4.2
Estimate Sums
?
Essential Question How can you use compatible numbers and rounding to
estimate sums?
Texas Essential
Knowledge and Skills
How can you use
compatible numbers and
rounding to estimate
sums?
Number and Operation—3.4.B
Round to the nearest 10 or 100 or use compatible numbers to
estimate solutions to addition and subtraction problems
MATHEMATICAL PROCESSES
3.1.C Select tools, technology, and techniques
3.1.D Communicate mathematical ideas and reasoning
Are You Ready?
Access Prior Knowledge
Use the Are You Ready? 4.2 in the
Assessment Guide to assess students’
understanding of the prerequisite skills
for this lesson.
Vocabulary
estimate, compatible numbers
Lesson Opener
Making Connections
Go to Multimedia eGlossary at
thinkcentral.com
Prompt students to tell you what they know about rounding numbers.
What place do you look at when rounding a number to the nearest ten? (ones) What
place do you look at when rounding a number to the nearest hundred? (tens)
Using the Digital Lesson
Can you think of some situations where a rounded number would be useful, and
other situations where an exact number would be needed? (Rounding is useful to
provide estimates for purchasing supplies that come in packages of 100, like nails. Exact
numbers are needed in situations like measuring lumber for a building project.)
Learning Task
• Is it possible for the sum of two rounded numbers to be the same as if the numbers
had not been rounded? (yes)
• Is it possible for the sum of two rounded numbers that are not compatible to be the
same as if the numbers had not been rounded? (no)
Literacy and Mathematics
• Have students draw number lines with a range from 400 to 600 and scaled in
increments of 25. Have them number the marks that make up the scale and then
draw the points that correspond to the numbers 441 and 572.
• Have students use place value charts or base-ten blocks to represent the numbers
441 and 572. Have them describe how the models represent the numbers.
• Have students use the Internet or other resources to find out more about acorns.
Have them write a short report about what acorns are, where they come from, and
what kinds of animals eat them.
Resources
For the student
For the teacher
Interactive
Student Edition
provides students
with an interactive learning
environment!
Digital Management
Center organizes program
resources by TEKS!
eTeacher
Edition
Math on the Spot
Video Tutor
Online Assessment
System
iTools Virtual
Manipulatives
Soar to Success Math
Online Intervention
Lesson 4.2 107A
Name
4.2
?
Unlock the Problem
Discuss with students situations where it is not
necessary to know the exact number, but only about
how much or about how many. An example would
be planning how many napkins are needed for a class
party. Then have students read the problem at the
top of the page.
Estimate Sums
Essential Question
How can you use compatible numbers and rounding
to estimate sums?
Unlock
Unlock the
the Problem
Problem
The table shows how many dogs went to Pine
Lake Dog Park during the summer months.
About how many dogs went to the park during
June and August?
Be sure students understand that they are finding
about how many dogs went to the park in June and
August.
You can estimate to find about how many or
about how much. An estimate is a number
close to an exact amount.
One Way Use compatible numbers.
One Way
Compatible numbers are numbers that
are easy to compute mentally and are
close to the real numbers.
This method uses compatible numbers to estimate
sums. Students use mental math to estimate a sum.
Math Talk
Mathematical Processes
432
July
317
August
489
Less than the exact sum; possible
explanation: 425 is less than 432,
and 475 is less than 489, so the sum
of the compatible numbers of the
compatible numbers will be less
than the exact sum.
Math Talk
Mathematical Processes
Will the sum of the
compatible numbers 425
and 475 be greater than
or less than the exact
sum? Explain.
What other compatible numbers could you have used?
Possible answers: 430 and 490; 400 and 500; 400 and 489
2.
© Houghton Mifflin Harcourt Publishing Company
the actual numbers that I can add mentally
425
+
475
__
Number of Dogs
June
900
So, about __
dogs went to Pine Lake
Dog Park during June and August.
1.
• Describe what compatible numbers are in your
own words. Possible answer: numbers that are close to
432 →
+
489 →
__
Pine Lake Dog Park
Month
900
Use Math Talk to focus on students’ understanding
of determining if the sum of the compatible
numbers used makes an estimate that is greater
than or less than an exact sum.
Have students share other compatible numbers they
think they could use. Discuss if the choices are close
enough to the actual numbers and easy to add. Point
out that they can also choose to change only one of
the numbers to make them compatible.
Number and
Operations—3.4.B
MATHEMATICAL PROCESSES
3.1.C, 3.1.D
About how many dogs went to the park during July
and August? What compatible numbers could you
use to estimate?
Possible answers: about 817; 317 + 500
Module 4 107
• How could you use compatible numbers to
estimate the sum of 589 and 275? Possible answer:
600 + 275 = 875
English Language Learners
Leveled Activities
ELPS
Beginning: Activity 8
2.I.4, 3.G.1, 3.H.3
Intermediate: Activity 23
2.I.4, 2.I.5, 3.F.1
Advanced: Activity 46
1.F, 2.I.4, 4.G.2
Advanced High: Activity 17
4.F.6, 4.F.10, 4.G.3
thinkcentral.com for the ELL Activity
Guide containing these leveled activities.
107 Module 4
ELL Language Support
Verbal / Linguistic
Small Group
ELPS 1.B.1, 2.E.3, 3.D.1
Strategy: Model Language
• Students practice pronouncing words that have the same spelling but
different pronunciations and meanings.
• Model the difference in pronunciation between estimate as a verb and
estimate as a noun.
• Have students repeat these sentences.
An estimate is a number close to an exact
225 1 219
amount. I can estimate the sum of those
two numbers.
Estimate the sum.
• Listen for correct pronunciation as
students talk about estimating sums.
400 is an estimate.
Another Way Use place value to round.
432 + 489 =
Math Talk
■
Mathematical Processes
Find the sum of the rounded numbers.
900
400 + 500 = _
Another Way
How would you round
432 and 489 to the
nearest ten? What would
be the estimated sum?
Explain.
First, find the place to which you want to round.
Round both numbers to the same place. The greatest
place value of 432 and 489 is hundreds. Round each
number to the nearest hundred.
In this method, place value is used to round numbers
to the nearest hundred.
• Which gives an estimate that is closer to the
exact sum: rounding each addend to the nearest
hundred or rounding to the nearest ten? Explain.
Possible explanation: to round 432 to the
nearest ten, look at the ones. 2 < 5, so the
tens digit stays the same. Write zero for the
ones digit. So, 432 rounds to 430. Look at the
rounding to the nearest ten; possible explanation: when
I round to the nearest ten, the numbers are closer to
the original numbers than when I round to the nearest
hundred.
ones in 489. 9 > 5, so you increase the tens
digit by one. Write zero for the ones digit.
So, 489 rounds to 490; 430 + 490 = 920.
Share
Share and
and Show
Show
Estimate the sum. Possible answers given.
Use compatible numbers.
1.
47
+ 23
_
→
→
2.
50
+ 25
_
75
Use rounding.
304
+ 494
__
→
→
300
500
+
__
800
Math Talk
Use Math Talk to focus on students’ understanding
of rounding numbers to the nearest ten to estimate
sums.
Use rounding or compatible numbers to estimate the sum. Possible answers given.
425
421
225
+
218
+
__ —
650
3.
250
267
500
+
+ 517
__
—
750
6.
4.
7.
369
+
480
__
375
+ 475
—
850
465
+ 478
__
500
+ 500
—
1,000
5.
8.
27
+ 78
_
25
75
+
—
100
Share and Show
Exercise 1 and 2 connect to the learning model.
278
275
+ 369 + 375
__
—
650
• Which method do you think is easier to use? Why?
Possible answer: rounding, because it is easier to round
than to find numbers that are both close to the actual
numbers and easy to add
Multi-Step Green Lawn Service ordered 186 bags of
top soil and 462 bags of fertilizer. Estimate to the nearest
hundred how many bags Green Lawn Service ordered.
Justify your answer. 700 bags: possible answer: Round
186 to 200; round 462 to 500, then add 200 + 500 to get 700
108
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem Solving
Solving
9.
Mathematical Processes
• What other compatible numbers could you use for
Exercise 1? Possible answer: 50 + 20
• In Exercise 2, how would your answer change if
you rounded each addend to the nearest ten? My
answer would be 300 + 490 = 790.
Use the checked exercises for Quick Check. Students
should show their answers for the Quick Check on the
MathBoard.
3
2
Quick Check
1
Enrich
Visual / Kinesthetic
Individual
Materials: calculators
IF
THEN
a student misses the checked exercises
Differentiate Instruction with
RtI Tier 1 Lesson 23
• Write the following exercise on the board.
749 1 236
• Have students estimate the sum and record their estimates. Possible
answer: 750 + 240 = 990
• Then have students use a calculator to find the actual sum. 985
• Have students write their own 3-digit addition exercises and repeat the
activity. Have students try different estimation strategies to find which
strategy gives them the estimate that is closest to the actual sum.
Go to Go to thinkcentral.com for additional enrichment
activities in the Enrich Activity Guide.
Lesson 4.2
108
Name
Problem
Problem Solving
Solving
Problem Solving
Dan’s Pet Supplies Sold
Use the table for 10–13.
In Problems 10–13 students use information from a
table to solve the problems. Read Problem 10 with
students and discuss what they need to find.
10.
Month
About how many pet bowls were
sold in June and July altogether?
Pet Bowls
Bags of
Pet Food
June
91
419
July
57
370
August
76
228
Possible answer: about 150 pet bowls
Problems
11.
In Problems 11–13, students use higher order thinking
skills and/or multiple steps to solve the problems.
Students are not provided with the scaffold problems
as they were on the previous pages. Instead, they
decide how to solve the problems.
What’s the Question?
The answer is about 800.
Possible question: About how many
bags of pet food were sold in June and
July altogether?
Go Deeper
12.
To extend students’ thinking in Exercise 13, discuss
whether rounding to the nearest hundred or using
compatible numbers give Dan different estimates.
Write Math
Show Your Work
Multi-Step Dan
estimated the lowest monthly sales
of both pet bowls and bags of pet
food to be about 300. What month
had the lowest sales? Explain.
August: possible explanation: In
August, pet bowls sold was 76. It rounds
COMMON ERRORS
C
Example In 494, students may look at the second
4 in 494 and round to 400 instead of 500.
Springboard to Learning Have students circle the
place to which they are rounding and underline the
number to the immediate right before rounding.
M
Math
on the Spot
Video Tutor
V
Through the Math on the Spot Video Tutor,
students will be guided through an interactive
solving of this type of H.O.T. problem. Use this
video to also help students solve the H.O.T.
problem in the Interactive Student Edition. With
these videos and the H.O.T. problems, students
will build skills needed in the TEXAS assessment.
to 100; In August, bags of pet food sold
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Image Source/Alamy Images
Error Students may round numbers incorrectly
because they do not look at the place to the
immediate right.
was 228. It rounds to 200; I then added
100 + 200 = 300 for the estimate.
13.
Multi-Step Dan said
the total number of bags of pet food
sold in June, July, and August was
about 1,000. How did Dan estimate?
Explain.
Possible explanation: Dan could have
rounded 419 to 400, 370 to 400, and 228
to 200. Then he could have added
400 + 400 + 200 to get 1,000.
3
Module 4 • Lesson 2 109
RtI Tier 1 Lesson 25
23
2
1
Enrich Activity
17
7
Name
Name
LESSON
23
3.4.B
Estimating the Crowd
It is Kids’ Month at the city baseball park. The table shows
how many people went to the baseball games during Kids’
Month. Estimate to answer each question.
An estimate is a number close to an exact amount.
Math on the Spot videos are in the
Interactive Student Edition and at
thinkcentral.com.
You can use compatible numbers to estimate.
Compatible numbers are easy to compute mentally
and are close to the given numbers.
Attendance
Game
Adults
Children
Game 1
235
324
Game 2
257
399
Game 3
189
404
Estimate. Round each number to
the nearest hundred.
Game 4
477
398
214 + 678 = ■
Game 5
317
197
Estimate. Use compatible numbers.
73
+ 21
73 + 21 = ■
75
+ 25
100
So, 73 + 21 is about 100.
Another way to estimate is to round numbers to
the same place value.
Step 1 Look at the digit to the right of the
hundreds place.
214
+ 678
• 1 < 5, so the digit 2 stays the same.
• 7 > 5, so the digit 6 increases by 1
to become 7.
200
+ 700
900
Step 2 Write zeros for the tens and ones places.
© Houghton Mifflin Harcourt Publishing Company
Enrich 17
1
Estimate Sums
OBJECTIVE Use compatible numbers and rounding to estimate sums.
So, 214 + 678 is about 900.
Which game did the fewest people attend?
2.
Which game did about 650 people attend? Game
3.
Which game did the most people attend? Game
4.
Stretch Your Thinking Suppose the total attendance at Game 6
4.
23
+
99
_
20
100
120
+
__
5.
254
+
167
__
250
150
400
+
__
2
4
was about 800 and there were more children than adults at
the game. About how many children and how many adults could
have attended? Explain how you know your answer is correct.
Use rounding or compatible numbers to estimate the sum.
Possible answers are given.
1.
2.
523
42
525
40
+
117 +
+
36 +
125
40
__
_
__
__
80
650
Game 5
1.
Answers will vary and should include a greater
3.
6.
235
+
374
__
299
+
199
__
225
375
600
+
__
300
200
500
+
__
number of children than adults. Possible explanation:
521 children and 278 adults; 521 is greater than 278,
so there are more children than adults. To the nearest
hundred, 521 rounds to 500 and 278 rounds to 300;
500 1 300 5 800. So, the total attendance is about 800.
Number and Operations
109 Module 4
45
Enrich
© Houghton Mifflin Harcourt Publishing Company
E17
Mathematical Processes
Model ¥ Reason ¥ Communicate
Daily
Daily Assessment
Assessment Task
Task
3
Daily Assessment Task
Fill in the bubble for the correct answer choice.
15.
16.
Use Tools The table shows the number of steps
from bottom to top for each pyramid. Which of
these statements shows the best estimate of how
many steps there are in both pyramids?
A
5 + 100 = 105
C
10 + 90 = 100
B
0 + 75 = 75
D
6 + 95 = 101
Pyramid
Djoser
Chichen Itzá
A
440
C
220
B
300
D
400
91
1,000 feet
C
1,300 feet
B
1,100 feet
D
1,500 feet
Tracy ordered 325 toys and 165 bags of food for her new
pet store. Which is the best estimate of the total number
of items Tracy ordered?
A
700
C
400
B
500
D
600
110
THEN
IF
NO
•
Soar to Success Math
Warm-Up 16.27
YES
•
•
Enrich 17
Homework and Practice
Lesson 4.2
TEXAS Test Prep Coach
Multi-Step The height of the Great Pyramid of
Giza is about 481 feet. The length of one side
of its base is 755 feet. What is the best estimate
of the sum of the height and length?
A
1
Can students use compatible numbers and
rounding to estimate sums?
6
Lea and Josh used sugar cubes to build a model of a
pyramid. First, they glued 196 cubes to make a square
base. Next, they used 144 cubes to make the first step.
Which is the best estimate of the number of sugar cubes
Lea and Josh used to build the first two steps of their
pyramid?
TEXAS Test Prep
17.
Number of Steps
In the Test Prep exercise, if students selected:
A They used compatible numbers that are not close
to the actual numbers.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Alistair Laming/Alamy
14.
2
C They incorrectly rounded the number of bags of
food.
D They incorrectly rounded the number of toys.
?
Essential Question
Write
Math
How can you use compatible numbers and rounding
to estimate sums? I can find numbers that are close to the
real numbers that are also easy to add, and then add them.
I can round the numbers to the same place and add the
rounded numbers.
Differentiated Centers Kit
Games
Games
Auto Addition
Students practice
2-digit addition
to move along
the game path.
Literature
So Many Seashells!
Students read about how
to use addition to find
the number of seashells
collected.
Activities
Roll to 100!
Students complete
orange Activity Card 1
by finding the sum of
three numbers.
Lesson 4.2
110
5
Ho mewo rk
and Practice
Fill in the bubble completely to show your answer.
Estimate Sums
9.
Use rounding or compatible numbers to estimate the sum. Possible answers are given.
1.
18 + 53
2.
20 + 50 = 70
3.
345 + 223
642 + 212
37 + 52
40 + 50 = 90
4.
350 + 225 = 575
5.
6.
650 + 200 = 850
Cal has $42. He gets $25 from his
grandparents for his birthday.
Which of these statements shows
the best estimate of the amount of
money Cal has now?
$50 + $30 = $80
$50 + $20 = $70
A
$100 + $200 = $300
$40 + $40 = $80
B
$125 + $150 = $275
$40 + $25 = $65
C
$100 + $100 = $200
D
$200 + $200 = $400
C
500 + 475 = 975
D
11.
100 + 700 = 800
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
Seth bought a pair of sneakers for $48
and a jacket for $64. Explain how you
can estimate to find the total amount
that he spent for the sneakers and
jacket.
8.
Elena drove 245 miles last week
and 222 miles this week. She
estimated that she drove about
475 miles in both weeks. How did
Elena estimate?
12.
Mr. Avery’s class made $118 for the
fundraiser. Mrs. Bolero’s class made
$189 for the fundraiser. Which of
these statements shows the best
estimate of the total amount both
classes raised?
B
509 + 478
109 + 688
10.
A
Which is the best estimate of
the total number of students in
kindergarten and first grade at
Wayside Elementary School?
A
7.
TEXAS Test Prep
Lesson
Lesson Check
Check
Name
Students at Wayside
Elementary School
Grade
350
Kindergarten
187
First Grade
203
B
300
Second Grade
382
C
400
Third Grade
238
D
500
Fourth Grade
178
Multi-Step Which is the best
estimate of the total number of
students in second, third, and fourth
grade at Wayside Elementary School?
13.
Multi-Step Which is the best
estimate of the total number of
students in all grades at Wayside
Elementary School?
Possible explanation: I can round each
Possible answer: Elena used compatible
number to the nearest ten and then add.
numbers to estimate.
A
500
A
900
48 → 50 and 64 → 60. Seth spent
245 → 250 and 222 → 225
B
400
B
1,200
250 + 225 = 475
C
700
C
1,100
D
800
D
1,000
about $110.
Module 4 • Lesson 2
Homework and Practice
Use the Homework and Practice pages to provide
students with more practice on the concepts and
skills of this lesson.
111-112
Module 4
111
112
Number of
Students
© Houghton Mifflin Harcourt Publishing Company
4.2
Number and Operations—3.4.B
MATHEMATICAL PROCESSES 3.1.C, 3.1.D