Transcript Module 1 Lesson 11 - Peoria Public Schools

Module 1 Lesson 11
Place Value, Rounding, and Algorithms for
Addition and Subtraction
Topic d: Multi-digit whole number addition
4.oa.3, 4.nbt.4, 4.nbt.1, 4 nbt.2
This PowerPoint was developed by Beth Wagenaar and Katie E. Perkins.
The material on which it is based is the intellectual property of Engage NY.
Lesson 11
Topic: Multi-Digit
Whole Number
Addition
• Objective: Use place value
understanding to fluently
add multi-digit whole
numbers using the standard
addition algorithm and
apply the algorithm to
solve word problems using
tape diagrams
Lesson 11
Round to Different Place Values
5 Minutes
4,000
<3,941
3,500
3,000
•
•
•
•
•
•
3,941 We are going to round to the nearest thousands
How many thousands are in 3,941?
I am going to label the lower endpoint with 3,000.
And 1 more thousand will be?
What is halfway between 3,000 and 4,000?.
Label 3,500 on your number line as I do the
same.
• Label 3,941 on your number line.
• Is 3,941 nearer to 3,000 or 4,000?
• 3,941 ≈ _______ Write your answer on your
board.
Round to Different Place Values
80,000
75,000
<74,621
70,000
Lesson 11
• 74,621 We are going to round to the nearest ten
thousands
• How many ten thousands are in 74,621?
• I am going to label the lower endpoint with 70,000.
• And 1 more ten thousand will be?
• What is halfway between 70,000 and 80,000?.
• Label 75,000 on your number line as I do the
same.
• Label 74,621 on your number line.
• Is 74,621 nearer to 70,000 or 80,000?
• 74,621 ≈ _______ Write your answer on your
board.
Round to Different Place Values
75,000
<74,621
74,500
74,000
Lesson 11
• 74,621 We are going to round to the nearest
thousands
• How many thousands are in 74,621?
• I am going to label the lower endpoint with 74,000.
• And 1 more thousand will be?
• What is halfway between 74,000 and 75,000?.
• Label 74,500 on your number line as I do the
same.
• Label 74,621 on your number line.
• Is 74,621 nearer to 74,000 or 75,000?
• 74,621 ≈ _______ Write your answer on your
board.
Lesson 11
Round to Different Place Values
700,000
<681,904
650,000
600,000
• 681,904 We are going to round to the nearest
hundred thousand
• How many hundred thousands are in 681,904?
• I am going to label the lower endpoint with 600,000.
• And 1 more hundred thousand will be?
• What is halfway between 600,000 and 700,000?.
• Label 650,000 on your number line as I do the
same.
• Label 681,904 on your number line.
• Is 681,904 nearer to 600,000 or 700,000?
• 681,904 ≈ _______ Write your answer on your
board.
Lesson 11
Round to Different Place Values
690,000
685,000
<681,904
680,000
• 681,904 We are going to round to the nearest ten
thousand
• How many ten thousands are in 681,904?
• I am going to label the lower endpoint with 680,000.
• And 1 more ten thousand will be?
• What is halfway between 680,000 and 690,000?.
• Label 685,000 on your number line as I do the
same.
• Label 681,904 on your number line.
• Is 681,904 nearer to 680,000 or 690,000?
• 681,904 ≈ _______ Write your answer on your
board.
Lesson 11
Round to Different Place Values
682,000
<681,904
681,500
681,000
• 681,904 We are going to round to the nearest
thousand
• How many thousands are in 681,904?
• I am going to label the lower endpoint with 681,000.
• And 1 more thousand will be?
• What is halfway between 681,000 and 682,000?.
• Label 681,500 on your number line as I do the
same.
• Label 681,904 on your number line.
• Is 681,904 nearer to 681,000 or 682,000?
• 681,904 ≈ _______ Write your answer on your
board.
Lesson 11
Multiply by Ten
(4 minutes)
Say the multiplication sentence.
On your boards, fill in the blank.
10 x ____ = 100
10 x 1 ten = ______
10 tens = ____hundred
____ ten x _____ ten = 1 hundred.
Lesson 11
Multiply by Ten
(4 minutes)
Say the multiplication sentence.
On your boards, fill in the blank.
1 ten x 60 = ________
10 x 6 tens = _______
20 tens = _____ hundreds
____ ten x _____ ten = 6 hundreds.
Lesson 11
Multiply by Ten
(4 minutes)
Say the multiplication sentence.
On your boards, fill in the blank.
1 ten x 30 = ____ hundreds
10 x 3 tens = ______.
30 tens = ______ hundreds
____ ten x _____ ten = 3 hundred
Lesson 11
Multiply by Ten
(4 minutes)
Say the multiplication sentence.
On your boards, fill in the blank.
1 ten x _____ = 900
10 x 9 tens = ______
90 tens = _____ hundred
____ ten x _____ ten = 9 hundred.
Lesson 11
Multiply by Ten
(4 minutes)
Say the multiplication sentence.
On your boards, fill in the blank.
7 tens x 1 ten = _____ hundreds
70 x 1 tens = _______
70 tens = _____ hundreds
____ ten x _____ ten = 7 hundreds
Lesson 11
Add Common Units
3 Minutes
• 303 Say the number in unit form.
• 303 + 202 = ______ Say the addition sentence
and answer in unit form.
• Did you say, ‘ 3 hundreds 3 ones + 2 hundreds 2
ones = 5 hundreds 5 ones?
• Write the addition sentence on your personal
white boards.
• Did you write 303 + 202 = 505?
Lesson 11
Add Common Units
3 Minutes
• 505 Say the number in unit form.
• 505 + 404 = ______ Say the addition sentence
and answer in unit form.
• Did you say, ‘ 5 hundreds 5 ones + 4 hundreds 4
ones = 9 hundreds 9 ones?
• Write the addition sentence on your personal
white boards.
• Did you write 505 + 404 = 909?
Lesson 11
Add Common Units
3 Minutes
• 5,005 Say the number in unit form.
• 5,005 + 5,004 = ______ Say the addition
sentence and answer in unit form.
• Did you say, ‘ 5 thousands 5 ones + 5 thousands
4 ones = 10 thousands 9 ones?
• Write the addition sentence on your personal
white boards.
• Did you write 5,005 + 5,004 = 10,009?
Add Common Units
3 Minutes
• 7,007 Say the number in unit form.
• 7,007 + 4,004 = ______ Say the addition
sentence and answer in unit form.
• Did you say, ‘ 7 thousands 7 ones + 4 thousands
4 ones = 11 thousands 11 ones?
• Write the addition sentence on your personal
white boards.
• Did you write 7,007 + 4,004 = 11,011?
Lesson 11
Lesson 11
Add Common Units
3 Minutes
• 8,008 Say the number in unit form.
• 8,008 + 5,005 = ______ Say the addition
sentence and answer in unit form.
• Did you say, ‘ 8 thousands 8 ones + 5 thousands
5 ones = 13 thousands 13 ones?
• Write the addition sentence on your personal
white boards.
• Did you write 8,008 + 5,005 = 13,013?
Application Problem
Lesson 11
7 Minutes
Meredith kept track of the calories she consumed for 3 weeks.
The first week, she consumed 12,490 calories, the second
week 14,295 calories, and the third week 11,116 calories.
About how many calories did Meredith consume altogether?
Which of these estimates will produce a more accurate
answer: rounding to the nearest thousand or rounding to the
nearest ten thousand? Explain.
C
12,490
Smaller Unit!
Ten thousand –>
Thousand ------->
14,295
11,116
10,000 + 10,000 + 10,000 = 30,000
12,000 + 14,000 + 11,000 = 37,000
Lesson 11
Concept Development
35 Minutes
Materials: Personal White Boards
Lesson 11
Problem 1
Add, renaming once using disks in a place value chart
• 3,134 + 2,493 Say this problem
with me.
• Draw a tape diagram to represent
this problem.
• What are the two parts that make up
the whole?
• Record that in the tape diagram.
• What is the unknown?
• Show the whole above the tape
diagram using a bracket and label the
unknown quantity a.
a
3,134
2,493
Problem 1 Continued
a = 5,627
3,134
Thousands
Hundreds
Tens
Lesson 11
Ones
===
=
===
====
==
====
=
===== ===
====
2,493
• Draw disks into the place value chart to represent the
first part, 3,134.
• Add 2,493 by drawing more disks into your place value chart.
• 4 ones plus 3 ones equals?
• 3 tens plus 9 tens equals?
• 1 hundred plus 4 hundreds plus 1 hundred equals?
• We can bundle 10 tens as 1 hundred.
• 3 thousand plus 2 thousands equals?
• We can represent this in writing. Write 12 tens as 1
hundred, crossing the line, and 2 tens in the tens column, • Say the whole equation with me:
• 3,134 plus 2,493 equals 5,627.
so that you are writing 12 and not 2 and 1 as separate
• Label the whole in the tape diagram, above the bracket
numbers.
with a = 5,627.
5
6
2
7
Lesson 11
Problem 2
Add, renaming in multiple units using the standard algorithm and the place
value chart.
• 40,762 + 30,473 Say this problem
with me.
• With your partner, draw a tape
diagram to represent this problem
labeling the two known parts and
the unknown whole, using B to
represent the whole.
B
40,762
30,473
Problem 2 Continued
a = 71,235
Ten Thousands
Thousands
llll
40,762
30,473
lll
7
lllll
ll
llll
l1
l
• With your partner, write the problem and draw disks
for the first addend in your chart. Then draw disks for
the second addend.
• 2 ones plus 3 ones equals?
• 6 tens plus 7 tens equals?
• We can group 10 tens to make 1 hundred.
• Watch me as I record the larger unit.
• 7 hundreds plus 4 hundreds plus 1 hundred equals 12
hundreds. Discuss with your partner how to record this.
• Regroup and then record.
Hundreds
1
2
Tens
Lesson 11
Ones
lllll ll
l
lllll lll
ll
3
5
• Say the whole equation with me.
• 40,762 plus 30,473 equals 71,235. Label the whole
in the bar diagram with 71,235, and write 71,235.
Lesson 11
Problem 3
• 207,426 + 128,744
• Draw a tape diagram
to model this
problem.
• With your partner, add
units right to left,
regrouping when
necessary.
336,170
207,426
207,426
+128,744
128,744
Problem 4
Lesson 11
Solve one-step word problem using standard algorithm modeled with a tape diagram.
The Lane family took a road trip. During the
first week, they drove 907 miles. The second
week they drove the same amount as the first
week plus an additional 297 miles. How many
miles did they drive during the second week?
M
907
297
• What information do we know?
• What is the unknown information?
• Draw a tape diagram to represent the
amount of miles in the first week, 907
miles.
• Since the Lane family drove an
additional 297 miles in the second
week, extend the bar for 297 more
miles. What does the bar represent?
• Use a bracket to label the unknown as
M for miles.
• How do we solve for M?
• Solve. What is M?
• Write a sentence that tells your answer.
• The Lane family drove 1,204 miles during
the second week.
Problem
Set
(10 Minutes)
Lesson 11
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Lesson 11
• When we are writing a sentence to express our answer, what part of the
original problem helps us to tell our answer using the correct words and
context?
• What purpose does a tape diagram have? How does it support your work?
• What does a variable, like the letter B in Problem 2, help us do when
drawing a tape diagram?
• I see different types of tape diagrams drawn for Problem 3. Some drew
one bar with two parts. Some drew one bar for each addend, and put the
bracket for the whole on the right side of both bars. Will these diagrams
result in different answers? Explain.
• In Problem 1, what did you notice was similar and different about the
addends and the sums for Parts (a), (b), and (c)?
• If you have 2 addends, can you ever have enough ones to make 2 tens, or
enough tens to make 2 hundreds, or enough hundreds to make 2
thousands? Try it out with your partner. What if you have 3 addends?
• In Problem 1, each unit used the numbers 2, 5, and 7 once, but the sum
doesn’t show repeating digits. Why not?
• How is recording the regrouped number in the next column of the
addition algorithm related to bundling disks?
• Have students revisit the Application Problem and solve for the actual
amount of calories consumed. Which unit when rounding provided an
estimate closer to the actual value?
Student
Debrief
Lesson 11
11 minutes
Objective: Use place value
understanding to fluently
add multi-digit whole
numbers using the
standard addition algorithm
and apply the algorithm to
solve word problems using
tape diagrams.
Exit Ticket
Lesson 11
Lesson 11
Lesson 11
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Lesson 11