3A · Chapter 1 · Lesson 04
Comparing and Ordering Numbers
Compare two numbers using highest differing place value., Order collections from least to greatest and reverse., Defend a comparison using words, symbols, or a place-value chart.
Your starting challenge
Which is greater: 4,099 or 4,100? Explain without subtracting.
By the end, you can…
- Compare two numbers using highest differing place value.
- Order collections from least to greatest and reverse.
- Defend a comparison using words, symbols, or a place-value chart.
Before starting, you should know…
- Read numerals and identify place values.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 In 6,372, what is the value of the digit in the thousands place?
Show answer and reasoning
Answer: 6,000
The thousands digit is 6; each unit has value 1,000, so its value is 6 × 1,000 = 6,000.
If your answer differs — Digit versus value: Circle the requested digit, name its column, then multiply the digit by 1,000, 100, 10, or 1. Review this concept. - E2 Expand 5,090 into the sum of its nonzero place values.
Show answer and reasoning
Answer: 5,000 + 90
Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 5,000 + 90.
If your answer differs — Lost place value: Use four labeled columns and write the value of every nonzero digit. Add the parts to check. Review this concept.
Vocabulary to know
| inequality | A statement comparing different quantities. |
|---|---|
| greater than | A value larger than another; symbol >. |
| less than | A value smaller than another; symbol <. |
| ascending | Least to greatest. |
| descending | Greatest to least. |
Learn the concept
Read left to right
Compare the thousands first. If equal, compare hundreds, then tens, then ones. Stop at the first place that differs.
Use the symbols accurately
The open side of > or < points toward the larger number. The statement 4,100 > 4,099 is true because the hundreds digits differ: 1 > 0.
Sort with a deliberate method
When ordering several numbers, sort first by thousands, then resolve ties with the hundreds, tens, and ones. Verify that every original number appears once.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Compare at the first differing place
Which is larger: 5,918 or 5,981?
- Both have 5 thousands and 9 hundreds.
- Compare tens: 1 ten versus 8 tens.
- 8 tens is larger.
Result: 5,981
Now you try · Understanding check 1
Insert <, >, or =: 7,421 ___ 7,412.Reveal answer and explanation
> — Compare digits from the highest place that differs. 7,421 > 7,412.
Worked example 2
Compare across a boundary
Compare 3,999 and 4,001.
- Compare thousands first: 3 versus 4.
- No later digit can reverse the higher-place result.
Result: 3,999 < 4,001
Now you try · Understanding check 2
Insert <, >, or =: 8,999 ___ 9,000.Reveal answer and explanation
< — Compare digits from the highest place that differs. 8,999 < 9,000.
Worked example 3
Order four values
Order 4,805; 4,580; 4,850; 4,508 from least to greatest.
- Thousands digits all equal 4.
- Hundreds digits are 8, 5, 8, 5.
- Within each tied pair, compare the tens and ones.
Result: 4,508 < 4,580 < 4,805 < 4,850
Now you try · Understanding check 3
Arrange from least to greatest: 6,090, 6,900, 6,009, 6,990.Reveal answer and explanation
6,009 < 6,090 < 6,900 < 6,990 — Compare the thousands place first, then hundreds, tens, and ones: 6,009, 6,090, 6,900, 6,990.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 Insert <, >, or =: 6,742 ___ 6,472.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 6,742 > 6,472.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - G2 Insert <, >, or =: 5,040 ___ 5,004.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 5,040 > 5,004.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - G3 Arrange from least to greatest: 8,204, 8,024, 8,240.
Show answer and reasoning
Answer: 8,024 < 8,204 < 8,240
Compare the thousands place first, then hundreds, tens, and ones: 8,024, 8,204, 8,240.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - G4 Insert <, >, or =: 9,998 ___ 10,000.
Show answer and reasoning
Answer: <
Compare digits from the highest place that differs. 9,998 < 10,000.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 Insert <, >, or =: 3,817 ___ 3,187.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 3,817 > 3,187.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I2 Insert <, >, or =: 5,509 ___ 5,590.
Show answer and reasoning
Answer: <
Compare digits from the highest place that differs. 5,509 < 5,590.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I3 Insert <, >, or =: 9,081 ___ 9,008.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 9,081 > 9,008.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I4 Arrange from least to greatest: 7,210, 7,021, 7,201, 7,120.
Show answer and reasoning
Answer: 7,021 < 7,120 < 7,201 < 7,210
Compare the thousands place first, then hundreds, tens, and ones: 7,021, 7,120, 7,201, 7,210.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I5 Insert <, >, or =: 4,999 ___ 5,000.
Show answer and reasoning
Answer: <
Compare digits from the highest place that differs. 4,999 < 5,000.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I6 Arrange from greatest to least: 9,803, 9,038, 9,308.
Show answer and reasoning
Answer: 9,803 > 9,308 > 9,038
Compare the thousands place first, then hundreds, tens, and ones: 9,803, 9,308, 9,038.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I7 Insert <, >, or =: 4,066 ___ 4,066.
Show answer and reasoning
Answer: =
Compare digits from the highest place that differs. 4,066 = 4,066.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - I8 Arrange from least to greatest: 6,100, 6,010, 6,001, 6,110.
Show answer and reasoning
Answer: 6,001 < 6,010 < 6,100 < 6,110
Compare the thousands place first, then hundreds, tens, and ones: 6,001, 6,010, 6,100, 6,110.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 Using the digits 4, 0, 8, and 2 exactly once, make the greatest four-digit number and the least four-digit number.
Show answer and reasoning
Answer: 8,420 and 2,048
For the greatest, arrange digits descending. For the least, start with the smallest nonzero digit (2), then 0, 4, 8.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - C2 Find all whole numbers between 5,207 and 5,211.
Show answer and reasoning
Answer: 5,208; 5,209; 5,210
Strictly between excludes both endpoints.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 Insert <, >, or =: 7,830 ___ 7,803.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 7,830 > 7,803.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - E2 Arrange from least to greatest: 4,098, 4,908, 4,809.
Show answer and reasoning
Answer: 4,098 < 4,809 < 4,908
Compare the thousands place first, then hundreds, tens, and ones: 4,098, 4,809, 4,908.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept. - E3 Insert <, >, or =: 10,000 ___ 9,999.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 10,000 > 9,999.
If your answer differs — Rightmost-digit trap: Compare from the LEFTMOST unequal place. One larger place outweighs all smaller places together. Review this concept.