enVision Math Common Core Grade 4 Answer Key Topic 1 Generalize Place Value Understanding

Go through the enVision Math Common Core Grade 4 Answer Key Topic 1 Generalize Place Value Understanding regularly and improve your accuracy in solving questions.

enVision Math Common Core 4th Grade Answers Key Topic 1 Generalize Place Value Understanding

Essential Questions:
How are greater numbers written? How can whole numbers be compared? How are place values related?

enVision STEM Project: Caves
Do Research Use the Internet or other sources to find the depths in feet of the 5 deepest caves in the world.
Journal: Write a Report Include what you found. Also in your report:

• Make a place-value chart that includes the five depths.
• Write each depth in expanded form.
• Use “greater than” or “less than” to compare the depths of two of the caves.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.

• expanded form
• place value
• number line
• rounding
• number name
• whole numbers

Question 1.
The numbers 0, 1, 2, 3, 4, and so on are called ___________.
Answer:
The numbers 0, 1, 2, 3, 4, and so on are called Whole Numbers.

Question 2.
A number written using only words is written using a __________
Answer:
A number written using only words is written using a Number Name .

Question 3.
Replacing a number with a number that tells about how many or how much is called _________.
Answer:
Replacing a number with a number that tells about how many or how much is called Place Value

Question 4.
_______ is the value given to the place of a digit in a number.
Answer:
Place Value is the value given to the place of a digit in a number.

Comparing Numbers

Compare each set of numbers using >, <, or =.
Question 5.
201 21
Answer:
201 < 21
Explanation :
201 is a three digit number
21 is a two digit number
three digit is greater than two digit numbers .

Question 6.
313 313
Answer:
313 = 313
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
313
313
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
313
313
The tens digit is also the same in both numbers.

Step 3
Look at the next digit. Compare the Ones.
313
313
The Ones digit is also the same in both numbers.
so, 313 = 313 .

Question 7.
289 290
Answer:

Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
289
290
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
289
290
8 tens < 9 tens
289 < 290 .

Question 8.
7 70
Answer:
Explanation :
7 is a one digit number
70 is a two digit number
one digit is lesser than two digit numbers .

Question 9.
725 726
Answer:
725 < 726
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
725
726
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
725
726
The tens digit is also the same in both numbers.

Step 3
Look at the next digit. Compare the Ones.
725
726
5 Ones < 6 Ones
so, 725 < 726 .

Question 10.
82 82
Answer:
82 = 82
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
82
82
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
82
82
The tens digit is also the same in both numbers.

Step 3
Look at the next digit. Compare the Ones.
82
82
The Ones digit is also the same in both numbers.
so,82 = 82

Question 11.
614 641
Answer:
614 < 641
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
614
641
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
614
641
1 Tens < 4 Tens .
614 < 641
614 is lesser than 641 .

Question 12.
618 618
Answer:
618 = 618
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
618
618
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
618
618
The tens digit is also the same in both numbers.

Step 3
Look at the next digit. Compare the Ones.
618
618
The Ones digit is also the same in both numbers.
so, 618 = 618 .

Question 13.
978   987
Answer:
978  <  987
Explanation :
Step 1
Write the numbers, lining up places. Begin at the left and compare.
978
987
The hundreds digit is the same in both numbers.

Step 2
Look at the next digit. Compare the tens.
978
987
7 Tens < 8 Tens .
978 < 987
978 is lesser than 987 .

Place Value

Tell if the underlined digit is in the ones, tens, hundreds, or thousands place.

Question 14.
9,482
Answer:
9,482 = 9 Thousands place

Question 15.
8,000
Answer:
8,000 = 0 Tens .

Question 16.
1,506
Answer:
1,506 = 0 Hundreds .

Question 17.
8,005
Answer:
8,005 = 8 thousands

Question 18.
5,100
Answer:
5,100 = 1 hundreds .

Question 19.
2,731
Answer:
2,731 = 2 Thousands .

Rounding

Question 20.
Construct Arguments Use the number line to describe how to round 450 to the nearest hundred.

Answer:

500
Explanation :
Nearest 100 of 450 will be 500 .

Pick a Project

PROJECT 1A
How many bones are in your body?
Project: Make a Bones Poster

PROJECT 1B
Would you like to be a construction manager?
Project: Design a Building

PROJECT 1С
Which stadium is your favorite?
Project: Create a Stadium Model

3-ACT MATH PREVIEW

Math Modeling
Page Through

Lesson 1.1 Numbers Through One Million

Solve & Share
Mrs. Darcy saved ten $100 bills. How much money did Mrs. Darcy save?
I can … read and write numbers through one million in expanded form, with numerals, and using number names.

Look Back! How did you decide how many zeros you needed to write in your answer?
Answer :
Number of bills = 10 .
Bill Amount = $100 .
Total Amount = $100 × 10 = $1000 .
Explanation :
When multiplying whole numbers by 10, simply add a 0 to the end of the number,
so , 100 × 10 = 1000 .

Essential Question
What Are Some Ways to Write Numbers to One Million?
Answer :
10000 × 100 = 1,000,000 .
1000 × 1000 = 1,000,000 .
100000 × 10 = 1,000,000 .

Visual Learning Bridge
The graph shows the attendance at a ballpark over one year. Write the total attendance in expanded form and using number names.

The place-value chart shows periods of three places, starting at the ones period from the right and including the thousands and millions period. Each period is separated by a comma and has three place values: ones, tens, and hundreds.

Each digit in 356,039 is written in its place on the chart. Expanded form shows the sum of the values of each digit.

Expanded form: 300,000 + 50,000 + 6,000 + 30 + 9
Number name: three hundred fifty-six thousand, thirty-nine is written.

Convince Me! Look for Relationships What pattern exists in the three places in each period?

Another Example!
21, 125 can be expanded and written in different ways.
20,000 + 1,000 + 100 + 20 + 5
21,000 + 100 + 25
20,000 + 1,100 + 20 + 5

Guided Practice

Do You Understand?
Question 1.
What do you notice about the comma in the number on the previous page?
Answer:
The commas separates the periods when number name is written .

Question 2.
Write an example of a number that would include 2 commas.
Answer:
2,000,000 = Two millions .

Do You Know How?
Question 3.
Write 7,320 in expanded form.
Answer:
Expanded form of  7,320 : 7,000 + 300 + 20 + 0 .

Question 4.
Write 55,426 using number names.
Answer:
Number name of 55,426 = fifty five thousands four hundred and twenty six .

Question 5.
In a recent year, 284,604 fans attended the hockey playoffs in Chicago. What digit is in the thousands place in 284,604?
Answer:
284,604 = 4 thousands .

Independent Practice

For 6-8, write each number in expanded form.
Question 6.
7,622
Answer:
Expanded form of 7,622 : 7,000 + 600 + 20 + 2 .

Question 7.
294,160
Answer:
Expanded form of 294,160 : 200,000 + 90,000 + 4,000 + 100 + 60 + 0 .

Question 8.
43,702
Answer:
Expanded form of 43,702 = 40,000 + 3,000 + 700 + 00 + 2 .

For 9-11, write each number name.
Question 9.
1,688
Answer:
Number name of 1,688 : One Thousand six hundred and Eighty Eight .

Question 10.
331,872
Answer:
Number name of 331,872 : Three hundred and thirty one-thousand and Eight hundred and seventy two .

Question 11.
44,444
Answer:
Number name of 44,444 :  Forty four thousand four Hundred and forty four .

Problem Solving

Question 12.
Letitia wrote one thousand, two hundred four in a place-value chart. What mistake did she make?

Answer:
one thousand, two hundred four : 1,204 .
Explanation :
The mistake is that the four should be written in the Ones place not in tens place value .

Question 13.
Reasoning in 2016, the world’s oldest tree was 5,066 years old. Write the number that is one hundred more using number names.
Answer:
Age of old tree = 5,066 years
One year more than 5,066 years = 5,066 + 100 = 5,166 years .
5,166 : Five thousand One hundred and sixty six .

Question 14.
Jessica wants to buy a new team jacket that costs $35. If Jessica saves $5 a week for 4 weeks and $4 a week for 3 weeks, will she have enough money to buy the team jacket? Explain.
Answer:
$ 32 < $ 35 .
No, she doesn’t have enough money she haves $3 less than the required amount .
Explanation :
Cost of Jacket = $35  .
Number of weeks = 4 weeks
Money saved for each week = $5
Amount saved for 4 weeks = 4 × $ 5 =  $20 .
Number of weeks = 3 weeks
Money saved for each week = $4
Amount saved for 4 weeks = 3 × $ 4 =  $12 .
Total Amount saved = $20 +$12 = $32 .
No, she doesn’t have enough money she haves $3 less than the required amount .

Question 15.
Vocabulary Drew wrote the following sentence: “A period is a group of any 3 three digits in a number.” Do you agree with Drew? If not, how would you correct him?
Answer:
In place value chart, the digits are grouped in the threes in a big number. The number is read from left to right as ………. billion ………. million ……….. thousands ……….. ones.
The place value chart of the International System is given below:

Question 16.
Higher Order Thinking Two numbers have the same digit in the millions period, the same digits in the thousands period, and the same digits in the ones period. Do these two numbers have the same value? Explain.
Answer:
No,
Explanation :
5,111,666,222
50,111,666,222
Both have same numbers in million,thousands and ones period but they have different numbers in billions periods .

Assessment Practice

Question 17.
Wallace writes the number 72,204 in a place-value chart. Select the places that will be filled on the chart.
☐ Ones
☐ Tens
☐ Thousands
☐ Ten thousands
☐ Hundred thousands
Answer:

Question 18.
Select all that are equal to 96,014.
☐ 96,000 + 10 + 4
☐ 90,000 + 60,000 + 10 + 4
☐ 90,000 + 6,000 + 4
☐ 90,000 + 6,000 + 10 + 4
☐ 96,000 + 14
Answer:

Lesson 1.2 Place Value Relationships

Solve & Share
Place-value blocks are shown below for 1, 10, and 100. What patterns in the shapes and sizes of the blocks do you see?
I can… recognize that a digit in one place has ten times the value of the same digit in the place to its right.

Look Back! Describe two ways 100 and 10 are related.
Answer :

Essential Question
How Are Place Values Related to Each Other?

Visual Learning Bridge
Kiana had bottle caps. She wants to collect ten times as many bottle caps. How many bottle caps will Kiana have in her collection then?

A hundreds flat represents 100 bottle caps.

To find ten times as many bottle caps, group 10 hundreds flats together.

One thousand is ten times 100.
100 × 10 = 1,000
One hundred is one-tenth of 1,000.
1,000 ÷ 10 = 100
Kiana will have 1,000 bottle caps in her collection.

Convince Me! Generalize Use place-value blocks to model 1 and 10, 10 and 100, 100 and 1,000. What pattern do you see?

Another Example!
Joe scored 2,000 points on a progressive video game. It took him 5 weeks to get his total point value to 20,000. It took him 3 months to get his total point value to 200,000 points. How many times greater than his first score were his points after 5 weeks? After 3 months?
After 5 weeks, Joe’s points were 10 times greater.
After 3 months, Joe’s points were 100 times greater.

2,000 × 10 = 20,000
20,000 × 10 = 200,000
10 × 10 = 100

Guided Practice

Do You Understand?
Question 1.
Is the value of the 2 in 23,406 ten times as great as the value of the 3? Explain.
Answer:
No,
Explanation :
Value of 2 in 23,406 = 20,000 .
Value of 3 in 23,406 = 3,000 .
value of the 2 in 23,406 ten times as great as the value of the 3 = 3,000 × 10 = 30,000 .
So, not equal .

Do You Know How?
For 2, use the relationship between the values of the digits to solve.
Question 2.
Write a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.
Answer:
345456 .
Explanation:
The value of 3 in 135864 is 30000.We want to write a number that is ten times 30000.We could write any 345456.
Just increase the place value to hundred thousands .

Independent Practice

For 3-5, use the relationship between the values of the digits to solve.
Question 3.
Baseten School District bought 5,000 pencils. They are distributing the pencils evenly to 10 schools in the district. How many pencils will each school get?
Answer:
Number of Pencils = 5,000
Number of schools  = 10 .
Number of pencils each school get = 5,000 ÷ 10 = 500 pencils .
5,000 is ten times the value of 500 .

Question 4.
Place Elementary School is raising money. They raise $90 a week. How long will it take them to raise $900?
Answer:
Amount rise for 1 week = $90
Risen Amount = $900 .
$900  is ten times greater than $90 .
So, Number weeks required to rise Amount = 10 weeks .

Question 5.
A donation of 50 rulers was given to Value Elementary School. The school had 10 times as many erasers donated. How many erasers were donated?
Answer:
Number of Rulers = 50 .
Number of erasers donated =10 times as many erasers donated = 10 × 50 = 500 erasers .

Problem Solving

Question 6.
What can you say about the 3s in 43,862 and 75,398?
Answer:
Place value of 3 in 43,862 = 3,000
Place value of 3 in 75,398 = 300 .
The place value of 3 in 43,862 is ten times greater than the place value in 75,398 .

Question 7.
Critique Reasoning
Mia says in 5,555, all the digits have the same value. Is Mia correct? Explain.
Answer:
No, she is not correct .
Explanation :
Place value from left to right is explained .
Place value of first 5 = 5,000 .
Place value of second 5 = 500 .
Place value of third 5 = 50 .
Place of fourth 5 = 5 .

Question 8.
Number Sense
In 1934, there was an extreme drought in the Great Plains. In the number 1,934, is the value of the 9 in the hundreds place ten times as great as the value of the 3 in the tens place? Explain.
Answer:
No, the place value in Hundreds place is not ten times the place value in tens place .
Explanation :
Place value of 9 in 1934 = 900
Place value of 3 in 1934 = 30 .
9 in the hundreds place ten times as great as the value of the 3 in the tens place = 30 × 10 = 300 .
where 900 and 300 are not equal .

Question 9.
Critique Reasoning Vin says in 4,346, one 4 is 10 times as great as the other 4. Is Vin correct? Explain.
Answer:
No, he is wrong
40 × 100 = 4,000 .
Explanation :
Place of 4 in 4,346 in thousands place = 4,000 .
Place of 4 in 4,346 in tens place = 40 .
Place of 4 in 4,346 in thousands place is 100 times greater than Place of 4 in 4,346 in tens place
40 × 10 = 400 .
40 × 100 = 4,000 .

Question 10.
Describe 2 ways to find the area of the shaded rectangle.

Answer:
Length of shaded rectangle = 3 squares = 3 square unit .
Breadth of Shaded Rectangle = 4 squares = 4 square unit .
Area of rectangle = Length × Breadth = 3 × 4 = 12 unit squares .

Number of squares shaded = 12 square units .
Area of shaded Rectangle = 12 unit squares .

Question 11.
Higher Order Thinking In 448,244, how is the relationship between the first pair of 4s the same as the relationship between the second pair of 4s?
Answer:
448,244
The place of first pair of 44 in 448,244 = 440,000.
The place of Second pair of 44 in 448,244 = 44.
The relationship between the first pair of 4s the same as the relationship between the second pair of 4s = First pair of 44 is 10,000 times greater than Second pair of 44 .
= 44 × 10,000 = 440,000 .

Assessment Practice

Question 12.
Which group of numbers shows the values of the 4s in 44,492?
A. 40,000; 4,000; 400
B. 40,000; 400; 40
C. 4,000; 400; 4
D. 400; 40; 4
Answer:
Option A .
Explanation :
The values of the 4s in 44,492 = 40,000 ; 4,000 ; 400 .

Question 13.
In which number is the value of the red digit ten times as great as the value of the blue digit?
A. 335,531
B. 335,531
C. 335,531
D. 335,531
Answer:

Lesson 1.3 Compare Whole Numbers

Solve & Share
A robotic submarine can dive to a depth of 26,000 feet. Which oceans can the submarine explore all the way to the bottom? Solve this problem any way you choose.
I can … use place value to compare numbers and record my comparisons using <, =, or >.

Look Back! Which of the oceans listed is the shallowest? Explain.
Answer :
Compare Depths :
28,232 ; 35,840 ; 23,376 .
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The ten thousands digit 2 is the same in both numbers 28,232 and 23,376 But the number is 3 in 35,840 .
that means 35,840 is the greatest number other than two numbers .
Step 2 :
Look at the next digit. Compare the thousands
28,232
23,376
8 thousands > 3 thousands .
so, 28,232 > 23,376 .
So, 35,840 > 28,232 > 23,376 .

Essential Question
How Do You Compare Numbers?

Visual Learning Bridge
Earth is not perfectly round. The North Pole is 6,356 kilometers from Earth’s center. The equator is 6,378 kilometers from the center. Which is closer to Earth’s center, the North Pole or the equator?

Step 1
Write the numbers, lining up places. Begin at the left and compare.
6,356
6,378
The thousands digit is the same in both numbers.

Step 2
Look at the next digit. Compare the hundreds.
6,356
6,378
The hundreds digit is also the same in both numbers.

Step 3
The first place where the digits are different is the tens place. Compare the tens.
6,356 5 tens < 7 tens,
6,378 so 6,356 < 6,378.
The North Pole is closer than the equator to Earth’s center.

Convince Me! Reasoning is a whole number with 4 digits always greater than or less than a whole number with 3 digits? Explain.

Guided Practice

Do You Understand?
Question 1. Which place do you use to compare the numbers 60,618 and 60,647?
Answer:
To compare the numbers 60,618 and 60,647 we see Tens place value as the ten thousand , thousand and hundred place values are the same .
1 tens < 4 tens .
so, 60,618 < 60,647 .

Question 2.
Morocco has a total area of 442,300 square kilometers. Uzbekistan has a total area of 447,400 square kilometers. Use >, <, or = to compare the two areas.
Answer:
Total Area of Morocco = 442,300 square kilometers.
Total Area of Uzbekistan = 447,400 square kilometers.
Step 1 :
As , hundred thousand and ten thousands are same compare from thousands place .
Step 2 :
Compare the thousands place .
442,300
447,400
2 thousands < 7 thousands .
442,300 < 447,400 .

Do You Know How?
For 3-7, complete by writing >, =, or < in each O.
Question 3.
2,643 2,643
Answer:
2,643 = 2,643
Explanation :
All the thousands , hundreds , tens and ones values are the same .
so, 2,643 = 2,643

Question 4.
62,519 64,582
Answer:
62,519 < 64,582
Explanation :
Step 1 :
Write the numbers, lining up places. Begin at the left and compare.
62,519
64,582
The ten thousands digit is the same in both numbers.
Step 2 :
Compare the next digit , the thousands place .
62,519
64,582
2 thousands < 4 thousands .
62,519 < 64,582 .

Question 5.
218,701 118,692
Answer:
218,701 > 118,692
Explanation :
Write the numbers, lining up places. Begin at the left and compare.
218,701
118,692
The Hundred thousands digit
2 hundred thousand > 1 hundred thousand
218,701 > 118,692 .

Question 6.
32,467 32,467
Answer:
32,467 = 32,467
Explanation :
Step 1 :
All the ten thousand , thousand , hundred , tens and ones digits are same
so, 32,467 = 32,467

Question 7.
19,219 19,209
Answer:
19,219 > 19,209
Explanation :
Step 1 :
All the ten thousand , thousand , hundred digits are same so start comparison from tens place .
Step 2  :
Compare ten place
1 ten > 0 ten
19,219 > 19,209 .

Independent Practice

For 8-12, complete by writing >,=, or < in each .
Question 8.
22,873 22,774
Answer:
22,873 > 22,774
Explanation :
Step 1  :
The given numbers contains same ten thousand and thousand places . compare from hundred place .
Step 2  :
Compare the next digit that is hundred places .
22,873
22,774
8 hundreds > 7 hundreds .
22,873 > 22,774

Question 9.
912,706 912,706
Answer:
912,706 = 912,706
Explanation :
Given numbers have same hundred thousands , ten thousands , thousands , hundreds , tens and ones place values same .
so, 912,706 = 912,706

Question 10.
22,240 2,224
Answer:
22,240 > 2,224
Explanation :
The 5 digit number is always greater than the 4 digit number .
So, 22,240 > 2,224

Question 11.
30,000 + 5,000 + 3 300,000 + 5,000
Answer:
30,000 + 5,000 + 3 300,000 + 5,000
35,003 350,000
35,003 < 350,000
Explanation :
The 6 digit number is always greater than the 5 digit number .
so, 35,003 < 350,000

Question 12.
40,000 + 2,000 + 600 + 6 240,000 + 3,000 + 10
Answer:
40,000 + 2,000 + 600 + 6 240,000 + 3,000 + 10
42,606 243,010
42,606 < 243,010
Explanation :
The 6 digit number is always greater than the 5 digit number .
so, 42,606 < 243,010 .

For 13-17, write which place to use when comparing the numbers.

Question 13.
394,284
328,234
Answer:
394,284 > 328,234
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The hundred thousands digit 3 is the same in both numbers 394,284 and 328,234 .
Step 2 :
Look at the next digit. Compare the ten thousands place value .
394,284
328,234
9 ten thousands > 2 ten thousands .
So, 394,284 > 328,234

Question 14.
6,716
6,714
Answer:
6,716 > 6,714
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The thousands digit 6 is the same in both numbers 6,716 and 6,714
Step 2 :
Look at the next digit. Compare the hundreds place value .
The hundreds digit 7 is the same in both numbers 6,716 and 6,714
Step 3 :
Look at the next digit. Compare the tens place value .
The tens digit 1 is the same in both numbers 6,716 and 6,714
Step 4 :
Look at the next digit. Compare the Ones place value .
6 Ones > 4 Ones .
So, 6,716 > 6,714

Question 15.
32,916
32,819
Answer:
32,916 > 32,819
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The ten thousands digit 3 is the same in both numbers 32,916 and 32,819
Step 2 :
Look at the next digit. Compare the hundreds place value .
The thousands digit 2 is the same in both numbers 32,916 and 32,819
Step 3 :
Look at the next digit. Compare the hundreds place value .
9 hundreds > 8 hundreds .
So, 32,916 > 32,819 .

Question 16.
12,217
11,246
Answer:
12,217 > 11,246
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The ten thousands digit 1 is the same in both numbers 12,217 and 11,246
Step 2 :
Look at the next digit. Compare the thousands place value .
2 thousands > 1 thousands .
So, 12,217 > 11,246 .

Question 17.
812,497
736,881
Answer:
812,497 > 736,881
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The hundred thousands digits
8 hundred thousands > 7 hundred thousands .
So, 812,497 > 736,881 .

Problem Solving

For 18-19, use the table at the right.

Question 18.
Which genres at Danny’s Books did NOT sell better than Science?
Answer:
Humor Books did not sell better than Science
Explanation :
As 41,843 > 14,843 .

Question 19.
Which genres at Danny’s Books sold better than Biography?
Answer:
Science , Fantasy and Fiction books sold better than Biography
Explanation :
As , 48143 > 42,843 >41,843 > 41,834 .

Question 20.
Celia bought 3 bags of 4 hamburger buns and 3 bags of 8 hot dog buns. How many hamburger and hot dog buns did Celia buy?
Answer:
Number of Hamburgers buns = 3 bags of 4 hamburger buns = 3 × 4 = 12 buns .
Number of hot dogs buns = 3 bags of 8 hot dog buns = 3 × 8 = 24 buns .
Total Number of hamburger and hot dog buns Celia brought = 12 + 24 buns = 36 buns .

Question 21.
Make Sense and Persevere Write three numbers for which you would use the hundreds place to compare to 35,712.
Answer:
35,712.
The Three numbers are 35,246 ; 35,812 and 35,075 .

Question 22.
enVision® STEM
The Illinoian Stage began about 300,000 years ago. The Wolstonian Stage began about 352,000 years ago. Compare 300,000 to 352,000.
Answer:
300,000 < 352,000.
Explanation :
Step 1:
Write the numbers, lining up places. Begin at the left and compare.
The hundred thousands digit 3 is the same in both numbers 300,000 and 352,000 .
Step 2 :
Look at the next digit. Compare the ten thousands place value .
The ten thousands digit
0 ten thousands < 5 ten thousands .
So, 300,000 < 352,000.

Question 23.
An orchard in Maine has 5,287 apple trees. An orchard in Vermont has 5,729 trees. Use <, >, or = to write a comparison between the number of trees in each orchard.
Answer:
Number of apple trees in Maine orchard = 5,287 apple trees
Number of trees in Vermont orchard = 5,729 trees
5,287 < 5,729
The Vermont orchard have more trees than Maine orchard .

Question 24.
In 2010, the population of Alaska was 710,231. Write this number in expanded form, and write the number name.
Answer:
The population of Alaska = 710,231
Expanded Form : 700,000 + 10,000 + 200 + 30 + 1
Number Name  : Seven Hundred ten thousands Two hundred and thirty one .

Question 25.
Higher Order Thinking Explain how you know 437,160 is greater than 43,716.
Answer:
437,160 > 43,716
Explanation :
437,160 is a 6 digit Number
43,716 is a 5 digit Number .
6 digit number is greater than 5 digit number .

Assessment Practice

Question 26.
Is each comparison true or false?

Answer:

Question 27.
Is each comparison true or false?

Answer:

Lesson 1.4 Round Whole Numbers

Solve & Share
List 7 numbers that round to 300. Use a variety of numbers. Solve this problem any way you choose.
I can … use place value to round numbers.

Look Back! What is the greatest number between 200 and 300 that is closer to 200 than 300? Explain.
Answer :

Essential Question
How Can You Round Numbers?

Visual Learning Bridge
James researched 10 facts about Tallahassee, Florida for an assignment. One of the facts he found was the population in Tallahassee for the year 2017. He chose to round the population on his Florida Facts poster. If James rounded the population in 2017 to the nearest thousand, what was the number James displayed?

Round 181,376 to the nearest thousand. 181,376 is between 181,000 and 182,000.

Find the number 181,376 is closer to.
Mark the halfway point on the number line.

181,376 is to the left of the halfway point.
The poster displayed the population as 181,000.

Convince Me!

Critique Reasoning
Ellie says, “When I round these three numbers, I get the same number for two of them.” Anthony says, “Hmmm, when I round these numbers, I get the same number for all three.” Who is correct? Explain.

Answer :
Both are correct .
Explanation :
Ellie statement is right when we round off all the 3 Numbers to Nearest hundred then
1483 is round off to 1500
1250 is round off to 1300
1454 is round off to 1500
That means two numbers have same round off for 1483 and 1454 numbers .
Antony statement is right when we round off the 3 numbers to Nearest thousands then
1483 is round off to 1000
1250 is round off to 1000
1454 is round off to 1000
that means three numbers have same round off .

Another Example!
You can use place value to round. Round 181,376 to the nearest hundred.

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Guided Practice

Do You Understand?
Question 1.
Explain how to round a number when 3 is the digit to the right of the rounding place.
Answer:
Rounding 1435 to nearest Hundred .

Explanation :

 

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 2.
What number is halfway between 421,000 and 422,000?
Answer:
A number which is halfway between 421,000 and 422,000 is 421,500 .

Do You Know How?
For 3-8, round each number to the place of the underlined digit.
Question 3.
128,955
Answer:
128,955 – Rounding to nearest thousands .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 4.
85,639
Answer:
85,639 – Rounding to nearest tens .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 5.
9,924
Answer:
9,924 – Rounding to nearest thousands .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 6.
194,524
Answer:
194,524 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 7.
160,656
Answer:
160,656 – Rounding to nearest hundred thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 8.
149,590
Answer:
149,590 – Rounding to nearest hundred thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Independent Practice

For 9-24, use a number line or place value to round each number to the place of the underlined digit.
Question 9.
493,295
Answer:
493,295 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 10.
39,230
Answer:
39,230 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 11.
277,292
Answer:
277,292 – Rounding to nearest hundred thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 12.
54,846
Answer:
54,846 – Rounding to nearest Hundred .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 13.
4,028
Answer:
4,028 – Rounding to nearest tens .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 14.
638,365
Answer:

638,365 – Rounding to nearest hundred thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 15.
453,280
Answer:
453,280 – Rounding to nearest thousands .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 16.
17,909
Answer:
17,909 – Rounding to nearest Hundred .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 17.
956,000
Answer:

956,000 – Rounding to nearest hundred thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 18.
55,460
Answer:
55,460 – Rounding to nearest thousands .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 19.
321,679
Answer:
321,679 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 20.
417,547
Answer:
417,547- Rounding to nearest tens .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 21.
117,821
Answer:
117,821 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 22.
75,254
Answer:
75,254 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 23.
949,999
Answer:
949,999 – Rounding to nearest ten thousands

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 24.
666,821
Answer:
666,821 – Rounding to nearest thousands .

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Problem Solving

Question 25.
For each zoo in the table, round the attendance to the nearest hundred thousand.

Answer:

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Question 26.
Number Sense Write four numbers that round to 700,000 when rounded to the nearest hundred thousand.
Answer:
The four numbers that round to 700,000 when rounded to the nearest hundred thousand are 702,000 ; 745,000; 699,860 ; 692,480 and 734,955 .

Question 27.
Reasoning
A forest ranger correctly rounded the number of visitors to a park to be 120,000 visitors. Write a number that could be the actual number of visitors if he rounded to the nearest ten thousand.
Answer:
The Number the X is rounded to nearest ten thousand is 120,000 visitors .
the Rounding number is  123,500 .

Question 28.
Amy counted the number of boys and girls at a party. She recorded the results in the tally chart below.

How many more boys than girls were at the party?
Answer:
Number of Girls = 3
Number of Boys = 7
Number of more Boys than Girls at the party = 7 – 3 = 4 boys .

Question 29.
Higher Order Thinking
Liz attended class every day since she started school as a kindergartner. She said she has been in school for about 1,000 days. What numbers could be the actual number of school days if Liz rounded to the nearest ten?
Answer:
Number of days attended to school = 1,000 days
Rounded to the nearest ten 1,000 = 1000 days  .

Assessment Practice

Question 30.
Complete the table. Round each number to the given place.

Answer:

Explanation :

• Find the digit in the rounding place.
• Look at the next digit to the right. 3 becomes a 4. If it is 5 or greater, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
• Change all digits to the right of the rounding place to 0.

Lesson 1.5 Problem Solving

Construct Arguments

Solve & Share
The land areas of three states are shown in the table. Mickey said Alaska’s land area is about 10 times greater than Georgia’s land area. Explain why Mickey is or is not correct. Construct a math argument to support your answer.
I can … construct arguments using what I know about place-value relationships.

Thinking Habits
Be a good thinker! These questions can help you.

• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?

Question :
Look Back! Construct Arguments Mary said Georgia’s land area is about 10 times greater than Hawaii’s land area. Is Mary correct? Construct a math argument to support your answer.
Answer :
Georgia’s land area = 57,513 square miles .
Hawaii’s land area = 6,423 square miles .
10 times area of Hawaii land is = 6,423 square miles × 10 = 60,423 square miles .
57,513 not equal to 60,423
Georgia’s land area not equal to 10 times area of Hawaii land .
So, the statement made is wrong .

Essential Question
How Can You Construct Arguments?

Visual Learning Bridge
The table shows the retail sales per person in three states. Bella says Arizona had more retail sales per person than Massachusetts.

How can you construct a math argument that supports Bella’s conjecture?
I will use what I know about place value to compare numbers.

How can I construct an argument?
I can

• give an explanation that is clear and complete.
• use numbers and symbols correctly in my explanation.
• use numbers, objects, drawings, or actions to justify my argument.
• use a counterexample in my argument.

Here’s my thinking.
Bella’s statement makes sense.
Start with the greatest place value. The digits are the same in the ten thousands place and in the thousands place. The digits are different in the hundreds place, so that place is compared.
$13,637
$13,533
600 > 500
S0, $13,637 > $13,533.
Bella is correct. Arizona had more retail sales per person than Massachusetts.

Convince Me!
Construct Arguments Gayle said Arizona had more retail sales than Massachusetts because 7 > 3, so $13,637 > $13,533. Construct an argument to explain whether or not Gayle is correct.
Answer :
The digits are the same in the ten thousands place and in the thousands place. The digits are different in the hundreds place, so that place is compared.
$13,637
$13,533
600 > 500 .
So, 13,637 >13,533
Explanation :
Step 1: Always start from the digits at the highest place value.
Step 2: Compare the digits at this place value in both numbers. The number with the bigger digit is greater. Step 3: If the digits are equal, move one place value to the right 👉, and repeat Step 2.

Guided Practice

Construct Arguments Use the table on the previous page. Jorge said Massachusetts has more retail sales per person than lowa.

Question 1.
What numbers would you use to construct an argument supporting Jorge’s conjecture?
Answer:
Sales in Lowa = $13,172
Sales in Massachusetts = $13,533

Question 2.
How could you support Jorge’s conjecture?
Answer:
Start with the greatest place value. The digits are the same in the ten thousands place and in the thousands place. The digits are different in the hundreds place, so that place is compared.
$13,172
$13,533
100 < 500
S0, $13,172 < $13,533.
Jorge is correct. Massachusetts had more retail sales per person than Lowa .

Question 3.
Is Jorge’s conjecture true? Justify your answer.
Answer:
Yes, Jorge’s conjecture is true
Explanation :
Start with the greatest place value. The digits are the same in the ten thousands place and in the thousands place. The digits are different in the hundreds place, so that place is compared.
$13,172
$13,533
100 < 500
S0, $13,172 < $13,533.
Jorge is correct. Massachusetts had more retail sales per person than Lowa .

Independent Practice

Construct Arguments
The population of Gerald’s city is three hundred thousand, twenty-seven. Gerald wrote the number as 327,000. Emily lives in a city that has a population of three hundred sixteen thousand, forty-two. Gerald concluded that his city’s population is greater than the population of Emily’s city.
Question 4.
Does Gerald’s explanation make sense? Identify any flaws in Gerald’s thinking
Answer:
Yes,
Population of Gerald’s city = three hundred thousand, twenty-seven = 300,027 .
but Gerald wrote as = 327,000 .

Question 5.
Construct a math argument that explains why Gerald did not write the population of his city correctly.
Answer:
Population of Gerald’s city = three hundred thousand, twenty-seven = 300,027 .
but Gerald wrote as = 327,000 .
Gerald wrote the population in wrongly as she taught it as three hundred and twenty-seven  thousands  .

Question 6.
Correct Gerald’s argument. Explain how to compare the populations of Gerald’s and Emily’s cities.
Answer:
Gerald’s Argument is Wrong .
Population of Gerald’s city = three hundred thousand, twenty-seven = 300,027 .
Population in Emily City = three hundred sixteen thousand, forty-two = 360,042 .
Population in Emily city is greater than Population of Gerald’s city .
Explanation :
Start with the greatest place value. The digits are the same in the hundred thousands place . The digits are different in the tens thousands place, so that place is compared.
300,027
360,042
0 < 60,000
So, 300,027 < 360,042 .
Population in Emily city is greater than Population of Gerald’s city

Problem Solving

Performance Task
Planets
The planets in our solar system are different sizes, as shown below. Nora conjectured that Jupiter’s equator is about 10 times as long as Earth’s equator.

Question 7.
Make Sense and Persevere What information do you have?
Answer:
Length of Earth Equator = 40,030 km
Length of Jupiter Equator =439,264 km
Length of Venus Equator = 38,025 km
Length of Mars Equator = 21,297 km

Question 8.
Be Precise What are possible estimates for the lengths of the equators of Jupiter and Earth?

Answer:
Length of Earth Equator = 40,030 km
Length of Jupiter Equator =439,264 km
length of Jupiter Equator is greater than length of Earth Equator .

Question 9.
Reasoning What is the relationship between the estimates you found for the lengths of the two equators?
Answer:
Length of Earth Equator = 40,030 km
Length of Jupiter Equator =439,264 km
length of Jupiter Equator is greater than length of Earth Equator .

Question 10.
Construct Arguments Construct an argument justifying Nora’s conjecture.
Answer:
No , Nora statement is wrong
Explanation :
Length of Earth Equator = 40,030 km
Length of Jupiter Equator = 439,264 km
Nora conjectured that Jupiter’s equator is about 10 times as long as Earth’s equator.
10 times the Length of Earth Equator = 40,030 km × 10 = 400,300 km .
10 times the Length of Earth Equator is not equal to Length of Jupiter Equator
400,300 # 439,264 kms .
So, Nora statement is wrong

Topic 1 Fluency Review Activity

Point & Tally
Find a partner. Get paper and pencil. Each partner chooses a different color: Light blue or dark blue.

Partner 1 and Partner 2 each point to a black number at the same time. Both partners multiply those numbers.

If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
I can … multiply within 100.

Topic 1 Vocabulary Review

Understand Vocabulary
Choose the best term from the box. Write it on the blank.
Word List

• conjecture
• expanded form
• greater than symbol (>)
• Less than symbol (<)
• millions
• period
• place value
• rounding

Question 1.
A group of three digits, separated by commas, starting from the right is called a ___________.
Answer:
A group of three digits, separated by commas, starting from the right is called a period

Question 2.
A process that determines which multiple of 10, 100, 1,000 (and so on) a number is closest to is called __________.
Answer:
A process that determines which multiple of 10, 100, 1,000 (and so on) a number is closest to is calle rounding

Question 3.
A statement that is believed to be true but has not yet been proven is called a ___________.
Answer:
A statement that is believed to be true but has not yet been proven is called a conjecture

Question 4.
The value given to a place a digit has in a number is called its ___________.
Answer:
The value given to a place a digit has in a number is called its place value

Question 5.
In a number, a period of three places to the left of the thousands period is called the __________ period.
Answer:
In a number, a period of three places to the left of the thousands period is called the Millions period.

For each of these terms, give an example and a non-example.
Question 6 – 8.

Answer:

Use Vocabulary in Writing
Question 9.
Describe the value of the 9 in 926,415. Use at least 2 terms from the Word List in your explanation.
Answer:
926,415 – 900,000 – 9 hundred thousands

Topic 1 Reteaching

Set A pages 5-8

Use a place-value chart to write 301,400.
Expanded form: 300,000 + 1,000 + 400
Number name: three hundred one thousand, four hundred

Remember that each period has hundreds, tens, ones, and the period name.

Write each number in expanded form and using number names.
Question 1.
7,549
Answer:

Expanded form: 7,000 + 500 + 40 + 9
Number name:  Seven thousand, five hundred and forty Nine .

Question 2.
92,065
Answer:

Expanded form: 90,000 + 2,000 + 60 + 5
Number name:  Ninety Two thousand and Sixty Five .

Set B pages 9-12

1,111 = 1,000 + 100 + 10 + 1
As you move left, each 1 × 10 = 10
numeral is 10 times greater 10 × 10 = 100
than the digit on its right. 100 × 10 = 1,000

Remember to use the relationship between the values of the digits.

For 1-2, solve.
Question 1.
How many times greater is the value of the 7 in 70,048 than the value of 7 in 17,992?
Answer:
the value of the 7 in 70,048 = 70,000
the value of 7 in 17,992 = 7,000 .
The value is 7 in 70,048 is 10 times greater than the value of 7 in 17,992  .
7,000 × 10 = 70,000 .
Explanation :
As you move left, each 1 × 10 = 10
numeral is 10 times greater 10 × 10 = 100
than the digit on its right. 100 × 10 = 1,000

Question 2.
Violet has 30 glass tiles. She would like to mosaic tile a tabletop with 10 times that number of tiles. How many tiles does Violet want to use?
Answer:
Number of Violet glass tile = 30
Number of tiles required =10 times that number of tiles = 30 × 10 =  300 titles .

Set C pages 13-16

Use place value to compare 45,423 and 44,897. Start comparing from the left. Look for the first digit that is different.
45,423
44,897
5 > 4
5,000 > 4,000
So, 45,423 > 44,897.

Remember that you can use place value to compare numbers.

Write < or > in the O.
Question 1.
291,846 291,864
Answer:
291,846 <  291,864
Explanation :
Start with the greatest place value. The digits are the same in the hundred thousands ,ten thousands place, thousands place and in the hundred’s place . The digits are different in the Tens place, so that place is compared.
291,846
291,864
40 < 60
So, 291,846 <  291,864 .

Question 2.
66,298 66,298
Answer:
66,298 = 66,298
Explanation :
Both the numbers have same digits in ten thousand, thousand , hundred , tens and ones place.
So, both the numbers are equal .

Question 3.
88,645 87,645
Answer:
88,645 > 87,645
Explanation :
Start with the greatest place value. The digits are the same in ten thousands place  . The digits are different in the thousands place, so that place is compared.
88,645
87,645
8,000 > 7,000
8 thousands > 7 thousands .
So, 88,645 > 87,645

Set D pages 17-20

Round 764,802 to the nearest hundred thousand.

764,802 is to the right of the halfway point.
So, 764,802 rounds to 800,000.

Remember to find the halfway point to help you round.

For 1-4, use number lines or place value to round each number to the place of the underlined digit.
Question 1.
166,742
Answer:
Round 166,742 to the nearest thousand.

166,742 is to the right of the halfway point.
So, 166,742 rounds to 167,000 .

Question 2.
76,532
Answer:
Round 76,532to the nearest thousand.

76,532 is to the right of the halfway point.
So, 76,532 rounds to 77,000 .

Question 3.
5,861
Answer:
Round 5,861 to the nearest thousand.

5,861 is to the right of the halfway point.
So, 5,861 rounds to 6000 .

Question 4.
432,041
Answer:
Round 432,041 to the nearest thousand.

432,041 is to the Left of the halfway point.
So, 432,041 rounds to 432,000 .

Set E pages 21-24

Think about these questions to help you construct arguments.
Thinking Habits

• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
  

Remember that you can use math to show why your argument is correct.

According to the 2000 census, the population of a city was 935,426. According to the 2010 census, the population of the same city was 934,578. Taylor says the 2000 population was greater than the 2010 population.
Question 1.
Construct an argument that supports Taylor’s conjecture.
Answer:
Population of the city in 2000 census = 935,426
Population of the city in 2010 census = 934,578
935,426 > 934,578
Taylor statement made is correct .
Explanation :
The digits are the same in the hundred thousands place and in the ten thousands place. The digits are different in the thousands place, so that place is compared.
935,426
934,578
5000 > 4000 .
So, 935,426 > 934,578
Step 1: Always start from the digits at the highest place value.
Step 2: Compare the digits at this place value in both numbers. The number with the bigger digit is greater. Step 3: If the digits are equal, move one place value to the right 👉, and repeat Step 2.

Question 2.
In 1870, the population was seventy-two thousand, five hundred six. Lupita wrote 72,560. Construct a math argument that explains whether Lupita wrote the number correctly.
Answer:
Population in 1870 = seventy-two thousand, five hundred six = 76,506 .
Population in 1870 written by Lupita = 72,560
Lupita wrote the number wrongly as she represented 6 in the tens place like seventy-two thousand, five hundred and sixty .

Topic 1 Assessment Practice

Question 1.
Choose all the numbers that round to 100,000 when rounded to the nearest hundred thousand.
☐ 9,999
☐ 89,006
☐ 109,999
☐ 119,999
☐ 999,999
Answer:

Question 2.
Which symbol makes the comparison true? Write >,=, or < in the .
111,011 110,111

Answer:
111,011 >110,111
The digits are the same in the hundred thousands place and in the ten thousands place. The digits are different in the thousands place, so that place is compared.
111,011
110,111
1 thousand > 0 thousand
So, 111,011 >110,111
Explanation :
Step 1: Always start from the digits at the highest place value.
Step 2: Compare the digits at this place value in both numbers. The number with the bigger digit is greater. Step 3: If the digits are equal, move one place value to the right 👉, and repeat Step 2.

Question 3.
Write three numbers that round to 40,000 when rounded to the nearest ten thousand.
Answer:
Three numbers that round to 40,000 when rounded to the nearest ten thousand are 38,990 ; 42,640 and 39,999 .

Question 4.
John wrote the numbers 678,901 and 67,890. How many times greater is the value of 7 in 678,901 than the value of 7 in 67,890?
A. 10,000
B. 1,000
C. 100
D. 10
Answer:
Option D
Explanation :
The place value of 7 in 678,901  = 70,000 .
The place value of 7 in 67,890  = 7,000 .
7,000 × 10 = 70,000 .
The place value of 7 in 678,901 is 10 times greater than The place value of 7 in 67,890 .

Question 5.
Look at the numbers in the table.

Which number has one digit that represents ten times the value of the digit to its right? Explain.
Answer:
375,595  has the one digit that represents ten times the value of the digit to its right .
Explanation :
The place value of 375,595 is 5,000
The place value of 375,595 is 500
The place value of 375,595 is 5,000 which is ten times the value of the digit to its right that is The place value of 375,595 is 500 .

Question 6
Write the number for 160,060 in expanded form and using number names.
Answer:
160,060
Expanded form – 100,000 + 60,000 + 60

Question 7.
A. For each number, give the whole number that represents the value of the underlined digit. Write your answers in the boxes.

Answer:

Question :
B. Look at your answers in Part A. In which number is the value of the underlined digit 10 times the value of the digit to the right of it?
A. 155,349
B. 651,907
C. 947,502
D. 317,055
Answer:
Option D .

Question 8.
Rhode Island has about three hundred fifty-six thousand acres of forested land. What is this number in standard form rounded to the nearest ten thousand?
A. 350,000
B. 400,000
C. 360,000
D. 356,000
Answer:
Rhode Island Area = three hundred fifty-six thousand = 356,000
356,000 rounded to the nearest ten thousand = 360,000 .

Question 9.
Which one of the following comparisons is correct?
A. 65,215 > 65,512
B. 292,200 < 229,200
C. 890,242 < 890,224
D. 101,111 < 111,111
Answer:
Comparisons which are correct is Option D .

Question 10.
Write <, =, or > to complete a true comparison for each pair of numbers.
72,013 _______ 72,103
87,210 _______ 87,210
126,999 _______ 152,999
400,602 _______ 400,062
147,634 _______ 146,734
Answer:
72,013 < 72,103
87,210 = 87,210
126,999 < 152,999
400,602 > 400,062
147,634 > 146,734

Question 11.
The table shows the areas of four states.

A. Which of the 4 states has the least area? the greatest area? Write the number name for the area of each of these states.
Answer:
Kansas have Least Area= 82,278 square miles .
Montana have Greatest Area = 147,042 square miles .
82,278 = Eighty two thousand two hundred and seventy eight .
147,042 = one hundred and forty seven thousand and forty two .

B. Draw a place-value chart. Record Kansas’s area. Explain how the value of the 2 in the thousands place compares with the value of the 2 in the hundreds place.
Answer:

The value of 2 in one thousands place = 2,000 .
The value of 2 in hundreds place = 200 .
2,000 = 200 × 10
The value of 2 in one thousands place is ten times greater than The value of 2 in hundreds place .

Topic 1 Performance Task

Video Games
Tanji, Arun, and Juanita are playing a video game with 3 levels. The opportunity to earn points increases as the levels of the game increase. To keep track of their progress, Tanji, Arun, and Juanita record and examine their scores at each level.
Question 1.
Use the Level 1 table to answer the following questions.

Part A
Question :
Tanji noticed he was the only player with 3s in his Level 1 score. What are the values of the 3s in Tanji’s score?
Answer:
Tanji’s Score = 4,337
the values of the 3s in tanji score = 300 and 30 .

Part B
Question :
Arun noticed the 5s in his score were next to each other. Describe the relationship between the 5s in Arun’s score.
Answer:
Arun’s score = 5,519
the values of the 5 s in Arun’s score =5,000 and 500 .
5,000 is ten times the 500 .
the value of one 5 in his score is ten times greater than the value of the other 5

Part C
Question :
Juanita says the value of one 8 in her score is ten times greater than the value of the other 8. Construct an argument and draw a place-value chart to determine if Juanita is correct.
Answer:
Juanita’s Score = 2,868

the value of one 8 in her score is ten times greater than the value of the other 8 is wrong because
the value of one 8 in her score is hundred times greater than the value of the other 8 .
The value of 8 in 2,868 is 800 .
The value of 8 in 2,868 is 8 .
800 = 8 × 100 .

Question 2.
Use the Level 2 table to answer the following questions.

Part A – Question
Juanita had the greatest score at Level 2, followed by Tanji and Arun. Write each player’s score in expanded form to compare each score by place value.
Answer:
Juanita’s Score = 60,114 = 60,000 + 100 + 10 + 4 .
Arun’s Score = 39,207 = 30,000 + 9,000 + 200 + 7
Tanji’s Score = 56,899 = 50,000 + 6,000 + 800 + 90 + 9

Part B – Question
Write each player’s score using number names.
Answer:
Juanita’s Score = 60,114 = Sixty thousand One hundred and fourteen .
Arun’s Score = 39,207 = Thirty nine thousand two hundred and seven .
Tanji’s Score = 56,899 = Fifty Six thousand eight hundred and ninety nine .

Part C – Question
Use >, =, or < to write comparisons between the Level 2 scores.
Answer:
Juanita’s Score = 60,114
Arun’s Score = 39,207
Tanji’s Score = 56,899
60,114 > 56,899  > 39,207 .

Part D – Question
Arun noticed his Level 2 score has a greater value in the thousands place than Tanji’s and Juanita’s Level 2 scores. Round Arun’s score to the nearest thousand.
Answer:
Arun’s Score = 39,207
Rounded to Nearest thousand is
39,207 = 39,000.