MATH GR4 CH1

Chapter 1
Place Value and Number Sense
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1

Lesson 1-1 Place Value Through Hundred
Thousands
Lesson 1-2 Place Value Through Millions
Lesson 1-3 Problem-Solving Strategy: The
Four-Step Plan
Lesson 1-4 Compare Whole Numbers
Lesson 1-5 Order Whole Numbers
Lesson 1-6 Round Whole Numbers
Lesson 1-7 Problem-Solving Investigation:
Choose a Strategy

1-1 Place Value Through Hundred Thousands

Five-Minute Check
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3


• I will read and write whole numbers to hundred
thousands.

• digit • standard form
• place value • word form
• period • expanded form


Standard 4NS1.1 Read and write whole
numbers in the millions.


Write the value of the underlined digit in 26,513.

Step 1 Write the number in a place-value chart.

2 6 5 1 3


Step 2 Identify the column in which the 6 is. Circle it.

2 6 5 1 3


Step 3 Replace all of the digits that are on the right
side of the 6 with zeros.

2 6 0 0 0


Write the value of the underlined digit in 14,317.

A. 30,000

B. 3,000

C. 300

D. 30


Write 86,012 in word form and expanded form.

8 6 0 1 2

Standard form: 86,012

Word form: eighty-six thousand, twelve

Expanded form: 80,000 + 6,000 + 10 + 2


Write 413,610 in word form and expanded form.

A. four hundred thirteen thousand, 6 hundred ten;
40,000 + 10,000 + 3,000 + 610
B. four hundred thirteen thousand, 6 hundred ten;
400,000 + 10,000 + 3,000 + 600 + 10
C. four hundred thirteen, 6 hundred ten;
400,000 + 10,000 + 3,000 + 600 + 10
D. four hundred thirteen, 6 hundred ten;
40,000 + 10,000 + 3,000 + 610


Write five thousand, four hundred six in standard
form and expanded form.

Standard form: 5,406

Expanded form: 5,000 + 400 + 6


Write four thousand, eight hundred twenty-one in
standard form and expanded form.

A. 482,001

B. 40,821

C. 4,801

D. 4,821

1-2 Place Value Through Millions

Five-Minute Check (over Lesson 1-1)
Main Idea
Example 1
Example 2

How Big is One Million?


• I will read and write whole numbers through the
millions.


Standard 4NS1.1 Read and write whole
numbers in the millions.


The students at Harvey Elementary School have
saved 3,100,750 pennies. Write 3,100,750 in
standard form, word form, and expanded form.

Standard form: 3,100,750

Word form: Three million, one hundred
thousand, seven hundred fifty

Expanded form: 3,000,000 + 100,000 + 700 + 50


A person’s heart that beats 65 beats per minute
on average, beats 34,187,400 per year. Write
34,187,400 in standard form, word form, and
expanded form.

A. standard form: 34,187,400
word form: thirty-four million, one
hundred eighty-seven
thousand, four hundred
expanded form: 30,000,000 + 4,000,000 +
100,000 + 80,000 + 7,000
+ 400


expanded form.

B. standard form: 34,187,400
word form: thirty-four hundred
million, one hundred seven
thousand and four
expanded form: 300,000,000 + 40,000,000 +
100,000 + 80,000 + 7,000
+ 400


expanded form.

C. standard form: 34,187,400
expanded form: 30,000,000 + 4,000,000 +
100,000 + 80,000 + 4


expanded form.

D. standard form: 34,187,400
expanded form: 30,000,000 + 40,000,000 +
100,000 + 800,000 +
700,000 + 400


Answer:

A. standard form: 34,187,400
expanded form: 30,000,000 + 4,000,000 +
100,000 + 80,000 + 7,000
+ 400


The total area of China is three million, seven
hundred five thousand, four hundred seven square
miles. Write this number in standard form.

This number is written in the place-value chart below.

3 7 0 5 4 0 7

Answer: Standard form: 3,705,407


The population of the state of New York is about
nineteen million, two hundred fifty-four
thousand, six hundred thirty. Write this number in
standard form.

A. 190,254,630

B. 19,254,630

C. 1,924,630

D. 1,254,630

1-3 Problem-Solving Strategy: The Four-Step Plan

Main Idea
Example 1: Problem-Solving Strategy


• I will use the four-step problem-solving plan to
solve problems.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


There are six girls in Dina’s scout troop. They
are planning a trip to the local amusement park.
Admission for children is $12. What is the total
cost of admission for everyone to go?


Understand
What facts do you know?
• There are six scouts who want to go.
• The price of admission is $12 for each girl.

What do you need to find?
• The total cost of admission for all the girls.


Plan
To find the total cost, you can use addition. There
are 6 girls, and it will cost $12 each. So, add 12
six times.


Solve
$12 + $12 + $12 + $12 + $12 + $12 = $72

Answer: So, the troop needs $72 to go to the
amusement park.


Check
Look back at the problem. One way to check the
answer is to use a drawing.

There are 72 squares, so the answer is correct.

1-4 Compare Whole Numbers

Example 1
Example 2


• I will compare whole numbers.

• number line • is less than ( )
• is greater than ( ) • is equal to ( )


Standard 4NS1.2 Order and compare
whole numbers and decimals to two decimal
places.

Standard 4NS1.1 Read and write numbers
in the millions.


A middle school principal earns $97,032 in one
year. An elementary school principal earns $94,485
in one year. Who gets paid more?

On a number line, numbers to the right are greater
than numbers to the left.


97,032 is to the right of 94,485.
So, 97,032 is greater than 94,485.
Therefore, 97,032 > 94,485.

Answer: So, the middle school principal gets paid
more than the elementary principal.


A secretary earns $32,567 in one year and a bus
driver earns $31,622 in one year. Who gets paid
more?

A. secretary

B. bus driver

C. both get paid the same

D. not enough information given


Jorge traveled 1,296 miles during his summer
vacation. Kai traveled 1,967 miles during her
summer vacation. Who traveled more miles?


Step 1 Line up the numbers so that the digits in the
ones place align.
1,296
1,967


Step 2 Begin at the greatest place. Compare the
digits.
1,296
1,967
Since 1 = 1, go to the next place.


Step 3 Compare the digits in the next place.
1,296
1,967
9>2

Answer: So, 1,967 is greater than 1,296.
Therefore, Kai traveled more miles during
her summer trip than Jorge.


Maria traveled 2,432 miles over spring break to
visit her grandparents. Jamal traveled 2,498 miles
to visit his grandparents over spring break. Who
traveled more miles?
A. Maria

B. Jamal

C. Both traveled the same amount

D. Not enough information given

1-5 Order Whole Numbers

Main Idea
Example 1
Example 2


• I will order whole numbers through the millions.


Standard 4NS1.2 Order and compare whole
numbers and decimals to two decimal places.

Standard 4NS1.1 Read and write numbers
in the millions.


Refer to the table. Order
the dog breeds from
least popular to most
popular.

Graph each number on a number line.


42,592 is the farthest to the left, so it is the least
popular.
45,868 is between 42,592 and 47,238.
47,238 is the farthest to the right, so it is the most
popular.

Answer: The order from least popular to most
popular is Beagle, German
Shepherd, Yorkshire Terrier.


Order the following numbers from least to greatest.
21,465, 21,333, 24,899, 24,751

A. 21,465; 21,333; 24,751; 24,899

B. 21,333; 21,465; 24,899; 24,751

C. 21,465; 21,333; 24,899; 24,751

D. 21,333; 21,465; 24,751; 24,899


The populations of three cities are listed below.
Use place value to order the population numbers
from least to greatest.


1,223,400 1,223,400
886,671 least 1,463,281 greatest
1,463,281

Answer: The numbers ordered from least to greatest
are 886,671; 1,223,400; and 1,463,281.


Use place value to order the following numbers
from least to greatest. 2,651,866; 2,571,322;
1,444,739; 1,498,200

A. 1,444,739; 1,498,200; 2,651,866; 2,571,322

B. 2,571,322; 2,651,866; 1,444,739; 1,498,200

C. 1,444,739; 1,498,200; 2,571,322; 2,651,866

D. 2,651,866; 2,571,322; 1,444,739; 1,498,200

1-6 Round Whole Numbers

Key Concept: Rounding Whole Numbers
Example 1
Example 2
Example 3


• I will round whole numbers through the millions.

• estimate
• rounding (or round)


Standard 4NS1.3 Round whole numbers
through the millions to the nearest ten, hundred,
thousand, ten thousand, or hundred thousand.


A library has 95,876 books. To the nearest
thousand, how many books does the library have?

On the number line, 95,876 is closer to 96,000 than
95,000.

Answer: So, round 95,876 to 96,000.


A local radio station has a collection of 38,245 CDs.
To the nearest thousand, how many CDs does the
radio station have?

A. 38,200

B. 39,000

C. 37,000

D. 38,000


A local radio station claims that it has 571,394
loyal listeners. How many listeners is this rounded
to the nearest ten thousand?

On the number line, 571,394 is closer to 570,000
than 580,000.

Answer: So, round 571,394 to 570,000.


A television show has 947,821 viewers per week.
How many viewers is this rounded to the nearest
ten thousand?

A. 900,000

B. 950,000

C. 940,000

D. 948,000


A wildlife refuge is said to be home to 569,400
birds. Round 569,400 to the nearest thousand.

You need to round 569,400 to the nearest thousand.

Step 1 Underline the digit in the 569,400
place to be rounded. In this
case the 9 in the thousands
place needs to be rounded.


Step 2 Look at the digit to the right 569,400
of the underlined digit, which
is 4.

Step 3 Since this digit is less than 569,400
5, do not change the
underlined digit.


Step 4 Replace all digits after the 569,000
underlined digit with zeros.

Answer: To the nearest thousand, 569,400 is
rounded to 569,000.

Check

The number line shows that the answer is correct.


Round 731,600 to the nearest thousand.

A. 730,000

B. 731,000

C. 732,000

D. 740,000

1-7 Problem-Solving Investigation: Choose a Strategy

Main Idea
Example 1: Problem-Solving Investigation


• I will choose the best strategy to solve a problem.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant
information, sequencing and prioritizing
information, and observing patterns.


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


TORY: My family is going on
vacation to Mexico. Before we
go, we have to trade our dollars
for Mexican pesos. For every
dollar we will get about 11
pesos.

YOUR MISSION: Find about how
many pesos Tory’s family will
get for $8.


Understand
What facts do you know?
• You know that one dollar is about 11 pesos.

What do you need to find?

• You will need to find about how many pesos
they will get for $8.


Plan
For every 1 dollar, they get 11 pesos. Make a
table to solve the problem.


Solve

There is a pattern of +11.

Answer: The family can expect to get about
88 pesos for $8.


Check
There is a second pattern in the table. When the
digit in the dollar row is changed to pesos, the
dollar digit is repeated twice. For example, $5 is
55 pesos. $8 is 88 pesos follows this pattern.

So, the answer is correct.

1

Five-Minute Checks

How Big is One Million?

1

Lesson 1-1
Lesson 1-2 (over Lesson 1-1)

1

Find the value of 10 × 3.

A. 30

B. 3

C. 300

D. 10

1

Find the value of 100 – 30.

A. 130

B. 3,000

C. 3

D. 70

1

Find the value of 16 4.

A. 64

B. 4

C. 12

D. 20

1

Find the value of 15 + 10.

A. 25

B. 5

C. 150

D. 75

1
(over Lesson 1-1)

Write the value of the underlined digit.
131,166

A. 6

B. 600

C. 60

D. 66

1
(over Lesson 1-1)

72,015

A. 70,000

B. 7,000

C. 72

D. 7

1
(over Lesson 1-1)

999,760

A. 999

B. 90,000

C. 900,000

D. 9

1
(over Lesson 1-1)

62,824

A. 2,000

B. 2

C. 200

D. 2,824

1
(over Lesson 1-2)

Write 5,376 in two different ways.

A. five hundred seventy-six; 500 + 70 + 6

B. five thousand three hundred seventy-six;
5,000 + 300 + 70 + 6

C. five thousand three seventy-six; 5,000 + 376

D. three thousand five hundred seventy-six;
3,000 + 500 + 70 + 6

1
(over Lesson 1-2)

Write twenty-five thousand, seven hundred
eighty-nine in two different ways.

A. 25,700,089; 25,000 + 700 + 89

B. 2,789; 2,000 + 700 + 80 + 9

C. 257,809; 25,000 + 700 + 80 + 9

D. 25,789; 20,000 + 5,000 + 700 + 80 + 9

1
(over Lesson 1-2)

Write 200,000 + 30,000 + 1 in two different ways.

A. 230,001; two hundred thirty thousand, one

B. 2,301; two thousand three hundred one

C. 230,100; two hundred thirty thousand, one
hundred

D. 500,001; five hundred thousand, one

1
(over Lesson 1-2)

Write 765,149,372 in two different ways.

A. seven hundred sixty-five thousand, one
hundred forty-nine, three hundred seventy-two;
700,000 + 60,000 + 5,000 + 100 + 40 + 9 + 300 +
70 + 2

B. seven hundred sixty-five million, one hundred
forty-nine thousand, three hundred seventy-
two; 700,000,000 + 60,000,000 + 5,000,000 +
100,000 + 40,000 + 9,000 + 300 + 70 + 2

1
(over Lesson 1-2)


C. seven hundred sixty-five billion, one hundred
two; 765,000,000,000 + 100,000 + 40,000 + 9,000
+ 300 + 70 + 2

D. seven hundred sixty-five thousand, one
hundred forty-nine thousand, three hundred
seventy-two; 700,000 + 60,000 + 5,000 +
100,000 + 40,000 + 9,000 + 300 + 70 + 2

1
(over Lesson 1-2)


B. seven hundred sixty-five million, one hundred
two; 700,000,000 + 60,000,000 + 5,000,000 +
100,000 + 40,000 + 9,000 + 300 + 70 + 2

1
(over Lesson 1-3)

Solve. Use the Four-Step Plan. A hamster can travel
about 5 times as fast as a roach. A roach can go 1
mile in an hour. How far can a hamster travel in one
hour?

A. 12 miles in one hour

B. 10 miles in one hour

C. 5 miles in one hour

D. 25 miles in one hour

1
(over Lesson 1-4)

Compare. Use <, >, or =.
4,908 4,718

A. 4,908 < 4,718

B. 4,908 > 4,718

C. 4,908 = 4,718

D. 4,718 > 4,908

1
(over Lesson 1-4)

16,547 62,050

A. 16,547 > 62,050

B. 62,050 < 16,547

C. 16,547 < 62,050

D. 16,547 = 62,050

1
(over Lesson 1-4)

8,342 8,342

A. 8,342 = 8,342

B. 8,342 > 8,342

C. 8,342 < 8,342

D. You can not compare these two numbers.

1
(over Lesson 1-4)

42,610 41,619

A. 42,610 < 41,619

B. 41,619 > 42,610

C. 42,610 = 41,619

D. 42,610 > 41,619

1
(over Lesson 1-5)

The Nile River is about 4,160 miles long. The
Mississippi River is about 2,340 miles long. The
Amazon River is about 4,000 miles long. Order the
rivers from shortest to longest.

A. Nile, Mississippi, Amazon

B. Amazon, Mississippi, Nile

C. Mississippi, Nile, Amazon

D. Mississippi, Amazon, Nile

1
(over Lesson 1-6)


A. 4,200

B. 4,000

C. 5,000

D. 3,000

1
(over Lesson 1-6)


A. 2,000

B. 2,700

C. 3,000

D. 1,000

1
(over Lesson 1-6)

Round 189,022 to the nearest hundred thousand.

A. 189,000

B. 200,000

C. 190,000

D. 100,000

1
(over Lesson 1-6)

Round 435,001 to the nearest hundred thousand.

A. 435,000

B. 500,000

C. 440,000

D. 400,000

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MATH GR4 CH1

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