Unit 5 - Professional Development

Transcription

Unit 5
Common Core
Landmarks and Large Numbers
Mathematical Practices (MP)
Domains
• Number and Operations in Base Ten (NBT)
• Measurement and Data (MD)
INVESTIG ATION 1
How Much Is 1,000?
Day
1 1.1
2
1.2
Session
How Much Is 1,000?
Finding Numbers to 1,000
DISCUSSION
Finding Numbers
3
1.3
TEN-MINUTE MATH
Have students also write the number in expanded form after
they have practiced writing or saying the number.
ACTIVITY
Teaching Note
Expanded Form Include expanded form in this activity.
Explain that when students use expanded form, they will
break a number apart by place. Write 435 = 400 + 30 + 5
under 435.
Introducing Practicing
Place Value
1.4
How Many Miles to 1,000?
TEN-MINUTE MATH
Practicing Place Value
5
6
7
CC26 Teaching Note
Greater Than, Less Than Signs Reintroduce greater than
(>) and less than (<) signs. After students share how they
located 541 on the 1,000 chart ask: Is 541 greater or less than
500? Is it greater or less than 600? Write 541 > 500 and
541 < 600 on the board. Throughout the unit, continue to
use greater than and less than signs to compare numbers.
Changing Places
4
Common Core Adaptation
1.5A Place-Value
Understanding
1.5 Assessment:
Numbers to 1,000
1.6 Adding and Subtracting
to 1,000
Common Core Standards
MP7
4.NBT.1, 4.NBT.2, 4.NBT.4
MP5, MP7
4.NBT.2, 4.NBT.4
MP5, MP7
4.NBT.2, 4.NBT.4
MP5, MP7
4.NBT.2, 4.NBT.4, 4.MD.2
See p. CC30.
MP5, MP7
4.NBT.2, 4.NBT.3
MP5, MP7
4.NBT.2, 4.NBT.4, 4.MD.2
MP5
4.NBT.2, 4.NBT.4, 4.MD.2
UNIT 5 Landmarks and Large Numbers
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INVESTIG ATION 2
Adding It Up
Day
8 2.1
Session
Solving Addition
Problems
TEN-MINUTE MATH
9
2.2
MP3, MP6, MP8
4.NBT.4, 4.MD.2
MP3, MP6, MP8
4.NBT.4, 4.MD.2
MP6, MP8
4.NBT.2, 4.NBT.4
Addition Strategies
10 2.3
Starter Problems
11 2.4
Studying the U.S.
Algorithm for Addition
TEN-MINUTE MATH
12 2.5
Close to 1,000
TEN-MINUTE MATH
SESSION FOLLOW-UP
Daily Practice: In addition to Student Activity Book page 32,
students complete Student Activity Book page 34 or C20
(School Enrollments) for reinforcement of the content of this
unit.
Daily Practice and
Homework
13 2.6
Assessment: Solving an
Addition Problem in Two
Ways
MP3, MP6, MP8
4.NBT.2, 4.NBT.4, 4.MD.2
MP2
4.NBT.2, 4.NBT.4
MP2, MP6
4.NBT.2, 4.NBT.4
Instructional Plan INV12_TE04_U05.indd
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CC27
5/4/11
8:49 AM
INVESTIG ATION 3
Working with Numbers to 10,000
Day
14 3.1
Session
Making a 10,000 Chart
15 3.2
How Much Is 10,000?
16 3.3
Working with the 10,000
Chart
Thousands of Miles
17 3.4
TEN-MINUTE MATH
18 3.5
Adding Numbers in the
Thousands
TEN-MINUTE MATH
19 3.6A Larger Place Values
CC28 Common Core Adaptation
MP1 , MP7
4.NBT.1, 4.NBT.2,
4.NBT.4
MP1
4.NBT.1, 4.NBT.2,
4.NBT.4
MP1
4.NBT.2, 4.NBT.4
MP1
Have students also write the number in expanded form after 4.NBT.2, 4.NBT.4,
4.MD.2
MP1
4.NBT.2, 4.NBT.4,
Have students also write the number in expanded form after 4.MD.2
See p. CC35.
MP1
4.NBT.1, 4.NBT.2,
4.NBT.3
UNIT 5 Landmarks and Large Numbers
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8:49 AM
INVESTIG ATION 4
Subtraction
Day
20 4.1
21 4.2
Session
Representing Subtraction
Problems
Strategies for Subtraction
Session Follow-up
Daily Practice and
Homework
22 4.3
23 4.4A Studying the U.S.
Algorithm for Subtraction
24 4.4 Do I Add or Subtract?
TEN-MINUTE MATH
See p. CC40.
MP8
4.NBT.2, 4.NBT.4
MP1
4.NBT.2, 4.NBT.4
MP1
4.NBT.2, 4.NBT.4, 4.MD.2
Session Follow-up
students complete Student Activity Book page 70B or C28
(Subtraction Practice) for reinforcement of the content of this
unit.
Solving Addition and
Subtraction Problems,
MP1
4.NBT.2, 4.NBT.4, 4.MD.2
End-of-Unit Assessment
MP1, MP2, MP8
4.NBT.4
continued
27 4.7
TEN-MINUTE MATH
Daily Practice and
Homework
MP4
4.NBT.2, 4.NBT.4
MP4
4.NBT.2, 4.NBT.4
MP4
4.NBT.2, 4.NBT.4
Solving Addition and
Subtraction Problems
26 4.6
students complete Student Activity Book page 60 or C24
(Areas of Countries) for reinforcement of the content of
this unit.
Assessment: Numbers to
10,000
TEN-MINUTE MATH
25 4.5
Instructional Plan INV12_TE04_U05.indd 29
CC29
6/14/11 2:03 PM
session 1.5A
Place-Value
Understanding
Math Focus Points
Rounding numbers to the nearest ten and the nearest
hundred
Vocabulary
Writing numbers to 1,000 in expanded form
expanded form
less than
greater than
Using >, =, and < to compare numbers to 1,000
Today’s Plan
Materials
activity
Rounding Numbers
•Students’ 1,000 books (from Session 1.1)
20 Min Groups
ACTIVITY
Expanded Form
•Student Activity Book, p. 13A or
20 Min Class
Activity
Comparing Numbers
Using >, =, and <
C17, Using Place Value Make copies.
(as needed)
Students’ 1,000 books
•
•Student Activity Book, p. 13B or
20 Min
Session Follow-Up
Pairs
C18, Comparing Numbers Make copies.
(as needed)
Students’ 1,000 books
•
•Student Activity Book, p. 13C or
C19, River Lengths Make copies. (as needed)
Student
Math Handbook, p. 6
•
Daily Practice
Ten-Minute Math
Practicing Place Value Say “six hundred eighty-three” and have students practice
writing the number. Make sure that all students can read, write, and say this number
correctly. Have students write 683 in expanded form. Ask students to solve these
problems mentally, if possible:
• What is 683 + 10? 683 + 20? 683 + 100? 683 + 200? 683 – 100?
Write each answer on the board. Have students compare each sum or difference with
683. Ask students:
• Which places have the same digits? Which do not? Why?
If time permits, pose additional similar problems using these numbers: 318 and 857.
CC30 Investigation 1 How Much Is 1,000?
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1 Activity 2 Activity 3 Activity 4 Session Follow-Up AC TIVIT Y
Rounding Numbers
20 Min groups
On the board, write the following three numbers:
100 183 200
One of the largest animals ever found was a blue whale that
weighed 183 tons. Is 183 tons closer to 100 tons or to 200 tons?
Talk in your group to figure this out. Then convince the rest of us
that your answer is right.
Students might say:
“183 is closer to 200. Here, look at my
1,000 book. 183 is on the page that goes
from 101 to 200. It’s pretty close to
200.”
“We made a number line. First we put an X on
150 because that’s halfway between 100
and 200. Then we could see that 183 is way
past that. So, it’s closer to 200.”
183
100
150
200
We say that 183 rounded to the nearest hundred is 200. When
you round a number, you get another number that can be used to
tell about how big the original number is. The blue whale
weighed about 200 tons.
Now I want you to work in your groups and figure out which two
tens 183 is between. Which ten is it closer to?
Ask students to share their reasoning.
We say that 183 rounded to the nearest ten is 180.
Explain that numbers halfway between two tens or two hundreds
are rounded up. Provide students a variety of numbers through
1,000 (such as 485, 732, 449, 223, 785, 127, 288, 369, 843, 958)
and have them round the numbers to the nearest ten or the nearest
hundred.
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CC31
6/3/11 1:29 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up
Name
Date
Ongoing Assessment: Observing Students at Work
Using Place Value
In Problems 1–4, round each number to the nearest ten.
1. 312
2. 78
3. 235
4. 97
Students round numbers to the nearest ten and the nearest
hundred.
• Can students round 2- or 3-digit numbers to the nearest
In Problems 5–8, round each number to the nearest hundred.
5. 460
6. 807
7. 650
8. 539
ten or nearest hundred? Do they remember to round up for
“halfway” numbers?
9. The base of the Statue of Liberty is 154 feet tall. Is this number closer
to 100 or 200? Explain.
In Problems 10–13, write each number in expanded form.
10. 173
Ac tivit y
© Pearson Education 4
11. 620
13. 308
Session 1.5A
Unit 5
13A
▲ Student Activity Book, Unit 5, p. 13A;
Resource Masters, C17
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20 Min
Expanded Form
12. 45
5/4/11
class
Write 724 on the board.
1:53 PM
How many hundreds are in this number? How many tens? How
many ones? You can use your 1,000 books for help.
Record students’ responses on the board.
Here’s a way to show the number of hundreds, tens, and ones. It’s
called expanded form. It clearly shows the value of each digit in
724.
Write 724 = 700 + 20 + 4 on the board.
724
7 hundreds, 2 tens, 4 ones
724 = 700 + 20 + 4
Discuss several other examples, such as 517, 48, 602, and 390.
Then have students complete Student Activity Book page 13A or
C17.
6/16/11 9:13 AM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up Name
Date
Ac tivit y
20 Min
PAIRS
Comparing Numbers Using >, =, and <
Write 354 and 614 on the board.
Comparing Numbers
1. How many hundreds are in 755?
How many hundreds are in 680?
Which number is greater, 755 or 680?
Students might say:
“We figured 354 has 3 hundreds, and 614
has 6 hundreds, so 614 is way bigger
because it has more hundreds.”
“We looked in our 1,000 books. 614 is a lot
closer to 1,000, which is the biggest
number in the book. So 614 has got to be
greater.”
How many tens are in 266?
In Problems 3–8, compare the numbers. Write <, >, or =.
3. 571
277
4. 62
5. 813
813
6. 152
7. 914
930
8. 41
26
55
41
9. Abdul has 304 coins, and Luke has 403 coins. Who has more coins?
Which number is greater? Talk with a partner to figure this out.
Then explain your thinking.
13B
Unit 5
Session 1.5A
▲ Student Activity Book, Unit 5, p. 13B;
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9:15 AM
Model writing a comparison using both words and the < symbol.
Explain that the symbol < means “is less than.” Then discuss how
to write the comparison in words and with the symbol. Explain
that this symbol > means “is greater than.”
354 is less than 614.
614 is greater than 354.
354
614
<
614
>
354
What if both numbers have the same number of hundreds? How
can you compare 781 and 749?
Students might say:
“You can’t tell from the hundreds. So move
to the tens and compare those. 8 tens is
more than 4 tens, so 781 is greater than
749.”
Have students complete Student Activity Book page 13B or C18.
Session 1.5A Place-Value Understanding CC33
6/14/11 2:05 PM
1 Activity 2 Activity 3 Activity 4 Session Follow-Up
Name
Date
Daily Practice
River Lengths
Use the data about U.S. rivers.
Pecos River
926 miles long
Yellowstone River
692 miles long
differentiation: Supporting the Range of Learners
note Students use placevalue understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000.
Some students may confuse the < and > symbols.
Point out that the pointy, “smaller” part of the arrow points to the
smaller number.
1. Write the length of each river in expanded form.
Pecos River:
Yellowstone River:
2. Round the length of each river to the nearest hundred.
Pecos River:
Yellowstone River:
Students who can easily compare numbers can be
challenged to order lists of 3-digit numbers.
3. Round the length of each river to the nearest ten.
Pecos River:
Yellowstone River:
4. Compare the lengths of the rivers. Write <, >, or =.
926
692
Session 1.5A
Unit 5
SESSION FOLLOW-UP
13C
▲ Student Activity Book, Unit 5, p. 13C;
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9:16 AM
Daily Practice
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 13C
or C19.
Student Math Handbook: Students and families may use
Student Math Handbook page 6 for reference and review. See
pages 203–206 in the back of Unit 5.
6/16/11 9:13 AM
session 3.6A
Larger Place Values
Math Focus Points
Understanding place-value concepts to 1,000,000
Using >, =, and < to compare numbers to 1,000,000
Writing numbers to 1,000,000 in expanded form
Rounding numbers to 1,000,000
Today’s Plan
Materials
Discussion
Place Value to 1,000,000
•Chart paper (Prepare the place-value chart
activity
Expanded Form
•Student Activity Book, p. 51A or
20 Min Class
Activity
Rounding Large Numbers
pictured on the next page.)
15 Min Groups
•
C21, Place Value to 1,000,000 Make copies.
(as needed)
Place-value chart (from discussion)
•Student Activity Book, p. 51B or
25 Min
Pairs
Session Follow-Up
Daily Practice
•
C22, Rounding Large Numbers Make
copies. (as needed)
10,000 chart (from Session 3.1)
•Student Activity Book, p. 51C or
•
C23, Concert Tickets Make copies. (as
needed)
Student Math Handbook, pp. 6–7
Ten-Minute Math
Practicing Place Value Say “five thousand two hundred eleven” and have students
practice writing the number. Make sure all students can read, write, and say this
number correctly. Have students write 5,211 in expanded form. Ask students to solve
these problems mentally, if possible:
• What is 5,211 + 30? 5,211 + 300? 5,211 – 10? 5,211 – 100? 5,211 – 1,000?
Write each answer on the board. Have students compare each sum or difference to
5,211. Ask students:
If time permits, pose additional similar problems using these numbers: 2,174 and 6,831.
Session 3.6A Larger Place Values CC35
6/3/11 1:39 PM
1 Discussion 2 Activity 3 Activity 4 Session Follow-Up
Differentiation
Some
students might come from a country in
which periods, not commas, are used to
separate groups of three digits in large
numbers. In these countries, commas are
used in decimals instead of periods.
1 English Language Learners Discussion
15 Min Groups
Math Focus Points for Discussion
Understanding place-value concepts through 1,000,000
On the board, write 566,141.
Recently this number was the population of Portland, Oregon.
Does anyone know how to read such a large number? Talk it over
in your groups.
Give students a chance to consider the number and share their
ideas. Then display the place-value chart you prepared for
this session.
Millions
Hundred
Ten
thousands thousands Thousands Hundreds
Tens
Ones
A place-value chart can help you understand and read large
numbers. This number is read “five hundred sixty-six thousand,
one hundred forty-one.” In large numbers, commas are used to
separate the digits into groups of three, starting at the right. 1
Two of the digits in this number are 6s. Do both 6s have the
same value?
Students might say:
“The 6 in the ten thousands place means
60,000, but the 6 in the thousands place
means only 6,000.”
“The same digit in different places can
never stand for the same amount. The value
of the digit on the left is always 10 times
the value of the digit on the right.”
CC36 Investigation 3 Working with Numbers to 10,000
6/3/11 1:42 PM
Write 560,332 in the place-value chart.
Name
Date
Recently the population of Oklahoma City, Oklahoma, was five
hundred sixty thousand, three hundred thirty-two. Is its
population greater than or less than the population of Portland?
How can the place-value chart help you figure this out?
Use the place-value chart to help you complete the problems.
Millions
Hundred
thousands
Ten
thousands Thousands
Hundreds
Tens
Ones
1. 38,956
Students might say:
“Portland is bigger. I could tell from the
chart that both populations have the
same number of hundred thousands and
ten thousands. But Portland has
more thousands.”
2. 7,104
3. 648,713
4. 305,501
5. Do all 6-digit numbers have 6 addends in their expanded form? Explain.
6. In the number at the right, circle
the 4 that has 10 times the value
of the underlined 4.
Ask a volunteer to write a comparison statement about the two
populations using the < or > symbol.
444,444
In Problems 7 and 8, write <, >, or =.
7. 42,551
Session 3.6A
40,725
8. 712,726
1,000,000
Unit 5
51A
▲ Student Activity Book, Unit 5, p. 51A;
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1:54 PM
Save the place-value chart for use during the next activity.
Ac tivit y
Expanded Form
20 Min
class
Direct the class’ attention to the place-value chart.
Let’s look at the first number, 566,141. How many hundred
thousands are in this number? How many ten thousands?
Thousands? Hundreds? Tens? Ones? We can show this using
expanded form.
Write the expanded form for 566,141.
566,141 =
500,000 + 60,000 + 6,000 + 100 + 40 + 1
Ask students to write the expanded form for the second number in
the chart, 560,332. Then have students complete Student Activity
Book page 51A or C21.
Session 3.6A Larger Place Values CC37
6/3/11 1:44 PM
Students write the expanded form of a large number.
• Do students write the correct value for each digit?
• Do students “skip” an addend when the digit is 0?
Some students may lose track of which digit has
which value. Provide these students with additional place-value
charts so they can record each number before they write its
expanded form.
Ac tivit y
25 Min
PAirs
Review rounding numbers to the nearest ten and the nearest
hundred. Then write 6,271 on the board.
How would you round this number to the nearest thousand? Talk
with your partner and then explain your reasoning.
Students might say:
“It rounds to 6,000. We pictured where
the number would go on the 10,000 chart
and we figured it’s closer to 6,000 than
to 7,000.”
Next, write 258,914 on the board.
How would you round this number to the nearest ten thousand?
It’s too big for the 10,000 chart. Can you and your partner figure
out a way to round any large number, even if it doesn’t fit on the
10,000 chart?
Students might say:
“It rounds to 260,000. Check the digit to
the right of where you’re rounding. It’s an
8, so that means the number is closer to
260,000 than to 250,000.”
CC38 Investigation 3 Working with Numbers to 10,000
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Ask students to round 96,225 to the nearest ten thousand. In this
problem they should notice that when they round the 9 up to the
next ten thousand, the result is 100,000. Have students complete
Student Activity Book page 51B or C22.
Name
Date
In Problems 1 and 2, round each number to the nearest thousand.
2. 8,325
1. 2,716
In Problems 3 and 4, round each number to the nearest ten thousand.
4. 97,300
3. 781,407
In Problems 5 and 6, round each number to the nearest hundred thousand.
Daily Practice
have students complete Student Activity Book page
51C or C23.
Student Math Handbook: Students and families may use
Student Math Handbook pages 6 and 7 for reference and
review. See pages 203–206 in the back of Unit 5.
5. 570,003
6. 116,325
7. Round each population to the nearest ten thousand.
City
Population
Austin, TX
786,382
Cleveland, OH
431,363
Oakland, CA
409,184
Nearest Ten Thousand
8. Suppose a number is rounded to the nearest hundred thousand.
What is a number less than 700,000 that rounds to 700,000?
What is a number greater than 700,000 that rounds to 700,000?
51B
Unit 5
Session Follow-Up
Session 3.6A
▲ S tudent Activity Book, Unit 5, p. 51B;
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6/2/11 4:08 PM
Name
Date
Daily Practice
Concert Tickets
Use the data about the number of concert tickets sold.
Holiday Rock Concert
413,125 tickets
Summer Jazz Concert
418,832 tickets
note Students use placevalue understanding to write numbers in expanded form, round numbers, and compare numbers through 1,000,000.
1. Write the number of tickets sold in expanded form.
Holiday Rock Concert:
Summer Jazz Concert:
2. Round the number of tickets sold to the nearest ten thousand.
3. Round the number of tickets sold to the nearest hundred thousand.
4. Compare the number of tickets sold. Write <, >, or =.
413,125
418,832
Session 3.6A
Unit 5
51C
▲ S tudent Activity Book, Unit 5, p. 51C;
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Session 3.6A Larger Place Values INV12_TE04_U05_S3.6A.indd 39
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1:54 PM
CC39
6/3/11 1:46 PM
session 4.4A
Studying the U.S. Algorithm
for Subtraction
Math Focus Points
Understanding the meaning of the steps and notation of
the U.S. algorithm for subtraction
Using clear and concise notation for recording addition
and subtraction strategies
Today’s Plan
Materials
activity
Examining the U.S. Algorithm
for Subtraction
30 Min Class
activity
•Student Activity Book, pp. 62A–62B or
The U.S. Algorithm
for Subtraction
20 Min Individuals
Discussion
Solving Problems with the
U.S. Algorithm
C25–C26, The U.S. Algorithm Make copies.
(as needed)
•Students’ completed copies of Student Activity
10 Min Class
Session Follow-Up
Book, pp. 62A–62B or C25–C26 (from Activity 2)
•Student Activity Book, p. 62D or
Daily Practice
C27, Using the U.S. Algorithm Make copies.
(as needed)
Ten-Minute Math
Practicing Place Value Write 7,472 on the board and have students practice saying it.
Make sure all students can read, write, and say this number correctly. Ask students to
write this number in expanded form. Then ask students to solve these problems
mentally, if possible.
• What is 7,472 – 50? 7,472 – 60? 7, 472 + 300? 7,472 + 400? 7,472 + 500?
Write each answer on the board. Have students compare each sum or difference with
7,472. Ask students:
CC40 Investigation 4 Subtraction
6/3/11 1:47 PM
1 Activity 2 Activity 3 Discussion 4 Session Follow-Up
Ac tivit y
Professional Development
Examining the U.S. Algorithm
for Subtraction
30 Min
class
Tell students that today they are going to examine a subtraction
strategy and notation that a number of people use–the U.S.
algorithm for subtraction. 1 2
Write this problem on the board:
283
– 137
In this strategy, each place is subtracted separately. The people
who invented this algorithm wanted to use only positive
numbers. They figured out a way to rewrite the top number so
they could subtract each place and get all positive numbers. Let’s
look at how we could rewrite the top number to solve
this problem.
When people use this U.S. algorithm, they start from the ones
place. To help us understand this strategy better, first let’s write
each number in expanded form.
Ask students how to write the numbers in expanded form, and
write the following on the board:
283 200 + 80 + 3
– 137 – (100 + 30 + 7)
I wrote the bottom number in parentheses to show that we are
subtracting all the parts. We start with the ones place, but we
don’t want to subtract 7 from 3. We want to change the way we’re
breaking up the number so that we get only positive differences. 3
We’re going to break up the 80 and combine part of it with the 3.
Write 200 + 70 + ___ on the board next to the other problems,
and ask students what number goes on the blank to still have the
sum of 283.
283 200 + 80 + 3
– 137 – (100 + 30 + 7)
200 + 70 + Why Study the U.S.
Conventional Algorithms?, Curriculum
Unit 5, p. 177
1 Teacher Note: Math Note
The U.S. algorithm
for subtraction, sometimes called
“borrowing” or regrouping, is a procedure
that was devised for compactness and
efficiency. One advantage of the
algorithm is that it requires only
subtraction of single digits from numbers
less than 20. However, its efficiency of
steps and notation obscures the place
value of the numbers. By examining the
numbers in expanded form (e.g., 400 +
60 + 3) and the equivalent notation that
results from regrouping the numbers
(e.g., 400 + 50 + 13), students study
the meaning of the algorithm. As with
other strategies, studying this one and
thinking through why these steps make
sense allows students to deepen their
knowledge about the operation of
subtraction. Students who have
developed good, efficient subtraction
methods that they understand and can
carry out easily (e.g., subtracting in parts,
adding up, or subtracting back) may also
benefit from practicing and becoming
fluent in the U.S. algorithm. However,
students are not expected to switch to
using this algorithm. Continuing to use
the methods they have developed will
serve them well for their computation
needs now and in the future.
2 The U.S. Algorithm A
student may say (or you may choose to
bring up) that you can subtract 7 from 3
and get –4 (negative four). Acknowledge
that this is correct but that the U.S.
algorithm for subtraction uses only
positive numbers.
3 Using Positive Numbers Only Session 4.4A Studying the U.S. Algorithm for Subtraction CC41
6/3/11 1:48 PM
Give students a moment to discuss this, and call on students to
explain their thinking. Write 13 on the blank. Rewrite the rest of
the problem. Then ask students what 13 – 7 is and write 6 under
13 – 7.
283 200 + 80 + 3 200 + 70 + 13
– 137 – (100 + 30 + 7) – (100 + 30 + 7)
6
This is what is sometimes called “borrowing” or regrouping. We
didn’t have enough ones to subtract from to get a positive
number, so we used one of the 8 tens and added it to 3. Then
instead of 200 + 80 + 3, we had 200 + 70 + 13, which is the
same amount that is just broken up differently.
Ask students to subtract the tens and then the hundreds and record
the results:
200 + 70 + 13
– (100 + 30 + 7)
100 + 40 + 6
If needed, spend a few more minutes discussing how breaking up
283 in a different way allowed subtraction by place with a positive
result in each place. Then move on to examining the standard
notation for this algorithm.
When people use this algorithm they use a shorthand notation
instead of writing out the new way to break the number apart like
we did. Let’s look at the notation.
283 200 + 80 + 3 200 + 70 + 13
– 137 – (100 + 30 + 7) – (100 + 30 + 7)
100 + 40 + 6 = 146
7
2∙813
– 137
146
As you write the algorithm on the board, talk through
the procedure.
I don’t want to subtract 7 from 3, so I take a ten from the tens
place and give it to the ones place. I show this by crossing out the
8, making it a 7, and writing a 1 next to the 3 to make it 13. 13
minus 7 is 6. Then 7 minus 3 is 4; that’s 7 tens minus 3 tens.
Then 2 minus 1 is 1. What do the 2 and the 1 mean?
6/3/11 1:52 PM
545 500 + 40 + 5 500 + 30 + 15
400 + 130 + 15
– 268 – (200 + 60 + 8) – (200 + 60 + 8) – (200 + 60 + 8)
200 + 70 + 7
= 277
Give students a few minutes to discuss these steps, and then discuss
the shorthand notation.
Name
Date
The U.S. Algorithm (page 1 of 2)
Use the U.S. algorithm for subtraction to solve the following
problems. (Then solve the problems using a different
strategy to make sure your final answer is correct.)
In Problems 1 and 2, the steps of the U.S. algorithm are
shown. Fill in the blanks with the correct numbers.
1.
757
4 2 8
−
757
4 2 8
−
41
2.
526
1 8 8
−
526
1 8 8
−
545
∙ 268
277
50
20
+
+
700
− (400
+
+
+
500
− (100
7
8)
+
+
+
+
20
8)
+
20
80
+
+
6
8)
+
+
1
4 11
62A
4 13 1
700
(400
−
− (100
+
+
+
+
+
80
8)
+
Spend a few more minutes talking through this notation. Then
work through another example in which both the tens and
hundreds places must be changed.
Unit 5
Session 4.4A
▲ S tudent Activity Book, Unit 5, p. 62A;
INV12_SE04_U5.indd
1
6/1/11
Name
9:20 AM
Date
For Problems 3 and 4, use the U.S. algorithm for subtraction
to solve each problem. Also, write the correct numbers in
the blanks, showing how you broke apart the original
numbers.
The U.S. Algorithm
for Subtraction
3.
361
1 4 3
−
300
− (100
361
1 4 3
−
− (
4.
844
7 5 7
−
800
(700
−
844
7 5 7
−
− (
20 Min Individuals
Students complete Student Activity Book pages 62A–62B or
C25–C26. They practice the U.S. algorithm for subtraction by
breaking apart the numbers by place and then regrouping in order
to use only positive numbers. They also practice the shorthand
As students work, ask them to explain what they are doing for each
step and why—particularly when they are regrouping and when
they are recording using shorthand notation. Pay attention to
whether they are able to use the algorithm to solve Problems 2 and
4 in which both the tens and hundreds places need to be changed.
+
+
60
40
+
+
+
+
+
+
+
+
40
50
+
+
+
+
+
+
1
3)
)
4
7)
)
Ac tivit y
Session 4.4A
Unit 5
62B
▲ S tudent Activity Book, Unit 5, p. 62B;
INV12_SE04_U5.indd
2
6/1/11
9:20 AM
• Do students understand how the numbers are broken
apart to show regrouping?
• Can students use this algorithm to solve
subtraction problems?
• Do they understand the shorthand notation of
the algorithm?
Session 4.4A Studying the U.S. Algorithm for Subtraction INV12_TE04_U05_S4.4A.indd 43
CC43
6/3/11 1:54 PM
Name
Date
Daily Practice
Using the U.S. Algorithm
Use the U.S. algorithm for subtraction to solve each
problem. Also, write the correct numbers in the blanks,
showing how you broke apart the original numbers.
498
2 7 9
−
400
(200
−
498
2 7 9
−
− (
2.
525
1 6 4
−
500
− (100
525
1 6 4
−
− (
+
+
90
70
+
+
+
+
+
+
+
+
20
60
+
+
+
+
+
+
For students who have been using (or trying to use) this
algorithm, these problems should provide support in helping
them understand the mathematics behind the algorithm.
8
9)
Students who have difficulty regrouping tens or
hundreds from one place to another may benefit from practice
breaking apart a number in different ways. For example, 863 can
be broken apart as 800 + 60 + 3 or 800 + 50 + 13 or
700 + 160 + 3, and so on.
)
5
4)
)
1.
note Students practice using the U.S. algorithm for subtraction by breaking apart the numbers by place and regrouping when necessary. They also practice the standard notation for this algorithm.
Session 4.4A
Unit 5
62D
▲ S tudent Activity Book, Unit 5, p. 62D;
INV12_SE04_U5.indd
4
6/1/11
9:21 AM
Students who can explain and use the U.S.
algorithm for the problems on these pages can be challenged
to solve problems that include zeros in the first number
(e.g., 903 – 264).
Discussion
Solving Problems with the
U.S. Algorithm
10 Min
class
Math Focus Points for Discussion
Understanding the meaning of the steps and notation of the
U.S. algorithm for subtraction
Have students look at their completed Student Activity Book pages
62A–62B or C25–C26.
What questions do you have after solving problems using the
U.S. algorithm? How is this strategy different from other
strategies we have discussed? How is it similar?
Refer students to the charts of subtraction strategies posted in
Session 4.3.
Session Follow-Up
Daily Practice
have students complete Student Activity Book page 62D
or C27.
10/26/11 3:33 PM
Name
Date
Using Place Value
In Problems 1–4, round each number to the nearest ten.
1. 312
2.78
3. 235
4.97
In Problems 5–8, round each number to the nearest hundred.
5. 460
6.807
7. 650
8.539
9.The base of the Statue of Liberty is 154 feet tall. Is this number closer
to 100 or 200? Explain.
10.173
11.620
12.45
13.308
Unit 5 Session 1.5A
INV12_BLM04_U5.indd 17
C17
Copyright (c) Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
6/17/11 11:01 AM
Name
Date
Comparing Numbers
In Problems 3–8, compare the numbers. Write <, >, or =.
3. 571
277
4.62
5. 813
813
6.152
7. 914
930
8.41
26
55
41
9. Abdul has 304 coins, and Luke has 403 coins. Who has more coins?
Unit 5 Session 1.5A
C18
6/17/11 11:01 AM
Name
Date
Daily Practice
River Lengths
notE Students use place-value
understanding to write numbers in
expanded form, round numbers, and
compare numbers through 1,000.
Use the data about U.S. rivers.
Pecos River
926 miles long
Yellowstone River
692 miles long
1. Write the length of each river in expanded form.
Pecos River:
Yellowstone River:
2. Round the length of each river to the nearest hundred.
Pecos River:
Yellowstone River:
3. Round the length of each river to the nearest ten.
Pecos River:
Yellowstone River:
4. Compare the lengths of the rivers. Write <, >, or =.
926
692
Unit 5 Session 1.5A
C19
6/22/11 6:09 PM
Name
Date
Daily Practice
School Enrollments
Use the data about school enrollments.
Bryant School
403 students
Holmes School
438 students
compare numbers through 1,000.
1. Write each school’s enrollment in expanded form.
Bryant School:
Holmes School:
2. Round each school’s enrollment to the nearest ten.
Bryant School:
Holmes School:
3. Round each school’s enrollment to the nearest hundred.
Bryant School:
Holmes School:
4. Compare the school enrollments. Write <, >, or =.
403
438
Unit 5 Session 2.5
C20
6/22/11 6:09 PM
Name
Date
Use the place-value chart to help you complete the problems.
Millions
Hundred
Ten
thousands thousands Thousands Hundreds
Tens
Ones
1. 38,956
2. 7,104
3. 648,713
4. 305,501
5.Do all 6-digit numbers have 6 addends in their expanded form? Explain.
6.In the number at the right, circle
the 4 that has 10 times the value of the underlined 4.
444,444
In Problems 7 and 8, write ,, ., or 5.
7. 42,551
40,725
Unit 5 Session 3.6A
8.712,726
C21
1,000,000
6/23/11 3:56 PM
Name
Date
In Problems 1 and 2, round each number to the nearest thousand.
1. 2,716
2.8,325
In Problems 3 and 4, round each number to the nearest ten thousand.
3. 781,407
4.97,300
In Problems 5 and 6, round each number to the nearest
hundred thousand.
5. 570,003
6.116,325
7.Round each population to the nearest ten thousand.
City
Population
Austin, TX
786,382
Cleveland, OH
431,363
Oakland, CA
409,184
Nearest Ten Thousand
8.Suppose a number is rounded to the nearest hundred thousand.
What is a number less than 700,000 that rounds to 700,000?
What is a number greater than 700,000 that rounds to 700,000?
Unit 5 Session 3.6A
C22
6/17/11 11:02 AM
Name
Date
Daily Practice
Concert Tickets
Use the data about the number of concert
tickets sold.
Holiday Rock Concert
413,125 tickets
Summer Jazz Concert
418,832 tickets
compare numbers through 1,000,000.
1. Write the number of tickets sold in expanded form.
2. Round the number of tickets sold to the nearest ten thousand.
3. Round the number of tickets sold to the nearest hundred thousand.
4. Compare the number of tickets sold. Write <, >, or =.
413,125
418,832
Unit 5 Session 3.6A
C23
6/22/11 6:09 PM
Name
Date
Daily Practice
Areas of Countries
expanded form and round numbers
through 1,000,000.
In Problems 1–4, use the data about the
areas of some countries.
Austria
32,382 square miles
Indonesia
741,096 square miles
Chile
292,258 square miles
1. Write each country’s area in expanded form.
Austria:
Indonesia:
Chile:
2. Round Austria’s area to the nearest ten thousand.
3. Round Indonesia’s area to the nearest thousand.
4. Round Chile’s area to the nearest hundred thousand.
5. Write three numbers that would round to 520,000 when rounded to the
nearest ten thousand.
Unit 5 Session 4.2
C24
6/22/11 4:46 PM
Name
Date
Use the U.S. algorithm for subtraction to solve the following
problems. (Then solve the problems using a different
strategy to make sure your final answer is correct.)
In Problems 1 and 2, the steps of the U.S. algorithm are
shown. Fill in the blanks with the correct numbers.
1. 7 5 7
− 4 2 8
41
7 5 7
− 4 2 8
2. 5 2 6
− 1 8 8
4 11 1
5 2 6
− 1 8 8
700
2 (400
700
2 (400
1
1
+
500
2 (100
2 (100
1
1
1
Unit 5 Session 4.4A
1
1
1
1
C25
50
20
20
20
80
80
1
1
1
1
7
8)
8)
+
1
1
1
1
6
8)
8)
1
6/23/11 3:59 PM
Name
Date
For Problems 3 and 4, use the U.S. algorithm for subtraction
to solve each problem. Also, write the correct numbers in
the blanks, showing how you broke apart the original
numbers.
3. 3 6 1
− 1 4 3
300
2 (100
3 6 1
− 1 4 3
1
2 ( 1
4. 8 4 4
− 7 5 7
800
2 (700
8 4 4
− 7 5 7
1
2 ( 1
Unit 5 Session 4.4A
1
1
1
1
C26
60
40
1
1
1
1
40
50
1
1
1
1
1
3)
)
4
7)
)
6/23/11 4:00 PM
Name
Date
Daily Practice
Using the U.S. Algorithm
Use the U.S. algorithm for subtraction to solve
each problem. Also, write the correct numbers
in the blanks, showing how you broke apart
the original numbers.
1. 4 9 8
− 2 7 9
400
− (200
4 9 8
− 2 7 9
+
− ( +
2. 5 2 5
− 1 6 4
500
− (100
5 2 5
− 1 6 4
+
− ( +
Unit 5 Session 4.4A
+
+
+
+
C27
notE Students practice using the
U.S. algorithm for subtraction by
breaking apart the numbers by place
and regrouping when necessary.
They also practice the standard
90
70
+
+
+
+
20
60
+
+
+
+
8
9)
)
5
4)
)
6/22/11 6:09 PM
Name
Date
Daily Practice
Subtraction Practice
Use the U.S. algorithm for subtraction to solve
each problem. Also, write the correct numbers
in the blanks, showing how you broke apart the
original numbers.
1. 7 8 1
− 5 9 3
700
− (500
7 8 1
− 5 9 3
+
− ( +
2. 9 3 3
− 6 4 7
900
− (600
9 3 3
− 6 4 7
+
− ( +
Unit 5 Session 4.5
+
+
+
+
C28
notE Students practice using the
U.S. algorithm for subtraction by
breaking apart the numbers by place
and regrouping when necessary.
They also practice the standard
80
90
+
+
+
+
30
40
+
+
+
+
1
3)
)
3
7)
)
6/22/11 6:10 PM
Nombre
Fecha
Números de referencia y números grandes
Usar el valor posicional
En los Problemas 1 a 4, redondea cada número a la decena
más cercana.
1. 312
2.78
3. 235
4.97
En los Problemas 5 a 8, redondea cada número a la centena
más cercana.
5. 460
6.807
7. 650
8.539
9. La base de la Estatua de la Libertad mide 154 pies de alto.
¿Se acerca este número más a 100 o a 200? Explica tu respuesta.
En los Problemas 10 a 13, escribe cada número en forma desarrollada.
10.173
11.620
12.45
13.308
Unidad 5 Sesión 1.5A
INV12_SP_BLM04_U5.indd 17
C17
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 4
6/20/11 9:17 PM
Nombre
Fecha
Comparar números
1. ¿Cuántas centenas hay en 755?
¿Cuántas centenas hay en 680?
¿Qué número es mayor, 755 o 680?
2. ¿Cuántas centenas hay en 266?
¿Cuántas centenas hay en 281?
¿Cuántas decenas hay en 266?
¿Cuántas decenas hay en 281?
¿Qué número es mayor, 266 o 281?
En los Problemas 3 a 8, compara los números. Escribe <, > o =.
3. 571
277
4.62
5. 813
813
6.152
7. 914
930
8.41
26
55
41
9. Abdul tiene 304 monedas y Luke tiene 403 monedas.
¿Quién tiene más monedas?
C18
7/25/11 1:07 PM
Nombre
Fecha
Práctica diaria
Longitudes de ríos
Usa los datos sobre ríos en los Estados Unidos.
río Pecos
926 millas de largo
río Yellowstone
692 millas de largo
notA Los estudiantes usan la
comprensión del valor posicional para
escribir números en forma desarrollada,
redondear números y comparar
números hasta 1,000.
1. Escribe la longitud de cada río en forma desarrollada.
río Pecos:
río Yellowstone:
2. Redondea la longitud de cada río a la centena más cercana.
río Pecos:
río Yellowstone:
3. Redondea la longitud de cada río a la decena más cercana.
río Pecos:
río Yellowstone:
4. Compara las longitudes de los ríos. Escribe <, > o =.
926
692
C19
7/25/11 1:07 PM
Nombre
Fecha
Práctica diaria
Inscripciones escolares
Usa los datos sobre las inscripciones escolares.
Escuela Bryant
403 estudiantes
Escuela Holmes
438 estudiantes
escribir números en forma desarrollada,
redondear números y comparar
números hasta 1,000.
1. Escribe las inscripciones de cada escuela en forma
desarrollada.
Escuela Bryant:
Escuela Holmes:
2. Redondea las inscripciones de cada escuela a la decena
más cercana.
Escuela Bryant:
Escuela Holmes:
3. Redondea las inscripciones de cada escuela a la centena
más cercana.
Escuela Bryant:
Escuela Holmes:
4. Compara las inscripciones escolares. Escribe <, > o =.
403
438
Unidad 5 Sesión 2.5
C20
7/25/11 1:07 PM
Nombre
Fecha
Valor posicional hasta 1,000,000
Usa la tabla de valor posicional como ayuda para completar los problemas.
Millones
Centenas
de millar
Decenas
de millar
Millares
Centenas
Decenas Unidades
En los Problemas 1 a 4, escribe cada número en forma desarrollada.
1. 38,956
2. 7,104
3. 648,713
4. 305,501
5. ¿Todos los números de 6 dígitos tienen 6 sumandos en su forma
desarrollada? Explica tu respuesta.
6. En el número de la derecha, encierra en un
círculo el 4 que tiene 10 veces el valor del 4 subrayado.
444444
En los Problemas 7 y 8, escribe <, > o =.
7. 42,551
40,725
8.712,726
C21
1,000,000
7/25/11 1:07 PM
Nombre
Fecha
Redondear números grandes
En los Problemas 1 y 2, redondea cada número al millar más cercano.
1. 2,716
2.8,325
En los Problemas 3 y 4, redondea cada número a la decena
de millar más cercana.
3. 781,407
4.97,300
En los Problemas 5 y 6, redondea cada número a la centena
5. 570,003
6.116,325
7. Redondea cada población a la decena de millar más cercana.
Ciudad
Población
Austin, TX
786,382
Cleveland, OH
431,363
Oakland, CA
409,184
Decena de millar más cercana
8. Supón que un número se redondea a la centena de millar
más cercana.
¿Qué número menor que 700,000 se redondea a 700,000?
¿Qué número mayor que 700,000 se redondea a 700,000?
C22
6/20/11 9:21 PM
Nombre
Fecha
Práctica diaria
Boletos para conciertos
Usa los datos sobre el número de boletos
vendidos para los conciertos.
Concierto de rock de
Navidad
413,125 boletos
Concierto de jazz de
verano
418,832 boletos
escribir números en forma
desarrollada, redondear números y
comparar números hasta 1,000,000.
1. Escribe el número de boletos vendidos en forma desarrollada.
Concierto de rock de Navidad:
Concierto de jazz de verano:
2. Redondea el número de boletos vendidos a la decena
3. Redondea el número de boletos vendidos a la centena
4. Compara el número de boletos vendidos. Escribe <, > o =.
413,125
418,832
C23
7/25/11 1:07 PM
Nombre
Fecha
Práctica diaria
Áreas de países
En los Problemas 1 a 4, usa los datos sobre
las áreas de algunos países.
Austria
escribir números en forma
desarrollada y redondear números
hasta 1,000,000.
32,382 millas cuadradas
Indonesia
Chile
1. Escribe el área de cada país en forma desarrollada.
Austria:
Indonesia:
Chile:
2. Redondea el área de Austria a la decena de millar más cercana.
3. Redondea el área de Indonesia al millar más cercano.
4. Redondea el área de Chile a la centena de millar más cercana.
5. Escribe tres números que podrían redondearse a 520,000 si tuvieras
que redondearlos a la decena de millar más cercana.
C24
7/21/11 7:20 AM
Nombre
Fecha
El algoritmo usual (página 1 de 2)
Usa el algoritmo usual de la resta para resolver los
siguientes problemas. (Luego resuelve los problemas usando
una estrategia diferente para asegurarte de que tu respuesta
final sea correcta).
En los Problemas 1 y 2 se muestran los pasos del
algoritmo usual. Completa los espacios en blanco con los
números correctos.
1. 7 5 7
− 4 2 8
41
7 5 7
− 4 2 8
2. 5 2 6
− 1 8 8
4 11 1
5 2 6
− 1 8 8
700
− (400
700
− (400
+
+
+
500
− (100
− (100
+
+
+
+
+
+
+
C25
50
20
20
20
80
80
+
+
+
+
7
8)
8)
+
+
+
+
+
6
8)
8)
+
7/21/11 7:20 AM
Nombre
Fecha
El algoritmo usual (página 2 de 2)
En los Problemas 3 y 4, usa el algoritmo usual de la resta
para resolver cada problema. También, escribe los números
correctos en los espacios en blanco, mostrando cómo
descompusiste los números originales.
3. 3 6 1
− 1 4 3
300
− (100
3 6 1
− 1 4 3
+
− ( +
4. 8 4 4
− 7 5 7
800
− (700
8 4 4
− 7 5 7
+
− ( +
+
+
+
+
C26
60
40
+
+
+
+
40
50
+
+
+
+
1
3)
)
4
7)
)
7/21/11 7:20 AM
Nombre
Fecha
Práctica diaria
Usar el algoritmo usual
Usa el algoritmo usual de la resta para
resolver cada problema. También, escribe
los números correctos en los espacios en
blanco, mostrando cómo descompusiste los
números originales.
1. 4 9 8
− 2 7 9
400
− (200
4 9 8
− 2 7 9
+
− ( +
2. 5 2 5
− 1 6 4
500
− (100
5 2 5
− 1 6 4
+
− ( +
+
+
+
+
C27
notA Los estudiantes practican el
uso del algoritmo usual de la resta al
descomponer los números por lugar y
reagruparlos cuando es necesario.
También practican la notación
estándar para este algoritmo.
90
70
+
+
+
+
20
60
+
+
+
+
8
9)
)
5
4)
)
7/21/11 7:20 AM
Nombre
Fecha
Práctica diaria
Práctica de resta
Usa el algoritmo usual de la resta para
resolver cada problema. También, escribe
los números correctos en los espacios en
blanco, mostrando cómo descompusiste
los números originales.
1. 7 8 1
− 5 9 3
700
− (500
7 8 1
− 5 9 3
+
− ( +
2. 9 3 3
− 6 4 7
900
− (600
9 3 3
− 6 4 7
+
− ( +
+
+
+
+
C28
notA Los estudiantes practican el
uso del algoritmo usual de la resta al
descomponer los números por lugar y
reagruparlos cuando es necesario.
También practican la notación
estándar para este algoritmo.
80
90
+
+
+
+
30
40
+
+
+
+
1
3)
)
3
7)
)
7/21/11 7:21 AM

Unit 5 - Professional Development

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