Learn on PengiEureka Math, Grade 4Chapter 2: Comparing Multi-Digit Whole Numbers

Lesson 2: Find 1, 10, and 100 thousand more and less than a given number.

In this Grade 4 Eureka Math lesson from Chapter 2, students practice finding 1 thousand, 10 thousand, and 100 thousand more and less than a given number using place value charts and number disks. Students build fluency with multi-digit numbers up to the hundred thousands place by identifying how specific units change when adding or subtracting these amounts. The lesson connects skip-counting, expanded form, and place value reasoning to deepen students' understanding of comparing multi-digit whole numbers.

Section 1

Mentally Find 1,000, 10,000, or 100,000 More or Less

Property

To find a number that is 1,0001,000, 10,00010,000, or 100,000100,000 more or less than a given number, identify the digit in the corresponding place value (thousands, ten thousands, or hundred thousands). Increase the digit by 1 to find the number that is more, or decrease it by 1 to find the number that is less.

Examples

Section 2

Regrouping Across Place Values

Property

When adding results in a value of 10 in a place, that place becomes 0 and we add 1 to the next higher place value (carrying over). When subtracting from a 0, we borrow from the next higher place value, which may require regrouping across multiple places.

Examples

Section 3

Find Missing Numbers in a Pattern

Property

To find a missing number in a sequence, first determine the rule of the pattern by finding the difference between two consecutive numbers. Then, apply this rule by adding or subtracting from a known number to find the unknown term.

Examples

Fill in the blank: 125,410; 135,410; ___125,410;\ 135,410;\ \_\_\_.

  • To find the pattern, look at how the numbers change — each increases by 10,00010,000.
  • The rule is to add 10,00010,000. So, 135,410+10,000=145,410135,410 + 10,000 = 145,410.

Fill in the blank: 788,204; ___; 768,204; 758,204788,204;\ \_\_\_;\ 768,204;\ 758,204.

  • Notice that the numbers are getting smaller each time, and the difference between them is 10,00010,000.
  • The rule is to subtract 10,00010,000. So, 788,20410,000=778,204788,204 - 10,000 = 778,204.

Fill in the blank: 499,000; ___; 501,000499,000;\ \_\_\_;\ 501,000.

  • To find the pattern, compare the first and last numbers: from 499,000499,000 to 501,000501,000, the increase is 2,0002,000. There are two equal steps, so each step must be 1,0001,000.
  • The rule is to add 1,0001,000. So, 499,000+1,000=500,000499,000 + 1,000 = 500,000.

Explanation

This skill involves analyzing a sequence of numbers to find the pattern, which could be adding or subtracting 1,000, 10,000, or 100,000. Once you identify the rule, you can find a missing number that is inside the sequence. This requires applying the rule forwards from the number before the blank or backwards from the number after the blank. This strengthens your understanding of place value and number relationships.

Book overview

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Continue this chapter

Chapter 2: Comparing Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Compare numbers based on meanings of the digits using >, <, or = to record the comparison.

  2. Lesson 2Current

    Lesson 2: Find 1, 10, and 100 thousand more and less than a given number.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Mentally Find 1,000, 10,000, or 100,000 More or Less

Property

To find a number that is 1,0001,000, 10,00010,000, or 100,000100,000 more or less than a given number, identify the digit in the corresponding place value (thousands, ten thousands, or hundred thousands). Increase the digit by 1 to find the number that is more, or decrease it by 1 to find the number that is less.

Examples

Section 2

Regrouping Across Place Values

Property

When adding results in a value of 10 in a place, that place becomes 0 and we add 1 to the next higher place value (carrying over). When subtracting from a 0, we borrow from the next higher place value, which may require regrouping across multiple places.

Examples

Section 3

Find Missing Numbers in a Pattern

Property

To find a missing number in a sequence, first determine the rule of the pattern by finding the difference between two consecutive numbers. Then, apply this rule by adding or subtracting from a known number to find the unknown term.

Examples

Fill in the blank: 125,410; 135,410; ___125,410;\ 135,410;\ \_\_\_.

  • To find the pattern, look at how the numbers change — each increases by 10,00010,000.
  • The rule is to add 10,00010,000. So, 135,410+10,000=145,410135,410 + 10,000 = 145,410.

Fill in the blank: 788,204; ___; 768,204; 758,204788,204;\ \_\_\_;\ 768,204;\ 758,204.

  • Notice that the numbers are getting smaller each time, and the difference between them is 10,00010,000.
  • The rule is to subtract 10,00010,000. So, 788,20410,000=778,204788,204 - 10,000 = 778,204.

Fill in the blank: 499,000; ___; 501,000499,000;\ \_\_\_;\ 501,000.

  • To find the pattern, compare the first and last numbers: from 499,000499,000 to 501,000501,000, the increase is 2,0002,000. There are two equal steps, so each step must be 1,0001,000.
  • The rule is to add 1,0001,000. So, 499,000+1,000=500,000499,000 + 1,000 = 500,000.

Explanation

This skill involves analyzing a sequence of numbers to find the pattern, which could be adding or subtracting 1,000, 10,000, or 100,000. Once you identify the rule, you can find a missing number that is inside the sequence. This requires applying the rule forwards from the number before the blank or backwards from the number after the blank. This strengthens your understanding of place value and number relationships.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Comparing Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Compare numbers based on meanings of the digits using >, <, or = to record the comparison.

  2. Lesson 2Current

    Lesson 2: Find 1, 10, and 100 thousand more and less than a given number.