Comparing and Ordering Numbers
4A · Chapter 1 · Lesson 4 · MATH-4A-C01-L04
Learning goal. Order large numbers using the first differing place and verify comparisons on a scaled line.
Before you begin
Recall: Grade 3: four-digit place value, regrouping, comparison and rounding; Number Patterns. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Extend this pattern: 986,224, 987,224, 988,224, ___.
Show answer & reasoning
Each term increases by 1,000; add that step once more.
Extend this pattern: 614,795, 615,045, 615,295, ___.
Show answer & reasoning
Each term increases by 250; add that step once more.
Extend this pattern: 877,876, 882,876, 887,876, ___.
Show answer & reasoning
Each term increases by 5,000; add that step once more.
Key vocabulary
- place value
- value determined by a digit position
- expanded form
- sum of each nonzero place value
- benchmark
- nearby convenient multiple
- midpoint
- number exactly halfway between two bounds
Understand the concept
To compare large numbers, start at the highest place. A six-digit number is greater than a five-digit positive number. For equal-length numerals compare the first differing digit from the left. In 403,210 and 402,999 the thousands digit settles the comparison even though 999 looks bigger than 210.
Model it: place-value comparison ladder. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Insert <, >, or =: 145,373 ___ 159,098.
Compare the leftmost place where the digits differ: 145,373 is less than 159,098.
Check your understanding 1
Insert <, >, or =: 299,622 ___ 286,854.
Show answer & reasoning
Compare the leftmost place where the digits differ: 299,622 is greater than 286,854.
Worked example 2
Insert <, >, or =: 124,265 ___ 128,967.
Compare the leftmost place where the digits differ: 124,265 is less than 128,967.
Check your understanding 2
Insert <, >, or =: 243,911 ___ 227,019.
Show answer & reasoning
Compare the leftmost place where the digits differ: 243,911 is greater than 227,019.
Worked example 3
Insert <, >, or =: 959,497 ___ 979,163.
Compare the leftmost place where the digits differ: 959,497 is less than 979,163.
Check your understanding 3
Insert <, >, or =: 222,986 ___ 236,818.
Show answer & reasoning
Compare the leftmost place where the digits differ: 222,986 is less than 236,818.
Guided practice
Insert <, >, or =: 154,598 ___ 137,831.
Show answer & reasoning
Compare the leftmost place where the digits differ: 154,598 is greater than 137,831.
Insert <, >, or =: 726,539 ___ 726,163.
Show answer & reasoning
Compare the leftmost place where the digits differ: 726,539 is greater than 726,163.
Insert <, >, or =: 598,494 ___ 587,838.
Show answer & reasoning
Compare the leftmost place where the digits differ: 598,494 is greater than 587,838.
Order these numbers from least to greatest: 603,919, 590,827, 342,424.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Order these numbers from least to greatest: 236,262, 226,668, 406,823.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Independent practice
Insert <, >, or =: 898,316 ___ 903,402.
Show answer & reasoning
Compare the leftmost place where the digits differ: 898,316 is less than 903,402.
Insert <, >, or =: 594,154 ___ 605,293.
Show answer & reasoning
Compare the leftmost place where the digits differ: 594,154 is less than 605,293.
Order these numbers from least to greatest: 328,951, 337,475, 892,109.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Order these numbers from least to greatest: 682,606, 675,360, 721,684.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Order these numbers from least to greatest: 102,907, 122,830, 299,047.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Insert <, >, or =: 948,199 ___ 933,314.
Show answer & reasoning
Compare the leftmost place where the digits differ: 948,199 is greater than 933,314.
Insert <, >, or =: 438,766 ___ 436,423.
Show answer & reasoning
Compare the leftmost place where the digits differ: 438,766 is greater than 436,423.
Insert <, >, or =: 785,174 ___ 785,710.
Show answer & reasoning
Compare the leftmost place where the digits differ: 785,174 is less than 785,710.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Which is greater, 128,090 or 129,010? A student compares only the last digit. Explain the mistake.
Show answer & reasoning
Compare from the highest place where digits differ. 129,010 exceeds 128,090 by 920, regardless of the final digit.
Insert <, >, or =: 830,125 ___ 836,578.
Show answer & reasoning
Compare the leftmost place where the digits differ: 830,125 is less than 836,578.
Exit check
Order these numbers from least to greatest: 334,385, 349,072, 139,930.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Order these numbers from least to greatest: 624,225, 637,806, 182,191.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.
Order these numbers from least to greatest: 676,521, 694,903, 155,828.
Show answer & reasoning
Compare digit lengths first, then compare the greatest differing place.