Math Steps Level 4 (Grade 4)

321 Pages·2016·28.81 MB·English

by  Houghton Mifflin.

Grateful acknowledgment is given for the contributions of

Student Book

Rosemary Theresa Barry

Karen R. Boyle

Barbara Brozman

Gary S. Bush

John E. Cassidy

Dorothy Kirk

Teacher Book
Contributing Writers

Dr. Judy Curran Buck

Assistant Professor of Mathematics

Plymouth State College

Plymouth, New Hampshire

Dr. Richard Evans

Professor of Mathematics

Plymouth State College

Plymouth, New Hampshire

Dr. Mary K. Porter

Professor of Mathematics

St. Mary's College

Notre Dame, Indiana

Sharon Ann Kovalcik

Bernice Kubek

Donna Marie Kvasnok

Ann Cherney Markunas

Joanne Marie Mascha

Kathleen Mary Ogrin

Dr. Anne M. Raymond

Assistant Professor of Mathematics

Keene State College

Keene, New Hampshire

Stuart P. Robertson, Jr.

Education Consultant

Pelham, New Hampshire

Dr. David Rock

Associate Professor,

Mathematics Education

University of Mississippi

Oxford, Mississippi

Copyright © 2000 by Houghton Mifflin Company. All rights reserved.

No part of this work may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopying and recording, or by any information
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Houghton Mifflin Company,222 Berkeley Street, Boston, MA 02116.

Printed in the U.S.A.

ISBN-13: 978-0-395-98535-9
ISBN-10: 0-395-98535-8

17 18 0928 17 16 15 14 13 12 11
4500311334

Judith Ostrowski

Jeanette Mishic Polomsky

Patricia Stenger

Annabelle L. Higgins Svete

Michelle Lynn Rock

Elementary Teacher

Oxford School District

Oxford, Mississippi

Dr. Jean M. Shaw

Professor of Elementary Education

University of Mississippi

Oxford, Mississippi

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Unit 1
Place Value
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1

Unit 2
Addition and Subtraction of Whole Numbers
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19

Unit 3
Multiplication of Whole Numbers
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Unit 4
Division with 1-Digit Divisors
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73

Unit 5
Fractions and Mixed Numbers
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109

Unit 6
Geometry
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139

Unit 7
Measurement
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173

Unit 8
Decimals
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211

Unit 9
Division with 2-Digit Divisors
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233

Unit 10 Data, Statistics, and Probability
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259

Unit 11 Algebra: Variables and Coordinate Graphing
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283

Tables of Measures ................... . ............. ' .. 309

Glossary
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311

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UNIT 1
•
TABLE OF CONTENTS

Place Value

Lesson
'
Page

1
Place Value: Hundred Thousands
.
. . . . . . . . . . . . . . 3

2
Comparing and Ordering Numbers
. . . . .
. . .
. . . . .
. 5

3
Rounding to the Nearest Ten, Hundred, or Thousand
'
"
7

4
Problem Solving A.pplication: Use a Graph . . .
. . . . . 9

5
Millions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1

6
Rounding Greater Numbers
. . . . .
. . . . . . . . . . . . . 1 3

7
Problem Solving Strategy: Find a Pattern
.
. . . . . . . 1 5

•
Unit 1 Review . . .
. . . .
. . .
. . . . . . . . . . . . . . . . 1 7

•
Cumulative Review * Test Prep . . . .
. . .
. . . . . . . . . 1 8

Unit 1
1

Dear Family,

During the next few weeks, our math
class will be learning and practicing
place value.

You can expect to see homework that
provides practice with rounding. Here is
a sa'mple you may want to keep handy
to give help if needed.

Rounding to the Nearest Hundred

We will be using this vocabulary:

place value the value given to the place,
or position, of a digit in a number

round to replace an exact number by
another number that is easier to use

compare to decide which number of a
group of numbers is greatest or least

order to arrange a group of numbers in a
certai n way, such as from least to
greatest or from g reatest to least

To round a number such as 4,175 to the nearest hundred, first find
the digit in the hundreds place.

Hundreds Place

�
4,175

t

greater than 5

Next, look at the digit in the place to the right (7). If the digit in the
place to the right is less than 5, round down. If it is greater than or
equal to 5, round up.

Since the digit to the right of the hundreds place is greater than 5,
round 4,175 up to 4,200, the nearest hundred.

During this unit, students will need to continue practicing rounding and
other skills related to place value, such as comparing numbers.

Sincerely,

Name _________________________ ____ __

---�
� --�Place Value: --

.;Thousands I
Period

Ones
Period

Hundred Thousands

The standard form of the number written in this
place-value chart is

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105,043

t

When writing
numbers in standard
form, remember to
use a comma to
separate the periods.

The number 105,043 is read as:
one hundred five thousand, forty-three. Each group
of 3 digits, separated by a comma, is called a period.

Place a comma in each number. Then write each
number in the place-value chart above.

1. 1 0 0 0 0 4
2 5 1 0 0
8 0 2 6 0 1
4 0 4 2

_ e_ " '�
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___ '''-
____ .. _.
.
.
__
� ____ __
. _________ _ _

Read each number. Then write it in words.

2. 70,051 ____ ____________________ ______________ �---------

3. 9,940 __________ ______________________________________ __

4. 800,306�-----------�------------

--.,-.-� -�.--�-
.
_- --

Write each number in standard form.

5. seven thousand, five hundred nine
6. six hundred three thousand, twenty

7. fifteen thousand, three hundred

--.�.-.---�.---�-
·
_.
_____ .
___
___
___ ,_ .�

Study the number 780,425. Write the digit that is in the

8. hundreds place __
_

9. ones place __
__

10. tens place

thousands place __ _

hundred thousands place __
_

ten thousands place __
__
_

Unit 1 Lesson 1
3

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Study the number 407,653. Write the place value
of each digit.

11.
5

12.
7

13.
3

_____ place

_____ place

_____ place

14.
6

15.
0

16.
4

place

place

_____ place

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Count by 100,000'5, as shown in the example below.

1 5,407,
1 1 5,407,
215,407,
31 5,407

17.
18,527,
___ ____________
_

18.
5,728, _____
_____ .
�----

19. 208,752, ____ , _____
____
_

20. 743,101, ____ ,
__ ___
____
_

rmng"i1J'Mi.i" Solve:Use the follo
ify
_.

_
Reasonmg
_ mystery number.

21. i am a 5-digit number.

My tens digit is the sum of my hu'ndreds digit and thousands digit.
My tens digit is twice my ones digit.
My hundreds digit is 1 more than zero . .
My thousands digit is seven times my hundreds digit.
My ten thousands digit is the same as my ones digit.
What is the mystery number?

.
Test Prep * Mixed Review

� Which number sentence belongs
to the same family of facts as
4 + 7 = II?
A 1 1 + 4 = 15
B 7 - 4= 3
C 1 1- 7 = 4

D 18 - 7 = 1 1

4
Unit 1 Lesson 1

@) Samuel had 4 pieces of colored paper.

He cut 3 paper birds from each piece .
of paper. How many birds did he cut
out in all?
F 8
G 9
H 12
J 16

Name __________________________ __
Comparbig and. Ordering
Numbers

Follow these steps to compare 27,409 and 27,490:

1. Line up the numbers using place value.

2. Begin at the greatest place value.

Find the first place value where the
digits are different.

3. Compare those digits. Write >, <, or =.

27,409
27,490

!
27,409
27,490
t

Because 9 > 0, you can say that 27,490 G 27,409.

> is greater than

< is less than

is equal to

Because 0 < 9, you can also say that 27,409 @ 27,490.

Write <, >, or = in each circle.

1.
43 0 73
58 0 50 + 8
36 0 26

2.
807 0 809
1,713 0 1,723
8,529 0 8,629

3.
28,916 0 27,916
35,499 0 35,500
67,999 0 68,000

4. 806,000 0 860,000
397,426 0 397,419
605,200 0 602,500

M�:l'''''I\_._':
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Compare to write the numbers in the column in
order from greatest to least.

5. 1 51,51 5
6. 950,564

7,207.
407,704

245,039
1,275

898,090
713,280

96,371
60,000

Unit 1 Lesson 2
5

- -

Writethe num
least

to greatest.

7. 50,020

52,000

52,020

50,200

52,002

8. 400,600

406,000

460,000

400,006

400,060

Write < or > in each circle.

9.
4,343 0 4,334

10.
53,742 0 53,821

11. 207,390 0 203,790

703 0 730

69,385 0 60,381

763,510 0 763,780

16,303 0 16,330

42,500 0 45,200

593,000 0 539,000

Solve.

12. What is the greatest 3-digit
number you can write using each
of the digits 4, 1, and 5 once?
What is the least three-digit
number?

13. What is the greatest 4-digit
number you can write using each
of the digits 2, 6, 3, and 9 once?
What is the least four�digit
number?

Test
* Mixed Beview

� Which number sentence belongs to the � At the playground, 32 students divided

same family of facts as 17 - 8 = 9?
into teams with 8 children on each

A 9 + 8 = 17
team. How many teams were there?

B 17 + 9 = 26
C 9 - 8= 1

D 17 + 8 = 25

6
Unit 1 Lesson 2

F 16
G 8
H 6
J 4

Name __________________________ __
Bounding to the Nearest Ten,
Hundred, or Thousand

You can use a number line to round numbers.

Round 1 32 to the nearest ten.

1. 132 is between 130 and 140.
7

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2. Since 132 is closer to 130 than
to 140, 132 rounds down to 130.
130
140

Round 857 to the nearest hundred.

1. 857 is between 800 and 900.

2. Since 857 is closer to 900 than
to 800, 857 rounds up to 900.
�
.. I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I II I •

600
700
800
900

Here's how to round without using a number line.

1 . Find the digit i n the place to the right of the
place you are rounding to.

2. If that digit is less than 5, round the number
down to the place you are rounding to. If that
digit is 5 or greater, round the number up to
the place you are rounding to.

Other Examples·

Round to tens.

�
132

L Less than 5

So, 1 32 rounds down to 1 30.

Round to hundreds.

�

L 5 or greater
So, 857 rounds up to 900.

Rounded to the nearest thousand,
1,462 rounds down to 1,000 because
the digit in the place to the right of
the thousands place is less than 5.

Rounded to the nearest thousand,
7,503 rounds up to 8,000 because the
digit in the place to the right of the
thousands place is 5 or greater.

_
_ .•
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.. __
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_. __
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Use the number line above to round each
number to the nearest ten.

1. 1 31 ____
_
136 ___
_

2. 137 __
__
133 ___
__

139 __
_
1 34 ___
_

135 __
__
138 __
_

-----".-.. ,-"----, . . ���-....
.-
--'
,--
---�,,-,-.-
.. -.-.---,
Use the number line above to round each
number to the nearest hundred.

3. 612 __
_
850 __
_

4. 820 __
�
688 __
_

760 ___
_

706 __
_

675 __
_

815 __
_

Unit 1 Lesson 3
7

''.'' ''''
. . �"" .. -,,, .. ,,,'-.
..•. '�-'-�',.".��--.
,.-,""-'-�-.'�-'-'-
Round to the nearest ten.

5. 25 _ _
_
16 __
_
9 __
_
631 __
_

6. 35 __
_
55 __
_
24 _
_
_
358 __
_

Round to the nearest hundred.

7. 348
__
_
420 _ _
_
3,283 _ _
_

8. 580 _--
940 __
_
5,775 _ _
_

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Round to the nearest thousand.

9. 2,500 _--
6,150
5,210 __
_

10. 3,500 __
7,250 __
_
5,795
_ _
_

11. 4,500 _ _
_
9,350
__
_
7,642 __
_

���b:fr
i�i�sfj:��
that

number. Then explain why.

12. The population of Beaumont,
13. The basketball team scored 20·

California, is about 1 5,000 people.
points in the first half of the game.

Quick Check

Write the value of 7 in each exercise.

14. 64,074
15. 1 07,234
16. 575,252

Compare. Write> or <.

17. 9,327 0 9,486
18. 27,087 0 27,807

19. 140,265 0 1 04,265
Round each number to the nearest thousand.

20. 4,509

8
Unit 1 lesson 3

21. 7,353
22. 8,099

Work Space.

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Name ____
__
__
__
__
______
__
__
__
__
__
__

How deep is the ocean? This bar graph
shows the estimated depth of four oceans.

In this lesson, you will use graphs to
compare, make estimates, and draw
conclusions about the data.

Tips to Remember:

1. Understand
2. Decide
3. Solve
4. Look back

. r

• Ask yourself: Have I solved a
problem like this one before? How
did I solve it?

• Compare the labels on the graph
with the words and numbers in the
problem. Find the facts you need
from the graph.

• When you can, make a prediction
about the answer. Then compare
your answer with your prediction.

1. What is the estimated depth of
the Arctic Ocean to the nearest
thousand feet?
Think: How do you estimate a
number using the graph?

Ansvver
__
__
__
______
__
__
__
__
__

3. Lake Baikal, the deepest lake in
the world, is about 1,800 feet
deeper than the Arctic Ocean.
Estimate the depth of Lake Baikal.

Problem Solving Application:

Use a Graph

Estimated Depth of Oceans

13,000
12,000
1 1,000
10,000

9,000
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8,000
<II
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7,000

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6,000
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4,000
3,000
2,000
1 ,000

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Ocean

2. Explain whether or not you can
use the graph to decide which
ocean is the largest ocean.
Think: What information is given
in the graph?

Ansvver
__
__
____ __ ____
______ __

4. What is the depth of the Atlantic
Ocean rounded to the nearest
hundred feet?

Unit 1 Lesson 4
9

Population of Countries with Few People

Nauru

>.
Tuvalu

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Palau

San Marino

Liechtenstein

0
5,000 10,000 15,000 20,000 25,000 30,000 35,000
Population

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Solve. Use the bar graph above.

5. Which country shown in the graph
has the greatest population? What
is the population to the nearest
thousand?

6. Which country has a population
about three times the population
of Tuvalu?

................................................................................................................................. ! ........................................................................................................................... .

7. Which two countries on the graph
have about the same population?

Extend Your Thinking

9. Can you use the graph to find
which country in the world has the
greatest population in the world?
Explain.

10
Unit 1 Lesson 4

8. Wichita, Kansas has a population
of 304,01 1 . Does this city have
more or fewer people than the
countries shown in the graph?
Explain.

10. Explain the method you used to
solve problem 6.

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Name
______
__
__
__ ______________
__
lVIillions

The period after the thousands period is called
the millions period.

Millions f Thousands I'·

' Ones','

The standard form for the numbers written in
this chart is 5,054,782. To read a number, say
the number in each period, beginning with the
greatest period, then say the name of each
period, except for the ones period.

The number 5,054,782 is read as: five million,
fifty-four thousand, seven hundred eighty-two.

·27,001,909

Read: twenty-seven million, one
thousand, nine hundred nine

300,518,040

Read: three hundred million, five hundred
eighteen thousand, forty

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Place commas in each number. Then write each
number in the place-value chart.

1. 1 2 0 0 0 1 7

2. 1 8 4 2 8 0 0 0

3.

4.

3,782,410

80,050,520

9 0 5 0 4 6 1

1 0 3 6 0 0 3 0 1

1 7 0 0 5 6 0 5

4 9 0 2 1 7 0 5 0

te ea
erinstandard iorm
'· ·'·�"��--�"�-=·�·�'=· ,�--
..
� ...
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--
.
, ...
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commas to separate the periods ..

5. eight million, two hundred fifty-one thousand,
six hundred ninety-seven

6. three million, one hundred thousand, fifteen

When a number is
written using digits, it is
written in standard
form. For example,
24,035,600 is written in
standard form.

Unit 1 Lesson 5
1 1