earlier grades to build an
understanding of the standard algorithm. The use of
place-value charts helps students begin to understand
the process of lining up numbers by place value. This is
an important concept to master, because in Grade 5
students will extend this concept to add and subtract
with decimals.
•Use the standard algorithm to subtract multi-digit
whole numbers.
Prerequisite SkilLs
In order to be proficient with the concepts/skills in this
lesson, students should:
•Recall basic addition facts.
•Recall basic subtraction facts.
•Understand place value.
Teacher Toolbox
•Recognize addition and subtraction as
inverse operations.
Vocabulary
There is no new vocabulary.
Ready Lessons
Teacher-Toolbox.com
Prerequisite
Skills
4.NBT.B.4
4.NBT.4
✓
✓
✓
✓
Tools for Instruction
Interactive Tutorials
CCSS Focus
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
ADDITIONAL STANDARDS: 4.NBT.A.2 (See page A44 for full text.)
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 2, 5, 7, 8 (see page A9 for full text)
L3: Add and Subtract Whole Numbers
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19
Part 1: Introduction
Lesson 3
At a Glance
Students read a word problem and answer a series of
questions to explore a method to add a 3-digit number
to a 4-digit number.
Develop skills and strategies
Lesson 3
Part 1: introduction
ccss
4.nbt.b.4
add and subtract Whole numbers
in this lesson, you will use place-value understanding and basic facts to add
and subtract numbers. take a look at this problem.
Step By Step
Katie has 3,437 stamps in her collection and Steve has 942 stamps in his
•Tell students that this page models how to add two
numbers by place value.
collection. How many stamps do Katie and Steve have in all?
explore it
•Have students read the problem at the top of the page.
use the math you already know to solve the problem.
What operation can you use to find the number of stamps Katie and Steve have
in all? addition
•Work through Explore It as a class.
•Ask students to explain how they found the total
number of ones.
What is the sum of the digits in the ones place?
9
What is the sum of the digits in the tens place?
7
What is the sum of the digits in the hundreds place?
13
What is the sum of the digits in the thousands place?
•Ask students to explain the significance of the fact
that there are more than 10 hundreds.
Which place value has a sum of more than 10?
3
hundreds
Explain how you can find the number of stamps Katie and Steve have in all.
you can think of 13 hundreds as 1 thousand 1 3 hundreds.
•Ask student pairs or groups to explain their answers
for the remaining questions.
then you can add the thousands, hundreds, tens, and ones:
3,000 1 1,000 1 300 1 70 1 9 5 4,379. so, katie and steve have
4,379 stamps in all.
SMP Tip: Students are learning how to make sense
of large numbers and their meaning in contextual
situations. Guide students to make connections
between place value, operations with large numbers,
and their relationships in problem situations.
(SMP 2)
16
L3: Add and Subtract Whole Numbers
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Mathematical Discourse
•How can place value be used to determine the sum or
difference of two numbers?
Students’ responses should include the concept
of finding the sum of each place value and then
regrouping when the sum of the digits in a
place value is greater than 10.
Likewise, you subtract the digits in each place
value and borrow and regroup when the top
digit is smaller than the bottom digit.
20
L3: Add and Subtract Whole Numbers
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Part 1: Introduction
Lesson 3
At a Glance
Students use the standard algorithm to add two
numbers. They learn that you can add the ones digits,
the tens digits, the hundreds digits, and the thousands
digits. Once they have partial sums for each place
value, the sum of the partial sums is the grand total.
Step By Step
•Read Find Out More as a class.
•Point out that there are four partial sums because
there are four digits in the greater number.
•Walk through the equation and make sure students
understand how each partial sum is derived. Pay
special attention to the sum of the digits in the
hundreds place.
Hands-On Activity
Use counters to understand adding numbers.
Materials: beads (4 different colors) or other form of
counters, one piece of paper for each student with a
line drawn horizontally to divide the paper in half
Part 1: introduction
Find out More
There are many different ways to add numbers. For example, you can use base-ten
blocks, or place-value drawings. You can break numbers apart and add the parts.
When you add numbers in the thousands, some methods are more convenient
than others.
You can stack the numbers and line up place values. Here is one way to find the sum
on page 16. Add from right to left. Add the ones, add the tens, add the hundreds, and
then add the thousands.
3,437
1 942
•Write an addition problem on the board.
•Students should represent each number using
their beads (for example, 1,423 would be 1 green,
4 yellow, 2 blue, and 3 red beads). Have students
put the beads for each number above the line on
their paper.
7 ones 1 2 ones 5 9 ones
3 tens 1 4 tens 5 7 tens
4 hundreds 1 9 hundreds 5 13 hundreds or 1 thousand 1 3 hundreds
3 thousands
9
70
1,300
1 3,000
4,379
Katie and Steve have 4,379 stamps in all.
reflect
1 Solve the problem above by adding left to right: thousands, hundreds, tens, ones.
Describe how the methods are alike and how they are different.
3,437
1 942
3,000
1,300
70
1
9
4,379
the answer is the same. the four sums are the same, but the order is
reversed.
L3: Add and Subtract Whole Numbers
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•Identify the place value represented by each color
(for example, red: ones, blue: tens, yellow:
hundreds, green: thousands). Post a visual
reminder of what each color represents on the
board for students.
Lesson 3
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17
Real-World Connection
Have students name everyday places and situations
in which large numbers are combined (added) or
separated (subtracted).
Examples: attendance at sporting events, number of
students attending a school, amount of money
earned by an adult or small business
•Show students how the beads can be grouped
together by color to represent addition by place
value. Have students group the beads together
below the line on their paper.
•Explain to students that if there is more than 10
of any one color they must exchange 10 of that
color for 1 bead of the next higher place value. For
example, 12 blue beads would be changed to 1 red
bead and 2 blue beads.
•Provide students with additional problems to
practice independently using the beads.
L3: Add and Subtract Whole Numbers
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21
Part 2: Modeled Instruction
Lesson 3
At a Glance
Part 2: Modeled instruction
Students use partial sums and the standard algorithm
to find the total of two given values.
Lesson 3
read the problem below. then explore different ways to add four-digit numbers.
At a fair, 4,657 ride tickets were sold on Saturday and 3,804 were sold on
Step By Step
Sunday. How many tickets were sold in all during those two days?
•Read the problem at the top of the page as a class.
Model it
you can use place value to add. add ones to ones, tens to tens, hundreds to
hundreds, thousands to thousands.
•Read the first Model It. Have a volunteer explain
which key words in the problem indicate that it is an
addition problem. [sold in all]
4,657
1 3,804
11
50
1,400
1 7,000
•Ask students how many partial sums are shown. [4]
7 ones 1 4 ones 5 11 ones or 1 ten 1 1 one
5 tens 1 0 tens 5 5 tens
6 hundreds 1 8 hundreds 5 14 hundreds or 1 thousand 1 4 hundreds
4 thousands 1 3 thousands 5 7 thousands
8,461
•Have students identify the place values in which
regrouping could occur. [ones and hundreds]
Model it
you can record the sums by showing regrouping above the problem.
1
•Read the second Model It.
4,657
1 3,804
•Ask students to explain why there is an extra digit
above the numbers in the tens column.
4,657
1 3,804
1
61
1
•Ask a volunteer to predict where another such small
digit may be placed if the addition problem continues
using this algorithm.
Use base-ten blocks to understand adding
numbers.
Materials: base-ten blocks (blocks, rods, flats,
and cubes)
•Present students with various 1-, 2-, 3- and 4-digit
numbers and have them practice representing
numbers with the base-ten blocks. Students
should have a strong understanding of
representing numbers before moving to addition.
1 ten 1 5 tens 1 0 tens 5 6 tens
1
4,657
1 3,804
461
1
6 hundreds 1 8 hundreds 5 14 hundreds or 1 thousand 1 4 hundreds
1
4,657
1 3,804
8,461
Hands-On Activity
7 ones 1 4 ones 5 11 ones or 1 ten 1 1 one
1
18
1 thousand 1 4 thousands 1 3 thousands 5 8 thousands
L3: Add and Subtract Whole Numbers
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Mathematical Discourse
•Explain how to add numbers with regrouping.
Students should be able to identify sums that
are 10 or greater and will require regrouping.
For example, the sum of 7 and 4 is 11, which is
10 1 1. The 1 more ten would need to be added
to the tens column.
•Present an addition problem using 3- and 4-digit
numbers on the board for the class.
•Students should represent each number using
their base-ten blocks.
•Show students how the blocks can be grouped
together to represent addition.
•Explain to the students how to regroup when
groups of 10 or 100 can be made.
•Provide students with additional problems to
practice independently using the blocks.
22
L3: Add and Subtract Whole Numbers
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Part 2: Guided Instruction
Lesson 3
At a Glance
Students revisit the problem on page 18.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 18.
Part 2: guided instruction
Lesson 3
connect it
now you will see how to solve the problem by showing all the steps at once.
2 Here is what the second model looks like showing all the steps at once.
1
1
4,657
1 3,804
8,461
•Have students explain their answer to problem 3.
Have students use a colored pencil or some other
media to connect the partial sums on page 17 to the
model on page 18.
The sum of the ones values is 11. Where do you see the 11 in the equation above?
the 1 above the tens place and the 1 in the ones place
3 The sum of the hundreds values is 1,400. Where do you see the 1,400 in the
equation above?
the 1 above the thousands place and the 4 in the hundreds place
4 Why are there numbers above the tens place and above the thousands place?
SMP Tip: Explain to students that there are
multiple ways to solve a problem and to arrive at
the correct solution. Students should begin to see
patterns in adding and subtracting large numbers
and become fluent in using more general methods
and shortcuts to solve problems. (SMP 8)
there are more than 10 ones, so you need to regroup 10 ones as 1 ten.
there are more than 10 hundreds, so you need to regroup 10 hundreds
as 1 thousand.
5 Explain how to add two four-digit numbers if you need to regroup tens and
hundreds. Possible answer: add the ones, add the tens, and regroup 10 tens
as 1 hundred. then add the hundreds, including the regrouped hundred,
and regroup 10 hundreds as 1 thousand. add the thousands including the
regrouped thousand.
try it
use what you just learned to solve this problem. show your work two ways on a
separate sheet of paper.
6 A video game company sold 5,680 copies of its new game on the first day and
3,235 copies on the second day. In just two days, how many copies of the game
did the company sell? 8,915 copies
L3: Add and Subtract Whole Numbers
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ELL Support
Students may show proficiency working with the
algorithms for adding or subtracting numbers
but not fully understand the vocabulary and
concepts of place value. Have students talk about
their mathematical thinking to ensure they fully
understand both the vocabulary and concepts.
Students may become confused when reading
word problems and determining the correct
operation. For example, the question “how many
are left” could be confusing if the student interprets
“left” as a directional word instead of a word
signaling subtraction.
L3: Add and Subtract Whole Numbers
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19
Try It Solutions
6Solution: 8,915 copies; Students may add the
numbers using partial sums or may use the
standard algorithm. The sum of the digits in the
tens place will have to be regrouped when using
the standard algorithm.
ERROR ALERT: Students who wrote 8,815 did not
regroup properly or they forgot to include the extra
1 when adding the hundreds. Students who wrote
8,816 did not regroup properly. Those students
regrouped the number of tens in the tens and ones
places instead of in the hundreds and tens places.
23
Part 3: Modeled Instruction
Lesson 3
At a Glance
Part 3: Modeled instruction
Students use a place-value chart to subtract one number
from another.
read the problem below. then explore different ways to subtract numbers.
Last week, Mr. Diaz flew 4,002 miles for work. This week, he flew 2,153 miles.
Step By Step
How many more miles did Mr. Diaz fly last week than this week?
•Read the problem at the top of the page as a class.
Model it
you can use place value to subtract 4,002 2 2,153.
•Read Model It. Have a volunteer explain which key
words in the problem indicate that it is a subtraction
problem. [more miles last week than this week]
You can’t subtract 3 from 2, so you need to borrow and regroup to subtract the ones
digits. Write 4,002 in a place-value chart. You can’t borrow from the tens or hundreds
places, so borrow from the thousands place. Keep regrouping until you can subtract.
thousands hundreds tens
4
0
0
•Have students explain why they need to regroup
4 thousands as 3 thousands and 10 hundreds. Look
for answers that indicate 1 hundred cannot be taken
away from 0 hundreds.
Materials: 1 digit number cards, wipe-off boards,
and dry-erase markers
2
4 thousands 5 3 thousands 1 10 hundreds
10
2
10 hundreds 5 9 hundreds 1 10 tens
9
10 1 2 5 12
3
10
0
3
9
3
9
2
20
Use number cards to understand subtracting
numbers.
ones
2
10 tens 5 9 tens 1 10 ones
Now you can subtract.
•Have students explain why they need to regroup
10 hundreds as 9 hundreds and 10 tens. Look for
answers that indicate 5 tens cannot be taken away
from 0 tens.
Hands-On Activity
Lesson 3
thousands hundreds tens
3
9
9
2
1
5
1
8
4
ones
12
3
9
L3: Add and Subtract Whole Numbers
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Mathematical Discourse
•How can you use estimation to check your answer to
a subtraction problem?
Listen for responses that use rounding each
number to the nearest thousand or hundred
and finding the estimated difference.
•Students select 4 cards and place them in order to
represent the ones, tens, hundreds, and thousands
places of a number.
•Students select 4 more cards to represent the
digits of the second number.
•Students write out the two numbers formed by
the cards on their wipe-off board, putting the
greater number on top and the lesser number on
the bottom.
•Students use place value or regrouping methods
to subtract the two numbers.
•This activity can be started by using only
2 number cards and working up to 4.
24
L3: Add and Subtract Whole Numbers
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Part 3: Guided Instruction
Lesson 3
At a Glance
Students revisit the problem on page 20.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 20.
•Have students explain their answer to problem 11.
Ask, Why do you need to regroup the amount in the
ones column? [You cannot take 3 ones away from
2 ones.]
•Ask, For every subtraction problem, will you always
have to regroup in each place value? [No; only when
there are more units in the place value position of
the number being subtracted than there are in the
number being subtracted from.]
Part 3: guided instruction
Lesson 3
connect it
now you will solve the problem from the previous page by showing regrouping
above the problem.
4,002
2 2,153
3 10
4,002
2 2,153
9
3 1010
4,002
2 2,153
99
3 101012
4,002
2 2,153
1,849
7 How is regrouping thousands shown in the problem above? 4 thousands is
changed to 3 thousands and the hundreds digit is changed to 10.
8 Why is the 10 crossed out in the hundreds column? 1 hundred needs to be
regrouped and added to the tens column.
9 Explain the regrouping shown in the tens column. First, 1 hundred is
regrouped as 10 tens, and then 1 ten is regrouped as 10 ones.
10 Why are 12 ones shown in the ones column? a ten is regrouped as 10 ones
and then added to the 2 ones.
11 Explain how to subtract two four-digit numbers if you need to regroup in all
places. Possible answer: regroup 1 thousand as 10 hundreds, then
1 hundred as 10 tens, and then 1 ten as 10 ones. add the 10 ones to the top
digit in the ones column, and then subtract the ones. then subtract the
tens, hundreds, and thousands.
try it
use what you just learned to solve these problems. show your work on a
separate sheet of paper.
12 There were 11,402 fans at the Hawks game and 9,617 fans at the Bulls game. How
many more fans attended the Hawks game than the Bulls game?
13 129,027 2 98,918 5
L3: Add and Subtract Whole Numbers
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Concept Extension
Help students see the connection between
regrouping in an addition problem and regrouping
in a subtraction problem.
•Explain to students that if you do not have
enough to subtract from in the ones column, then
you need to borrow a group of 10 ones from the
tens column.
•Demonstrate with base-ten blocks how to take
10 (one rod) from the tens column and change it
into 10 unit blocks to add to the ones column.
Emphasize to students that even though the
number looks different, the value has not changed.
•Further develop the concept of regrouping with
subtraction by pointing out what to do if there are
no tens to borrow from. Demonstrate with baseten blocks how to borrow a group of 100 (one flat)
from the hundreds column and change it into
10 rods. Explain that there are now enough tens
to borrow from for the ones column.
L3: Add and Subtract Whole Numbers
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1,785 fans
30,109
Copying is not permitted.
21
Try It Solutions
12 Solution: 1,785 fans; Students need to regroup
the digits in each place-value position. Before
subtracting, the number representing the fans
at the Hawks game will have 0 ten thousands,
10 thousands, 13 hundreds, 9 tens, and 12 ones.
ERROR ALERT: Students who wrote 18,215
subtracted the lesser digit from the greater digit in
each place-value position. Those students need to
be reminded that they are in essence changing the
location of digits from one number to another and
are thereby changing the meaning of the given
information.
13 Solution: 30,109; Students should regroup digits as
needed. They will not need to regroup digits more
than once in the tens and thousands places.
25
Part 4: Guided Practice
Lesson 3
Part 4: guided Practice
Lesson 3
study the model below. then solve problems 14–16.
Student Model
The student regrouped
1 ten to make 10 ones.
Sallie earned $4,580 last month. Her bills for that month
totaled $3,178. How much money does Sallie have left after she
Part 4: guided Practice
15 On Friday, 13,728 tickets were sold for a play. On Saturday,
15,419 tickets were sold, and 12,399 tickets were sold on Sunday.
What was the total number of tickets sold for the play?
Lesson 3
Does this problem use
addition or subtraction?
Show your work.
pays her bills?
Look at how you could show your work.
7 10
4,580
2 3,178
1,402
Pair/share
What is another way
you could solve this
problem?
What operation can
you use to solve this
problem?
Solution: $1,402
Pair/share
14 The population of Turtle Valley is 407,989. The population of
Art Creek is 86,966. What is the total population of the two cities?
Show your work.
Solution: 41,546 tickets
16 The Pyramid of Khafra, in Egypt, is 448 feet tall. The Eiffel Tower,
in France, is 1,063 feet tall. How much taller is the Eiffel Tower
than the Pyramid of Khafra? Circle the letter of the correct answer.
How can you check
your answer?
Do you need to regroup
to solve this problem?
a 515 feet
Pair/share
How did you decide
which operation to use?
Solution: 494,955
b
615 feet
c
625 feet
D 1,511 feet
Cara chose D as the correct answer. How did she get that answer?
she added the numbers instead of subtracting.
22
L3: Add and Subtract Whole Numbers
Pair/share
How can you tell if
Cara’s answer is
reasonable by looking
at the two given
heights?
L3: Add and Subtract Whole Numbers
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Copying is not permitted.
23
At a Glance
Solutions
Students use place-value charts and the standard
algorithm to solve problems involving addition and
subtraction of whole numbers.
Ex The standard algorithm is shown as one way to
solve the problem. Students need to regroup the
number of tens as 7 and the number of ones as
10 before subtracting in each place-value position.
Step By Step
14 Solution: 494,955; Students regroup 15 ones as 1 ten
and 5 ones, 15 tens as 1 hundred and 5 tens,
19 hundreds as 1 thousand and 9 hundreds, and
14 thousands as 1 ten thousand and 4 thousands.
(DOK 1)
•Ask students to solve the problems individually and
label units in their calculations.
•When students have completed each problem, have
them Pair/Share to discuss their solutions with a
partner or in a group.
15 Solution: 41,546 tickets; Students can add the
numbers in any order. (DOK 2)
16 Solution: B; Finding the difference between two
heights requires subtraction: 1,063 2 448 5 615.
Explain to students why the other two answer
choices are not correct:
A is not correct because 10 hundreds 2 4 hundreds
5 6 hundreds, not 5 hundreds.
C is not correct because the top ones digit was
subtracted from the bottom ones digit, so no
regrouping was done. (DOK 3)
26
L3: Add and Subtract Whole Numbers
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Part 5: Common Core Practice
Part 5: common core Practice
Lesson 3
Solve the problems.
1
4
Lesson 3
Seventh- and eighth-grade students attend the junior high school. This year there are
122 more seventh graders than there were last year. Use this information to fill in the
data that are missing from the table.
7th Graders
8th Graders
Total
20,313
Last Year
1,043
1,142
2,185
B
21,313
This Year
1,165
1,027
2,192
C
101,713
D
181,713
5
Prince Edward Island in Canada is made up of three counties: Kings, Prince, and
Queens. In 2011, there were 17,990 people living in Kings. There were 44,348 people
living in Prince. How many people were living in Queens if the total number of people
living on Prince Edward Island was 140,204?
A
3
Part 5: common core Practice
Josh’s web site had 805,289 visitors. Diego’s site had 784,976 visitors. How many more
visitors did Josh’s site have than Diego’s?
A
2
Lesson 3
A school raised $13,809 during its fall fundraiser and $20,786 during its winter
fundraiser. The goal for all fundraisers is $50,000. How much more money does the
school need to raise during the spring fundraiser to reach its goal?
Show your work.
Possible work:
Money raised
1
62,338
B
77,866
C
122,134
D
202,542
1
50,000
2 34,595
15,405
Answer The school needs to raise
6
Tell whether each number sentence is True or False.
3 True
a.
538 1 491 5 1,029
b.
8,902 2 3,407 5 5,405
True
c.
16,234 2 5,235 5 999
True
d.
729 1 385 5 1,014
True
False
3 False
3 False
3 False
Money left to raise
4 9 9 9 10
13,809
1 20,786
34,595
$15,405
during the spring fundraiser.
Effie’s store has 10,908 more comic books than Brody’s store. Brody’s store has
45,607 comic books. How many comic books do Effie’s and Brody’s stores have
altogether?
Show your work.
Possible work:
effie’s store
1
1
45,607
1 10,908
56,515
Answer The stores have
102,122
both stores
11
1
56,515
1 45,607
102,122
comic books altogether.
self check Go back and see what you can check off on the Self Check on page 1.
24
L3: Add and Subtract Whole Numbers
L3: Add and Subtract Whole Numbers
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At a Glance
Students use place-value concepts and regrouping to
solve problems that might appear on a mathematics test.
Solutions
1Solution: A; Subtract the number of visitors to
Diego’s site from the number of visitors to Josh’s site.
(DOK 1)
2Solution: B; Find the population of Kings and
Prince. Subtract the sum from the population of
Prince Edward Island. (DOK 2)
3Solution: a. True b. False c. False d. False (DOK 2)
L3: Add and Subtract Whole Numbers
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Copying is not permitted.
25
4Solution: See completed table above; Add last
year’s 7th graders (1,043) and 122 to find this year’s
7th graders (1,165). Then add 1,165 and this year’s
8th graders (1,027) to find the total for this year
(2,192). Finally, subtract last year’s 7th graders
(1,043) from last year’s total (2,185) to find last
year’s 8th graders (1,142). (DOK 2)
5Solution: $15,405; Add the amounts raised in the fall
and winter. Subtract that sum from the goal
amount, $50,000. (DOK 2)
6Solution: 102,122; Add to find the number of comic
books in Effie’s store. Then add the number of
comic books in Effie’s store (56,515) and the
number of comic books in Brody’s store (45,607).
(DOK 2)
27
Differentiated Instruction
Lesson 3
Assessment and Remediation
•Ask students to find the difference of 46,487 and 39,728. [6,759]
•For students who are still struggling, use the chart below to guide remediation.
•After providing remediation, check students’ understanding. Ask students to explain their thinking while
finding the difference of 34,716 and 15,743. [18,973]
•If a student is still having difficulty, use Ready Instruction, Level 3, Lesson 9.
If the error is . . .
Students may . . .
To remediate . . .
86,215
have added.
Remind students that “difference” means subtraction.
13,361
have subtracted each
lesser digit from each
greater digit.
Remind students that if the digits in the number being
subtracted are greater than the digits they are subtracting from,
they need to regroup.
17,769
not have regrouped
the ten thousands,
thousands, or
hundreds places.
Remind students that they must regroup two place values each
time they need to regroup a number.
16,759
not have regrouped the
ten thousands.
Remind students that they must regroup all of the place values,
including the ten thousands place.
Hands-On Activity
Challenge Activity
Use paper money to understand adding and
subtracting whole numbers.
Adding and Subtracting with Decimals
Materials: paper money from a game (ones, fives,
tens, twenties, fifties, and hundreds)
•Present each group of students with problems
where they will need to add money or make
change using whole dollar amounts only.
•For adding money, have the students count out
each dollar amount for the two addends. Using the
paper money, find the total amount in the two
groups. Have students represent their total amount
of money using the smallest number of bills.
Connect this to regrouping using place value.
Extend the concepts of adding and subtracting with
regrouping and using place value to decimals. Have
students solve the problem below.
During the first two football games of the season,
Will played 2.75 quarters in the first game and
2.25 quarters in the second game. How many
quarters did he play in his first two games? [5]
If Will played a total of 15.25 quarters in the
season, how many quarters of playing time did he
have in the remaining games? [10.25]
•Have students do the same addition problem on
paper to see the connection with regrouping.
•Follow the same methodology for subtraction with
regrouping and connect the concept to making
change.
28
L3: Add and Subtract Whole Numbers
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