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Chapter 1Place Value and Number Sense

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Chapter 1Place Value and Number Sense

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Lesson 1-1 Number Patterns

Lesson 1-2 Problem-Solving Strategy: Use the Four-Step Plan

Lesson 1-3 Place Value Through 1,000

Lesson 1-4 Place Value Through 10,000

Lesson 1-5 Problem-Solving Investigation: Use the Four-Step Plan

Lesson 1-6 Compare Numbers

Lesson 1-7 Order Numbers

Lesson 1-8 Round to the Nearest Ten and Hundred

Lesson 1-9 Round to the Nearest Thousand

11Place Value and Number Sense

Five-Minute Check

Main Idea and Vocabulary

California Standards

Example 1

Example 2

Example 3

1-11-1 Number Patterns

• I will find patterns in numbers.

• pattern

Standard 3NS1.1 Count, read, and write whole numbers to 10,000.

Since the second number is the first number plus 4; the third number is the second number plus 4; and the fourth number is the third number plus 4, I added 4 to the fifth number to get 24.

Answer: 24

Identify the pattern in 8, 12, 16, 20, ___. What is the missing number?

A. Add 4; 28

B. Add 7; 30

C. Add 6; 30

D. Add 6; 28

Identify the pattern in 6, 12, 18, 24, ___. What is the missing number?

Adam rode his bike 2 miles on Monday, 4 miles on Tuesday, and 6 miles on Wednesday. If the pattern continues, how many miles will he ride on Thursday?

Since the second number is the first number plus 2; the third number is the second number plus 2; I added 2 to the third number to get 8.

Answer: 8

Maria delivered 3 pizzas on Monday, 6 pizzas on Tuesday, and 9 pizzas on Wednesday. If the pattern continues, how many pizzas will Maria deliver on Thursday?

Notice that 10 is subtracted from each number.

Answer: The missing numbers are 80 and 60.

Identify the pattern in 100, 90, ___, 70, ___, 50. What are the missing numbers?

Identify the pattern in 60, 55, ___, 45, ___, 35. What are the missing numbers?

A. Subtract 5; 50 and 40

B. Subtract 10; 50 and 40

C. Subtract 5; 45 and 30

D. Subtract 10; 30 and 30

Five-Minute Check (over Lesson 1-1)

Main Idea

Example 1: Problem-Solving Strategy

1-21-2 Problem-Solving Strategy: Use the Four-Step Plan

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

Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.

Standard 3NS2.1 Find the sum or difference of two whole numbers between 0 and 10,000.

Daniela’s family went to a zoo. They learned that a roadrunner is 1 foot tall. An African elephant is 12 feet tall. How much taller is an African elephant than a roadrunner?

Understand

What facts do you know?

• The roadrunner is 1 foot tall.

• The African elephant is 12 feet tall.

What do you need to find?

• Find how much taller an African elephant is than the roadrunner.

To find out how much taller the African elephant is than the roadrunner, subtract.

Answer: So, the elephant is 11 feet taller than the roadrunner.

121–11

Since addition and subtraction are inverse operations, you can use addition to check subtraction.

So, the answer is correct.

Example 1

Example 2

Example 3

1-31-3 Place Value Through 1,000

Place Value

• I will read, write, and identify place value of whole numbers through thousands.

• digit

• place value

• standard form

• expanded form

• word form

Standard 3NS1.3 Identify place value for each digit in numbers to 10,000.

Standard 3NS1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

Identify the place value of the underlined digit in 2,657. Then write the value of the digit.

Create a place value chart.

Answer: The underlined digit is 6. It is in the hundreds place, so its value is 600.

2 6 5 7

What is the value of the underlined digit in the number 3,498?

B. 9,000

C. 900

The length of the Golden Gate Bridge is 8,981 feet. Identify the place value of the underlined digit. Then write its value.

Answer: The underlined number, 8, is in the tens place, so it has a value of 80.

8 9 8 1

C. 700

D. 7,000

The length of one main cable on the Golden Gate Bridge is 7,650 feet. Write 7,650 three ways.

Standard Form: 7,650

Expanded Form: 7,000 + 600 + 50

Word Form: seven thousand six hundred fifty

A. three thousand four seven six

B. three four seventy six

C. three thousand four hundred seventy six

D. thirty four seventy six

3,476 written in word form looks like which of the following?

Example 1

Example 2

Example 3

• I will read, write, and identify place value of whole numbers through ten thousands.

• period

Standard 3NS1.3 Identify place value for each digit in numbers to 10,000.

Standard 3NS1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

Identify the place of the underlined digit in 54,062. Then write its value.

Answer: The underlined digit 5, is in the ten thousands place, so its value is 50,000.

5 4 0 6 2

A. 400

B. 4,000

C. 40,000

Write the number 41,093 in three ways.

Standard Form: 41,093

Expanded Form: 40,000 + 1,000 + 90 + 3

Word Form: forty-one thousand, ninety-three

A. 57,000 + 257

B. 50,000 + 7,000 + 200 + 50 + 7

C. fifty seven thousand two hundred fifty seven

D. fifty seven and two fifty seven

Which is a correct representation of the number 57,257 written in expanded form?

Refer to the chart below. Write the width of Saturn in expanded form.

Answer: 70,000 + 2,000 + 300 + 60 + 8 = 72,368

A. 30,000 + 1,000 + 500 + 10 + 8

B. 70,000 + 2,000 + 300 + 60 + 8

C. 50,000 + 1,000 + 300 + 3

D. 80,000 + 6,000 + 800 + 20 + 2

Using the chart, write the width of Jupiter in expanded form.

Main Idea

Example 1: Problem-Solving Investigation

1-51-5 Problem-Solving Investigation: Use the Four-Step Plan

• Use the four-step plan to solve a problem.

Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant and irrelevant information, sequencing and prioritizing information, and observing patterns.

Standard 3NS2.1 Find the sum or difference of two whole numbers between 0 and 10,000.

DERRICK: My sister gave me drawing paper for my birthday. There were 32 sheets. I want to make it last 8 days.

YOUR MISSION: To find how many sheets he can use each day.

Understand

What facts do you know?

• There are 32 sheets of paper.

• Derrick wants it to last for 8 days.

What do you need to find?

• Find how many sheets he can use each day.

You know the total number of sheets of paper and how many days they need to last. You can show this using counters.

Use 32 counters to represent the 32 sheets of paper. Make 8 equal groups of counters, placing them one at a time into each group until the counters are gone.

Answer: Each group has 4 counters. So, he can use 4 sheets of paper each day.

Look back at the problem.

4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32

So, the answer is correct.

Example 1

Example 2

Example 3

1-61-6 Compare Numbers

• I will compare numbers through ten thousands.

• is greater than ( )

• is less than ( )

• is equal to ( )

Standard 3NS1.2 Compare and order whole numbers to 10,000.

Brianna sold 7 bracelets at the arts-and-crafts fair. Jeremy sold 12 bracelets. Which one sold fewer bracelets?

You can use a number line to compare 7 and 12.

7 is to the left of 12

Answer: So, Brianna sold fewer bracelets.

7 is less than 12

7 < 12

12 is to the right of 7

12 is greater than 7

12 > 7

A. Louise

B. Ajeya

Louise bought 2 bags of apples. Ajeya bought 5 bags of apples. Who bought more apples?

In June, Danilo rode his bike 78 miles. He rode his bike 72 miles in July. During which month did Danilo ride his bike more?

Step 1 Line up the numbers by place value.

Step 2 Compare. Start with the greatest place value position.

Since 2 is less than 8, the number 72 is less than 78.

Answer: So, Danilo rode his bike more in the month of June.

A. Monday

B. Tuesday

C. Wednesday

D. Thursday

Irvin walked 5 miles on Monday, 7 miles on Tuesday, 3 miles on Wednesday, and 8 miles on Thursday. On which day did he walk the furthest?

Which is greater, 762 or 1,239?

You need to compare 762 and 1,239. Line up the numbers. Then compare.

Answer: 1 thousand is greater than 0 thousands, so, 1,239 > 762.

1 2 3 9

A. 548

B. 2,465

C. neither

Which is greater, 548 or 2,465?

Main Idea

Example 1

Example 2

1-71-7 Order Numbers

• I will use a number line and place value to order numbers through ten thousands.

Standard 3NS1.2 Compare and order numbers to 10,000.

Use a place value chart to line up the numbers by their place value. Compare from the left.

The third grade at Harper sold raffle tickets. Mr. Pond’s class sold 187 tickets. Mrs. Fisher’s class sold 145 and Mrs. Sen’s class sold 176 tickets. Order the numbers from least to greatest.

Answer: The order from least to greatest is 145, 176, 187.

A. 130, 400, 368, 211

B. 130, 211, 368, 400

C. 400, 368, 211, 130

D. 211, 130, 400, 368

Which of the following shows numbers listed from least to greatest?

Namid delivers 87 newspapers on Sundays, 42 newspapers on Mondays, and 57 newspapers on Tuesdays. Order the numbers from greatest to least.

Use a place value chart to line up the numbers by their place value. Compare from the left.

Answer: The order from greatest to least is 87, 57, 42.

A. 27, 56, 89, 99

B. 56, 27, 89, 99

C. 89, 27, 56, 99

D. 99, 89, 56, 27

Which of the following shows numbers listed from greatest to least?

Example 1

Example 2

Example 3

Example 4

1-81-8 Round to the Nearest Ten and Hundred

• I will round numbers to the nearest ten and hundred.

• round

Standard 3NS1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

The closest ten less than 24 is 20.

Marco drank 24 ounces of water today. Round 24 to the nearest ten.

The closest ten greater than 24 is 30.

So, use a number line from 20 to 30.

Answer: Since 24 is closer to 20 than to 30, round 24 to 20.

Paco had 37 crayons. Round 37 to the nearest ten.

LaToya walked 65 miles this week. Round 65 to the nearest ten.

The closest ten less than 65 is 60.

The closest ten greater than 65 is 70.

So, use a number line from 60 to 70.

Notice that 65 is exactly between 60 and 70. When this happens, round up.

Answer: So, 65 will round to 70.

Imani made 45 baskets during the basketball game. Round 45 to the nearest ten.

The goldfish tank at the pet store was filled with 117 goldfish. Round 117 to the nearest hundred.

The closest hundred less than 117 is 100.

The closest hundred greater than 117 is 200.

Use a number line from 100 to 200, counting by tens.

Answer: 117 is closer to 100 than to 200. Round 117 to 100.

A. 350

B. 400

C. 300

D. 450

The swing holds 342 pounds. Round 342 to the nearest hundred.

Shawn collected 1,489 stamps. Round 1,489 to the nearest hundred.

The closest hundred less than 1,489 is 1,400.

The closest hundred greater than 1,489 is 1,500.

Use a number line from 1,400 to 1,500, counting by tens.

Answer: 1,489 is closer to 1,500 than to 1,400. Round 1,489 to 1,500.

A. 1,700

B. 1,000

C. 2,000

D. 1,600

Robyn and her class collected 1,671 cans of food for the food drive. Round 1,671 to the nearest hundred.

Main Idea

Key Concept: Rounding Whole Numbers

Example 1

Example 2

Example 3

1-91-9 Round to the Nearest Thousand

• I will round numbers to the nearest thousand.

Standard 3NS1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

Step 1 Underline the digit in the place to be rounded. In this case, the 4 is in the thousands place.

A newspaper stand sold 4,850 magazines last month. Round to the nearest thousand.

Step 2 Look at the 8, the digit to the right of the underlined digit.

Step 3 This digit is greater than 5, so add 1 to the underlined digit.

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

Answer: Since 4,850 is closer to 5,000 than to 4,000, round 4,850 to 5,000.

A. 3,400

B. 3,500

C. 3,000

D. 4,000

Antonio sold 3,417 ride tickets at the carnival last week. Round to the nearest thousand.

The book store sold 6,238 books this month. Round to the nearest thousand.

The closest thousand less than 6,238 is 6,000.

The closest thousand greater than 6,238 is 7,000.

A. 1,000

B. 2,000

C. 1,700

D. 1,800

Zy-Aeria and Lin sold 1,765 raffle tickets at the open house. Round to the nearest thousand.

The movie theater sold 2,513 tickets over the weekend. To the nearest thousand, about how many tickets were sold?

Step 1 Underline the digit in the place to be rounded. In this case, the 2 is in the thousands place.

Step 2 Look at the 5, the digit to the right of the underlined digit.

Step 3 This digit is 5, so change the underlined digit by rounding up 1.

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

A. 7,000

B. 7,500

C. 8,000

D. 7,600

Jamie’s new pool holds 7,544 gallons of water. To the nearest thousand, about how many gallons will the pool hold?

Five-Minute Checks

Place Value

Lesson 1-1

Lesson 1-2 (over Lesson 1-1)

Compare. Replace each with <, >, or =.

64 102

301 313

486 461

172 172

124 56

883 961

Identify the pattern. Then find the missing number.

(over Lesson 1-1)

2, 4, ___, 8

(over Lesson 1-1)

5, 10, 15, ___, 25

(over Lesson 1-1)

6, 9, ___, 15

(over Lesson 1-1)

8, 12, 16, 20, ___

A. 3 barrettes

B. 12 barrettes

C. 4 barrettes

D. 2 barrettes

Solve. Use the Four-Step Plan strategy. Juanita bought 8 barrettes on Thursday and 6 on Friday. Then she bought 4 more barrettes on Saturday. If the pattern continues, how man barrettes will she buy on Sunday?

(over Lesson 1-2)

A. tens; 80

B. hundreds; 200

C. tens; 200

D. thousands; 3,000

Identify the underlined digit in 3,280. Then write the value of the underlined digit.

(over Lesson 1-3)

A. tens; 1

B. thousands; 6,000

C. hundreds; 200

D. tens; 90

(over Lesson 1-3)

A. thousands; 1,000

B. tens; 2

C. tens; 70

D. ones; 2

(over Lesson 1-3)

A. ones; 10

B. hundreds; 500

C. hundreds; 1,000

D. ones; 0

(over Lesson 1-3)

A. ten thousands; 40,000

B. thousands; 40,000

C. ten thousands; 30,000

D. hundreds; 900

Identify the place of the underlined digit in 34,908. Then write the value of the digit.

(over Lesson 1-4)

A. hundreds; 400

B. hundreds; 800

C. hundreds; 700

D. tens; 80

(over Lesson 1-4)

A. thousands; 9,000

B. ten thousands; 90,000

C. ten thousands; 9,000

D. hundreds; 900

(over Lesson 1-4)

A. tens; 2

B. ones; 0

C. ones; 2

D. tens; 0

(over Lesson 1-4)

Use the Four-Step Plan to solve. Paloma has 20 pages to read. She reads 5 pages an hour. How many hours will it take her to finish 20 pages?

(over Lesson 1-5)

Use the Four-Step Plan to solve. Emilio worked 32 hours last week. He worked 8 hours each day. How many days did Emilio work?

(over Lesson 1-6)

Compare. Write >, <, or =.

430 403

(over Lesson 1-6)

1,212 1,212

(over Lesson 1-6)

763 709

A. 46, 49, 63

B. 49, 63, 46

C. 46, 63, 49

D. 63, 49, 46

Order the numbers from least to greatest.

(over Lesson 1-7)

46, 63, 49

(over Lesson 1-7)

A. 294, 279, 299

B. 279, 294, 299

C. 299, 279, 294

D. 279, 299, 294

Order the numbers from least to greatest.

294, 279, 299

(over Lesson 1-7)

A. 893, 748, 562

B. 896, 748, 562

C. 748, 562, 893

D. 562, 748, 896

Order the numbers from greatest to least.

748, 893, 562

(over Lesson 1-7)

A. 202, 2,100, 1,200

B. 202, 1,200, 2,100

C. 2,100, 1,200, 202

D. 2,100, 202, 1,200

Order the numbers from greatest to least.

1,200, 202, 2,100

Round 67 to the nearest ten.

(over Lesson 1-8)

A. 260

C. 200

D. 300

(over Lesson 1-8)

A. 400

B. 410

C. 500

D. 420

(over Lesson 1-8)

A. 580

B. 500

C. 600

Round 588 to the nearest hundred.

(over Lesson 1-8)

A. 1,200

B. 1,230

C. 1,000

D. 230

Round 1,230 to the nearest hundred.

(over Lesson 1-8)

A. 700

B. 650

D. 600

Round 653 to the nearest hundred.

(over Lesson 1-8)

A. 1,700

B. 1,000

C. 1,780

D. 1,800

Round 1,781 to the nearest hundred.

(over Lesson 1-8)

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