Download Use Place Value to Add and Subtract Lesson 9

Develop Skills and Strategies
Lesson 9
Part 1: Introduction
CCSS
3.NBT.A.2
Use Place Value to Add and Subtract
In this lesson you will add and subtract by breaking apart and adding numbers.
Look at the problem below.
Rodney has 147 songs on his MP3 player, and Elaine has 212 songs on her
MP3 player. How many songs do Rodney and Elaine have in all?
Rodney’s songs:
Elaine’s songs:
Explore It
Use the math you already know to solve the problem.
147 can be written as 100 1 40 1 7. Write 212 in the same way. Add the hundreds from both numbers. Add the tens from both numbers. Add the ones from both numbers. Explain how to find the number of songs Rodney and Elaine have in all.
72
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 1: Introduction
Lesson 9
Find Out More
There are different ways to break apart numbers. You decide the way that works best
for the problem you need to solve.
147 5 (100 1 40 1 7), (100 1 20 1 20 1 7), or (140 1 7)
7 5 (1 1 6), (2 1 5), or (3 1 4)
Breaking apart numbers can make it easier to add and subtract. You can add and
subtract hundreds and hundreds, tens and tens, and ones and ones.
Here are two ways to show the sum of 147 and 212:
147 212 100 1 40 1 7
200 1 10 1 2
300 1 50 1 9 or 359
147
1 212
9 50 300 359
7 ones 1 2 ones 5 9 ones
4 tens 1 1 ten 5 5 tens
1 hundred 1 2 hundreds 5 3 hundreds
Reflect
1 Show how to break apart numbers to add 240 1 130.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
73
Part 2: Modeled Instruction
Lesson 9
Read the addition problem below. Then explore different ways to find sums of
three-digit numbers.
Garcia has 130 trading cards. Mark has 280 trading cards. How many trading
cards do Garcia and Mark have in all?
Picture It
You can use base-ten blocks to help add three-digit numbers.
The model below shows the
130 trading cards Garcia has.
The model below shows the
280 trading cards Mark has.
The model below shows the total number of trading cards Garcia and Mark have.
10 tens 5 1 hundred
Regroup 11 tens as 1 hundred 1 1 ten. Add 4 hundreds 1 1 ten 5 410.
Model It
You can also use place value to help add three-digit numbers.
130
1 280
0
110
300
There are 0 ones in both numbers.
3 tens 1 8 tens 5 11 tens, or 1 hundred 1 1 ten, or 110
1 hundred 1 2 hundreds 5 3 hundreds, or 300
410
74
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 2: Guided Instruction
Lesson 9
Connect It
Now you will solve the problem from the previous page by showing regrouping
with digits.
2 Add the ones, 0 1 0. Record the sum in the ones place
below the line.
3 Add the tens. How many tens are in the sum?
How do you regroup the tens as hundreds and tens?
1
1
3
0
2
8
0
hundred and ten
4 Record the regrouped tens in the addition problem. Put the number of hundreds
in the box above the hundreds column. Write the number of tens below the line in
the tens column.
5 Now add the hundreds. Be sure to include the hundred
in the box. What numbers do you need to add?
Record the sum in the hundreds column.
6 How could you use this method to add when both tens
and ones need to be regrouped? Show with the
problem 158 1 363.
1
1
5
8
3
6
3
Try It
Use what you just learned about regrouping to solve these problems.
7
8
1
1
9
2
1
1
4
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
1
2
8
4
2
5
8
75
Part 3: Modeled Instruction
Lesson 9
Read the subtraction problem below. Then explore different ways to find the
difference of 3-digit numbers.
Julie kept track of the weather for 365 days. It was sunny for 186 of the days.
How many days were not sunny?
Picture It
You can use base-ten blocks to help subtract three-digit numbers.
This model shows 365 2 186. All the blocks show 365. One ten and one hundred are
regrouped. The blocks crossed out show 186.
10 tens 5 1 hundred
10 ones
5 1 ten
Blocks that are left: 1 hundred 1 7 tens 1 9 ones 5 179
Model It
You can also use place value to help subtract three-digit numbers.
Write each number as hundreds, tens, and ones.
365 5 3 hundreds 1 6 tens 1 5 ones, or
2 hundreds 1 16 tens 1 5 ones, or
2 hundreds 1 15 tens 1 15 ones
186 5 1 hundred 1 8 tens 1 6 ones
76
Subtract hundreds, tens, and ones.
Combine these differences.
2 hundreds 2 1 hundred 5 1 hundred
15 tens 2 8 tens 5 7 tens
15 ones 2 6 ones 5 9 ones
1 hundred 1 7 tens 1 9 ones 5 179
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 3: Guided Instruction
Lesson 9
Connect It
Now you will solve the problem from the previous page by regrouping and
subtracting hundreds, tens, and ones.
Step 1: 365 5 300 1 60 1 5
Step 2:
200 1 160 1 5
Step 3:
200 1 150 1 15
Step 1: 186 5 100 1 80 1 6
9 Look at 365. Are there enough hundreds, tens, and ones to subtract 186?
10 Explain the regrouping used to go from Step 1 to Step 2.
Explain the regrouping used to go from Step 2 to Step 3.
11 Subtract each place: 200 2 100 = 150 2 80 = 15 2 6 = Now find what is left by adding the three differences: 12 Explain how to subtract three-digit numbers when you need to regroup hundreds
and tens.
Try It
Use what you just learned about subtraction to solve these problems. Show
your work on a separate sheet of paper.
13 362
2 125
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
14 425
2 289
77
Part 4: Modeled Instruction
Lesson 9
Read the subtraction problem below. Then explore how to subtract by
adding on.
Perez has 205 flower seeds. He plants 137 seeds. How many flower seeds does
Perez have left?
Model It
You can use a number line to subtract by adding on.
To solve the problem, subtract 205 2 137. You can also solve the problem with
5 205. Use a number line to add on to 137
the addition equation 137 1
to get to 205.
130 140 150 160 170 180 190 200 210
Find the numbers that you add to get to the next number.
137 1 3 5 140
Add on a number to get to the next ten.
140 1 60 5 200
Add on a number to get to the hundred you are looking for.
200 1 5 5 205
Add on a number to get to the total.
You added 3 1 60 1 5 5 68.
137 1 68 5 205
78
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 4: Guided Instruction
Lesson 9
Connect It
How many ones do you add to get to the
next ten? 16 What do you add to get to the hundred you
need? Write the answer in the chart.
17 Now what do you add to get to 205? Write
your answer in the chart.
18 Write a number sentence to show what you
137
Ones
Hundreds
15 Start at 137. What is the next 10? Tens
Now you can use a chart to track the numbers you add on.
3
140
200
205
added. 19 Explain how you would add on to subtract 202 2 195.
Try It
Use what you just learned about using place value to solve these problems.
Show your work on a separate sheet of paper.
20 Edith had $600. She spent $84. How much does Edith have left? 21 Juan sent and received 800 text messages. He sent 379 text messages. How many
text messages did Juan receive? L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
79
Part 5: Guided Practice
Lesson 9
Study the model below. Then solve problems 22–24.
Student Model
The student broke apart
617 and 219 into
hundreds, tens, and
ones. That makes it easy
to add the two numbers.
On Monday, a flower store sold 617 roses. On Tuesday,
279 roses were sold. How many roses were sold on Monday
and Tuesday?
Look at how you could show your work by breaking apart
617 and 279.
617 1 279 5 (600 1 200) 1 (10 1 70) 1 (7 1 9)
Pair/Share
5 800 1 80 1 16
5 896
Solution: 896 roses
How else could you
solve this problem?
How many magnets
does Roger have?
22 Diana has 109 magnets. Roger has 56 more magnets than Diana.
How many magnets do Diana and Roger have in all?
Show your work.
Pair/Share
How did you decide
which operation to use?
80
Solution: L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 5: Guided Practice
23 Corey works 144 hours a month. He has worked 72 hours so far
this month. How many more hours does Corey have to work
this month?
Lesson 9
Do you need to regroup?
Show your work.
Pair/Share
Solution: 24 Chad practiced batting for 205 minutes this week. Doug practiced
batting for 110 minutes. How many more minutes did Chad
practice than Doug?
How can you use
adding on to solve
this problem?
To find how many more
minutes, should you add
or subtract?
A 90 minutes
B 95 minutes
C 195 minutes
D 315 minutes
Sam chose D as the correct answer. How did he get that answer?
Pair/Share
How can you use
estimation to see
if Sam’s answer
makes sense?
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
81
Part 6: Common Core Practice
Lesson 9
Solve the problems.
1 Mr. Coleman drove 129 miles on Monday. He drove 78 more miles on Tuesday than on
Monday. How many miles did Mr. Coleman drive altogether on Monday and Tuesday?
A51
B207
C285
D336
2 Which of the following diagrams or solutions represent the difference 354 2 298?
Circle the letter for all that apply.
A
B
C
290
82
300
310
320
D
2 hundreds 2 2 hundreds 5 0 hundreds
15 tens 2 9 tens 5 6 tens
14 ones 2 8 ones 5 6 ones
E
3 hundreds 2 2 hundreds 5 1 hundred
15 tens 2 9 tens 5 6 tens
14 ones 2 8 ones 5 6 ones
330
340
350
360
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 6: Common Core Practice
Lesson 9
3 The number sentence below can be solved using tens and ones.
68 1 16 5 ? tens and ? ones.
Select one number from each column to make the number sentence true.
Tens
s 2
s 7
s 8
s 9
Ones
s 4
s 9
s 12
s 14
4 Sam has 308 craft sticks. She buys a package of 625 craft sticks. She uses 245 craft sticks
for a project. How many craft sticks does Sam have left?
Show your work.
Answer Sam has craft sticks left.
5 The digits in a three-digit number represent the amounts of hundreds, tens, and ones.
Fill in the chart to show the amounts of hundreds, tens, and ones in the number 746.
Number
746
Hundreds
Tens
Ones
Write a number that meets the following conditions.
• The number must be between 1 and 9.
• When the number is added to 746, the digit in the ones place of the sum is less than
the ones place of 746.
Self Check Go back and see what you can check off on the Self Check on page 61.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
83
Develop Skills and Strategies
Lesson 9
Use Place Value to Add and Subtract
Lesson Objectives
The Learning Progression
•Use a variety of strategies to add up to three-digit
numbers.
In grade 2, students learned to use concrete models,
drawings, and strategies based on place value and
properties to add and subtract two- and three-digit
numbers. In grade 3, this work is continued, with the
focus being on achieving fluency with the strategies
they have learned. This understanding will prepare
students for learning standard algorithms for addition
and subtraction in grade 4.
•Use a variety of strategies to subtract up to threedigit numbers.
•Estimate to determine if an answer is reasonable.
Prerequisite SkilLs
In order to be proficient with the concepts/skills in this
lesson, students should:
Teacher Toolbox
•Know basic addition and subtraction facts.
Teacher-Toolbox.com
Prerequisite
Skills
•Understand place value concepts, such as the value
of digits and writing numbers in expanded form.
Ready Lessons
•Understand and apply properties of addition.
Tools for Instruction
•Understand the inverse relationship between
addition and subtraction.
Interactive Tutorials
3.NBT.A.2
✓
✓
✓✓
Vocabulary
There is no new vocabulary.
CCSS Focus
3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/
or the relationship between addition and subtraction.
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 1, 2, 7, 8 (see page A9 for full text)
82
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 1: Introduction
Lesson 9
At a Glance
Students read a word problem and answer questions
designed to help them add two 3-digit numbers.
Develop skills and strategies
Lesson 9
Part 1: introduction
ccss
3.nbt.a.2
use Place value to add and subtract
Step By Step
in this lesson you will add and subtract by breaking apart and adding numbers.
Look at the problem below.
•Tell students that this page models how to add two
3-digit numbers.
Rodney has 147 songs on his MP3 player, and Elaine has 212 songs on her
MP3 player. How many songs do Rodney and Elaine have in all?
Rodney’s songs:
•Have students read the problem at the top of the page.
Elaine’s songs:
•Work through Explore It as a class.
•Guide students to understand that they need to write
212 as the sum of hundreds, tens, and ones.
explore it
use the math you already know to solve the problem.
147 can be written as 100 1 40 1 7. Write 212 in the same way. 200 1 10 1 2
•You may want to suggest that students write
100 1 40 1 7 and 200 1 10 1 2 vertically so the
hundreds, tens and ones are aligned. As they write
the sum for each place, tell students to also write plus
signs between hundreds and tens and tens and ones.
•Ask: How could you use rounding and estimation to
check your answer for reasonableness? [Round each
number to the nearest ten. 147 rounds to 150 and
212 rounds to 210. The sum of the rounded numbers
(150 1 210 5 360) is close to the actual number of
songs, 359. So the answer is reasonable.]
SMP Tip: The representation of the numbers in
their place-value form here helps students to focus
on the value of the digits, providing more support
for quantitative reasoning (SMP 2).
Add the hundreds from both numbers. 100 1 200 5 300
Add the tens from both numbers. 40 1 10 5 50
Add the ones from both numbers. 7 1 2 5 9
Explain how to find the number of songs Rodney and Elaine have in all.
you can add the hundreds, add the tens, and add the ones from each
number: 300 1 50 1 9 5 359. they have 359 songs in all.
72
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
Mathematical Discourse
•What does the model show you about the value of the
numbers?
Listen for answers that demonstrate that
students understand the numbers are being
broken into their component parts and that
each of these parts has a name associated with
it; “hundreds,” “tens,” and “ones.”
•What are the parts of the numbers you are adding?
Listen for answers that include the phrase
“place value.” Try to guide the students to see
the relationship between the component parts
of one number and the other number. They are
adding the components with like place value.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
83
Part 1: Introduction
Lesson 9
At a Glance
Students use place-value concepts to add numbers.
They break apart the addends by place-value position.
Step By Step
•Read Find Out More as a class.
•Emphasize that these are only some examples of how
the numbers 147 and 212 can be broken apart.
Challenge students to find other ways to write these
numbers.
•Recognize that some students may know other
strategies that can be used to add the numbers.
Encourage them to share those strategies.
Part 1: introduction
Lesson 9
Find out More
There are different ways to break apart numbers. You decide the way that works best
for the problem you need to solve.
147 5 (100 1 40 1 7), (100 1 20 1 20 1 7), or (140 1 7)
7 5 (1 1 6), (2 1 5), or (3 1 4)
Breaking apart numbers can make it easier to add and subtract. You can add and
subtract hundreds and hundreds, tens and tens, and ones and ones.
Here are two ways to show the sum of 147 and 212:
147
212
100 1 40 1 7
200 1 10 1 2
300 1 50 1 9 or 359
147
1 212
9
50
300
359
7 ones 1 2 ones 5 9 ones
4 tens 1 1 ten 5 5 tens
1 hundred 1 2 hundreds 5 3 hundreds
reflect
1 Show how to break apart numbers to add 240 1 130.
240 5 200 1 40 and 130 5 100 1 30
add the hundreds: 200 1 100 5 300; add the tens: 40 1 30 5 70
300 1 70 5 370
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Hands-On Activity
Use base-ten blocks to understand using
place value to add and subtract.
Materials: base-ten blocks (hundreds, tens, ones)
Copying is not permitted.
73
Real-World Connection
Ask students to identify two situations with friends
where they needed to add or subtract three-digit
numbers. Responses might include keeping score in
a game or buying items in a store.
•Place students in groups.
•Distribute base-ten blocks to each group of
students.
•Tell students to use the blocks to model both
numbers of songs.
•Have students combine the hundreds from both
models. Ask: How many total hundreds are there?
[300]
•Continue having students combine tens and then
ones. Ask students to say and write the total
number of hundreds, tens, and ones.
[300 1 50 1 9] Guide them to understand that
this is 359, which is the sum of 147 and 212.
84
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 2: Modeled Instruction
Lesson 9
At a Glance
Part 2: Modeled instruction
Students use base-ten models and partial sums to find
the sum of two 3-digit numbers.
Lesson 9
read the addition problem below. then explore different ways to find sums of
three-digit numbers.
Step By Step
Garcia has 130 trading cards. Mark has 280 trading cards. How many trading
cards do Garcia and Mark have in all?
•Read the problem at the top of the page as a class.
Picture it
•Read Picture It.
you can use base-ten blocks to help add three-digit numbers.
The model below shows the
130 trading cards Garcia has.
•Discuss the fact that when the tens from both
numbers are combined there are more than 10 tens.
Emphasize that 10 tens equal 1 hundred, so 10 tens
can be traded in and regrouped as 1 hundred.
The model below shows the
280 trading cards Mark has.
The model below shows the total number of trading cards Garcia and Mark have.
•Guide students through each step in Model It.
•For students struggling with this concept, use
color-coding to help them make sense of the method.
Use three different colors for recording the sum of
the ones, tens, and hundreds.
10 tens 5 1 hundred
Regroup 11 tens as 1 hundred 1 1 ten. Add 4 hundreds 1 1 ten 5 410.
Model it
you can also use place value to help add three-digit numbers.
130
1 280
SMP Tip: The use of a visual model in Picture It,
along with a mathematical model in Model It, helps
reinforce that numbers are structured according to
place value (SMP 7).
Concept Extension
Help students understand why regrouping is
sometimes necessary in addition.
•Direct attention to the illustration of the blocks in
the student book. Ask a volunteer to count by 100
to count the hundreds.
0
110
300
There are 0 ones in both numbers.
3 tens 1 8 tens 5 11 tens, or 1 hundred 1 1 ten, or 110
1 hundred 1 2 hundreds 5 3 hundreds, or 300
410
74
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
Mathematical Discourse
•How you can use the base-ten models to count on and
find the sum of the two numbers?
Students might first count on by hundreds
(100, 200, 300), and then by tens (310, 320 . . .
410).
•Then ask a different student to count by tens. Stop
the student at 100 and emphasize that 10 tens
equal 1 hundred, so you need to regroup.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
85
Part 2: Guided Instruction
Lesson 9
At a Glance
Students revisit the problem on page 74.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 74.
•Direct students attention to the addition problem
next to problems 2 and 3. Tell students that the
smaller box below the problem is used for recording
the regrouping. The sum will be written in the bigger
box at the bottom.
•As you read problem 3, refer students to the visual
model of regrouping on page 74.
•Walk students through problem 6. As they add the
digits in each place, ask if regrouping is necessary.
Stress the importance of aligning all digits of the
same place value.
Concept Extension
Part 2: guided instruction
Lesson 9
connect it
now you will solve the problem from the previous page by showing regrouping
with digits.
2 Add the ones, 0 1 0. Record the sum in the ones place
1
below the line.
3 Add the tens. How many tens are in the sum?
11
How do you regroup the tens as hundreds and tens?
1
hundred and
1
1
ten
1
3
2
8
0
0
4
1
0
4 Record the regrouped tens in the addition problem. Put the number of hundreds
in the box above the hundreds column. Write the number of tens below the line in
the tens column.
5 Now add the hundreds. Be sure to include the hundred
in the box. What numbers do you need to add?
11112
Record the sum in the hundreds column.
6 How could you use this method to add when both tens
and ones need to be regrouped? Show with the
problem 158 1 363.
1
try it
1
1
1
5
8
3
6
3
5
2
1
use what you just learned about regrouping to solve these problems.
7
8
1
1
1
9
2
1
1
4
3
0
6
1
1
1
2
8
4
2
5
8
5
4
2
Explore addition problems that require regrouping.
•Ask students to write an addition problem that
requires regrouping.
•Have students exchange problems with a partner.
Students then solve the problems and write an
explanation of how they knew regrouping was
necessary and how they performed the
regrouping.
•Have several volunteers explain their answers to
the class.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
75
Try It Solutions
7Solution: 306; Add the ones: 2 1 4 5 6. Add the
tens: 9 1 1 5 10. Regroup the 10 tens as 1 hundred
and 0 tens. Add the hundreds: 1 1 1 1 1 5 3.
So, 192 1 114 5 306.
Error Alert: Students who wrote 206 did not
add the 10 tens that were regrouped as 1 hundred.
Students who wrote 216 did not regroup properly.
Those students regrouped 10 tens as 1 ten.
8Solution: 542; Add the ones: 4 1 8 5 12. Regroup
the 12 ones as 1 ten and 2 ones. Add the tens:
8 1 5 1 1 5 14. Regroup the 14 tens as 1 hundred
and 4 tens. Add the hundreds: 2 1 2 1 1 5 5.
So, 284 1 258 5 542.
86
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 3: Modeled Instruction
Lesson 9
At a Glance
Part 3: Modeled instruction
Students use base-ten models and place-value concepts
to find the difference of two 3-digit numbers.
Lesson 9
read the subtraction problem below. then explore different ways to find the
difference of 3-digit numbers.
Step By Step
Julie kept track of the weather for 365 days. It was sunny for 186 of the days.
How many days were not sunny?
•Read the problem at the top of the page as a class.
Picture it
•Read Picture It. Use base-ten blocks to show
3 hundreds, 6 tens, and 5 ones or make a place-value
drawing on the board.
you can use base-ten blocks to help subtract three-digit numbers.
This model shows 365 2 186. All the blocks show 365. One ten and one hundred are
regrouped. The blocks crossed out show 186.
•Count the ones to show that 365 has 5 ones. Ask:
How many ones are in 186, the number that is being
subtracted from 365? [6 ones] How can you subtract 6
ones from 5 ones? [You have to regroup a ten into 10
ones.]
10 tens 5 1 hundred
Blocks that are left: 1 hundred 1 7 tens 1 9 ones 5 179
Model it
you can also use place value to help subtract three-digit numbers.
•Perform the regrouping and point out that 365 is
now shown as 3 hundreds, 5 tens, and 16 ones. Have
students identify the number of tens in 186. [8 tens]
Invite a volunteer to show or describe how to
regroup a hundred in order to subtract the tens.
[Regroup 1 hundred as 10 tens]
•Guide students to see that the illustration on page
76 shows the base-ten blocks for 365 after both
regroupings. Ask a student to count the remaining
blocks and state the difference.
10 ones
5 1 ten
Write each number as hundreds, tens, and ones.
365 5 3 hundreds 1 6 tens 1 5 ones, or
2 hundreds 1 16 tens 1 5 ones, or
2 hundreds 1 15 tens 1 15 ones
186 5 1 hundred 1 8 tens 1 6 ones
76
Subtract hundreds, tens, and ones.
Combine these differences.
2 hundreds 2 1 hundred 5 1 hundred
15 tens 2 8 tens 5 7 tens
15 ones 2 6 ones 5 9 ones
1 hundred 1 7 tens 1 9 ones 5 179
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
•Read Model It.
•Have a volunteer explain the trading, or regrouping,
that occurred when 365 was rewritten in a new form.
Visual Model
Mathematical Discourse
•Use a tree diagram to show how to break up 365
into different groupings of hundreds, tens, and
ones and then regroup 1 hundred and 1 ten.
3 hundreds
1
3 hundreds
1
5 tens
1
2 hundreds 1 1 hundred 1
5 tens
1
2 hundreds 1 10 tens
5 tens
2 hundreds 1
1
6 tens
15 tens
1
5 ones
1 ten
1
5 ones
1 ten
1
5 ones
1 10 ones 1
5 ones
1
•How is regrouping for subtraction different from
regrouping for addition?
Listen for answers that demonstrate the
students understand that when they are adding
they are regrouping to the larger place value
but when they are subtracting they are taking
from the larger place value to make more of the
lower place value.
15 ones
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
87
Part 3: Guided Instruction
Lesson 9
At a Glance
Students revisit the problem on page 76.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 76.
•To help students answer problem 10, ask questions
such as: Did the hundreds change from Step 1 to Step 2?
Did it get smaller or larger? How did the tens change?
After students write about the regroupings, ask a
volunteer to share his or her explanation.
•Discuss students’ answers to problem 12. Together,
create a summary of the process and write it on the
board. Then show the problem “423 2 255” on the
board. Ask a pair of students to go to the board. One
student describes the process while the other applies
is to solve the subtraction problem.
Concept Extension
Use this technique to help students explain their
thought process in a precise way.
•Ask students to verbalize their answer to Number
12 slowly, step by step.
•Use numbers, symbols, and words to show what
the student is saying.
•Discuss any revisions that need to be made to the
student’s explanation.
Part 3: guided instruction
Lesson 9
connect it
now you will solve the problem from the previous page by regrouping and
subtracting hundreds, tens, and ones.
Step 1: 365 5 300 1 60 1 5
Step 2:
200 1 160 1 5
Step 3:
200 1 150 1 15
Step 1: 186 5 100 1 80 1 6
9 Look at 365. Are there enough hundreds, tens, and ones to subtract 186?
there are enough hundreds, but not enough tens and ones.
10 Explain the regrouping used to go from Step 1 to Step 2.
regroup 300 as 200 1 100, then add 100 1 60.
Explain the regrouping used to go from Step 2 to Step 3.
regroup 160 as 150 1 10, then add 10 1 5.
11 Subtract each place: 200 2 100 =
100
150 2 80 =
70
15 2 6 =
9
Now find what is left by adding the three differences: 100 1 70 1 9 5 179
12 Explain how to subtract three-digit numbers when you need to regroup hundreds
and tens.
regroup 1 hundred as 10 tens. combine all of the tens. regroup 1 ten as
10 ones. combine all of the ones. subtract in each place.
try it
use what you just learned about subtraction to solve these problems. show
your work on a separate sheet of paper.
13
362
2 125
237
14
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
425
2 289
136
77
Try It Solutions
13 Solution: 237; Regroup 1 ten as 10 ones. Subtract the
ones: 12 2 5 5 7. Subtract the tens: 50 2 20 5 30.
Subtract the hundreds: 300 2 100 5 200. Add the
differences: 200 1 30 1 7 5 237.
Error Alert: Students who wrote 243 subtracted
each lesser digit from each greater digit. Students
who wrote 247 did not regroup properly. Those
students regrouped 1 ten as 10 ones, but did not
rename the digit in the tens place.
14 Solution: 136; Regroup 1 ten as 10 ones. Subtract the
ones: 15 2 9 5 6. Regroup 1 hundred as 10 tens.
Subtract the tens: 110 2 80 5 30. Subtract the
hundreds: 300 2 200 5 100. Add the differences:
100 1 30 1 6 5 136.
88
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 4: Modeled Instruction
Lesson 9
At a Glance
Part 4: Modeled instruction
Students find the difference of two 3-digit numbers by
adding on to subtract.
Lesson 9
read the subtraction problem below. then explore how to subtract by
adding on.
Step By Step
Perez has 205 flower seeds. He plants 137 seeds. How many flower seeds does
Perez have left?
•Read the problem at the top of the page as a class.
Model it
•Read Model It.
you can use a number line to subtract by adding on.
To solve the problem, subtract 205 2 137. You can also solve the problem with
5 205. Use a number line to add on to 137
the addition equation 137 1
to get to 205.
SMP Tip: Discuss with students the importance of
using structure and connections in math. Point out
that addition and subtraction are opposite
operations, meaning that they undo each other.
Recognizing this connection has helped to develop
the strategy of using addition to solve a subtraction
problem (SMP 8).
130 140 150 160 170 180 190 200 210
Find the numbers that you add to get to the next number.
137 1 3 5 140
140 1 60 5 200
200 1 5 5 205
Add on a number to get to the next ten.
Add on a number to get to the hundred you are looking for.
Add on a number to get to the total.
You added 3 1 60 1 5 5 68.
137 1 68 5 205
•Direct attention to the number line. Make sure
students recognize 137 as the starting point and 205
as the ending point.
•Say: 137 1 3 5 140. I added 3 to get to the next ten.
•Invite volunteers to describe the next two jumps on
the number line.
78
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
•Emphasize that you must add all of the jumps to find
the total that is added to 137 to find 205.
Hands-On Activity
Use base-ten blocks to keep track of adding on.
Materials: base-ten blocks
•Walk through the problem with students,
describing each number that is added on. Have
students model each number added on with
base-ten blocks. Then have them use the blocks to
find the answer to 137 1 ? 5 205. [98]
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
ELL Support
•Provide some basic examples to help students
make sense of the concept of opposites. For
example, some opposites are up/down, back/front,
and left/right.
89
Part 4: Guided Instruction
Lesson 9
At a Glance
•After completing problem 15, point out where in the
place-value chart this number is recorded. Explain
that 3 ones were added to 137 to get to 140.
•Suggest that students refer to the model on the
previous page to help complete the chart.
•Invite volunteers to share their answers to
problem 19.
connect it
now you can use a chart to track the numbers you add on.
15 Start at 137. What is the next 10?
140
How many ones do you add to get to the
3
next ten?
16 What do you add to get to the hundred you
need? Write the answer in the chart.
137
17 Now what do you add to get to 205? Write
your answer in the chart.
18 Write a number sentence to show what you
140
ones
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 78.
Lesson 9
tens
Step By Step
Part 4: guided instruction
hundreds
Students revisit the problem on page 78.
3
6
200
5
205
30 1 60 1 5 5 68
added.
19 Explain how you would add on to subtract 202 2 195.
Possible answer: start with 195. add 5 to get 200. then add 2 to get 202.
Find the total added: 5 1 2 5 7. so, 202 2 195 5 7.
try it
use what you just learned about using place value to solve these problems.
show your work on a separate sheet of paper.
$516
20 Edith had $600. She spent $84. How much does Edith have left?
21 Juan sent and received 800 text messages. He sent 379 text messages. How many
text messages did Juan receive?
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
421
79
Try It Solutions
20 Solution: $516; Start with 84. Add 6 to get to the
next ten: 84 1 6 5 90. Add 10 to get to the next
hundred: 90 1 10 5 100. Add 500 to get to the
total: 100 1 500 5 600. Add: 500 1 10 1 6 5 516.
Error Alert: Students who wrote $506 or $516
may have missed some of the numbers added on as
they found the total.
21 Solution: 421; Start with 379. Add 1 to get to the
next ten: 379 1 1 5 380. Add 20 to get to the next
hundred: 380 1 20 5 400. Add 400 to get to the
total: 400 1 400 5 800. Add: 400 1 20 1 1 5 421.
90
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Part 5: Guided Practice
Lesson 9
Part 5: guided Practice
Lesson 9
study the model below. then solve problems 22–24.
Student Model
The student broke apart
617 and 219 into
hundreds, tens, and
ones. That makes it easy
to add the two numbers.
On Monday, a flower store sold 617 roses. On Tuesday,
279 roses were sold. How many roses were sold on Monday
Part 5: guided Practice
23 Corey works 144 hours a month. He has worked 72 hours so far
this month. How many more hours does Corey have to work
this month?
Lesson 9
Do you need to regroup?
Show your work.
Possible student work:
and Tuesday?
144 2 72 5 72
Look at how you could show your work by breaking apart
617 and 279.
617 1 279
5 (600 1 200) 1 (10 1 70) 1 (7 1 9)
5 800 1 80 1 16
Pair/share
5 896
Pair/share
Solution: 896 roses
How else could you
solve this problem?
Solution:
72 more hours
24 Chad practiced batting for 205 minutes this week. Doug practiced
How many magnets
does Roger have?
22 Diana has 109 magnets. Roger has 56 more magnets than Diana.
How many magnets do Diana and Roger have in all?
Possible student work:
109 1 56 5 165
80
b
95 minutes
c
195 minutes
D 315 minutes
roger has 165 magnets.
Pair/share
To find how many more
minutes, should you add
or subtract?
a 90 minutes
Show your work.
How did you decide
which operation to use?
batting for 110 minutes. How many more minutes did Chad
practice than Doug?
How can you use
adding on to solve
this problem?
Sam chose D as the correct answer. How did he get that answer?
165 1 109 5 274
Possible answer: sam added the minutes to get the total.
Solution: 274 magnets
he should have subtracted to find the difference.
L9: Use Place Value to Add and Subtract
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
At a Glance
Students use place value concepts to solve problems
involving adding and subtracting whole numbers up to
3 digits.
Step By Step
•Ask students to solve the problems individually and
show all the steps in their calculations.
•When students have completed each problem, have
them Pair/Share to discuss their solutions with a
partner or in a group.
Solutions
Ex Breaking apart two 3-digit numbers is shown as one
way to solve the problem. After breaking apart
the numbers, add the hundreds, tens, and ones
to get 896.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
©Curriculum Associates, LLC
Copying is not permitted.
Pair/share
How can you use
estimation to see
if Sam’s answer
makes sense?
81
22 Solution: 274 magnets; Add 109 and 56 to find the
number Rogers has. Roger has 109 1 56 5 165
magnets. Add the number of magnets Diana and
Roger have: 109 1 165 5 274 magnets. (DOK 2)
23 Solution: 72 more hours; Subtract the ones. Regroup
1 hundred as 10 tens. Subtract the tens. There are
no hundreds left. Add the differences: 70 1 2 5 72.
(DOK 1)
24 Solution: B; Subtract the number of minutes Doug
practiced from the number of minutes Chad practiced.
Explain to students why the other two answer
choices are not correct:
A is not correct, because 5 ones 2 0 ones is 5 ones,
not 0 ones. (DOK 3)
C is not correct because 1 hundred is regrouped,
leaving 1 hundred 2 1 hundred 5 0 hundreds.
(DOK 3)
91
Part 5: Common Core Practice
Part 6: common core Practice
Lesson 9
Lesson 9
Solve the problems.
Part 6: common core Practice
3
The number sentence below can be solved using tens and ones.
68 1 16 5
1
2
Mr. Coleman drove 129 miles on Monday. He drove 78 more miles on Tuesday than on
Monday. How many miles did Mr. Coleman drive altogether on Monday and Tuesday?
A
51
B
207
C
285
D
336
?
4
?
ones.
tens
tens
s
s 22
d
s 77
s
s 88
s
s 99
ones
ones
s
s 44
s
s 99
s
s 12
12
d
s 14
14
tens
s 2
s 7
d 8
s 9
ones
d 4
s 9
s 12
s 14
Sam has 308 craft sticks. She buys a package of 625 craft sticks. She uses 245 craft sticks
for a project. How many craft sticks does Sam have left?
Show your work.
A
Possible student work:
308 1 625 5 933
933 2 245 5 688
B
Answer
5
C
290
E
tens and
Select one number from each column to make the number sentence true.
Possible answers:
Which of the following diagrams or solutions represent the difference 354 2 298?
Circle the letter for all that apply.
D
Lesson 9
300
310
320
330
340
350
360
Sam has
688
craft sticks left.
The digits in a three-digit number represent the amounts of hundreds, tens, and ones.
Fill in the chart to show the amounts of hundreds, tens, and ones in the number 746.
2 hundreds 2 2 hundreds 5 0 hundreds
15 tens 2 9 tens 5 6 tens
14 ones 2 8 ones 5 6 ones
number
746
hundreds
tens
ones
7
4
6
Write a number that meets the following conditions.
3 hundreds 2 2 hundreds 5 1 hundred
15 tens 2 9 tens 5 6 tens
14 ones 2 8 ones 5 6 ones
• The number must be between 1 and 9.
• When the number is added to 746, the digit in the ones place of the sum is less than
the ones place of 746.
Possible answers: 4, 5, 6, 7, 8, or 9
self check Go back and see what you can check off on the Self Check on page 61.
82
L9: Use Place Value to Add and Subtract
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC
Copying is not permitted.
At a Glance
Students use adding and subtracting to solve problems
that might appear on a mathematics test.
Solutions
1Solution: D; On Tuesday, Mr. Coleman drove
129 1 78 5 207 miles. Add the number of miles
Mr. Coleman drove on Monday and Tuesday.
129 1 207 5 336 miles on Monday and Tuesday.
(DOK 2)
2Solution: B; The place-value blocks total 354. There
are 298 blocks crossed out to represent 354 2 298.
C; The number line shows points at 298 and 354.
The curved lines between represent the difference
between the two numbers. (DOK 2)
92
©Curriculum Associates, LLC
Copying is not permitted.
83
3Solution: See possible completed tables on student
page above. 68 1 16 5 84, which is equivalent to
7 tens and 14 ones or 8 tens and 4 ones. (DOK 1)
4Solution: 688; Add: 308 1 625 5 (300 1 600) 1
(0 1 20) 1 (8 1 5) 5 933. Subtract:
933 2 245 5 688. (DOK 2)
5Solution: See completed table on student page above.
Adding any of the following numbers to 746 would
result in a sum that has a digit less than 6 in the
ones place: 4 (sum would be 750), 5 (sum would be
751), 6 (sum would be 752), 7 (sum would be 753),
8 (sum would be 754), or 9 (sum would be 755).
(DOK 2)
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
Differentiated Instruction
Lesson 9
Assessment and Remediation
•Ask students to subtract 433 2 298. [135]
•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
adding 372 1 537. [909]
If the error is . . .
Students may . . .
To remediate . . .
235
not have regrouped the
hundreds.
Demonstrate using base-ten blocks that when regrouping
1 hundred as 10 tens, there is 1 less hundred.
245
not have regrouped the
hundreds or tens.
Remind students that when regrouping 1 hundred as 10 tens,
there is 1 less hundred, and when regrouping 1 ten as 10 ones,
there is 1 less ten.
265
have subtracted each
lesser digit from each
greater digit.
Demonstrate using Base-10 blocks that 8 ones cannot be
subtracted from 3 ones. Students need to realize they should
regroup 1 ten as 10 ones before subtracting.
731
have added.
Remind students that the symbol “2” means subtraction, not
addition.
Hands-On Activity
Challenge Activity
Understand place value to add and subtract.
Plan a road trip.
Materials: Base-ten blocks, bag
Tell students that they are planning a summer
vacation road trip. They must determine how many
miles they are going to travel so they can plan for a
gas budget.
•Group each student with a partner.
•Have a student volunteer grab a handful of baseten blocks from the bag and lay them out to model
a number. Repeat the process again for a second
number. If the first number is smaller than the
second, make this an addition problem, otherwise,
make it a subtraction problem.
•Have one student solve the problem on paper and
the other student solve it with the manipulatives.
•Have students compare answers.
•Students should switch roles and repeat the
procedure.
Students must do the following:
•Select 4 cities.
•Use a mileage chart in an atlas or online to find
the distances between the cities.
•Plan a route from city to city and add up the
mileage for their round trip.
•Tell students to change their route and leave out
the last city. Have them calculate the mileage for
the adjusted route.
Have each group present their trip route, total
mileage model, and adjusted mileage model.
L9: Use Place Value to Add and Subtract
©Curriculum Associates, LLC Copying is not permitted.
93