Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-003
Compare Multi-Digit Whole Numbers
Represent and solve compare multi-digit whole numbers problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve compare multi-digit whole numbers problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for compare multi-digit whole numbers works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Compare Multi-Digit Whole Numbers relies on the base-ten system: each place is ten times the value of the place immediately to its right. Algorithms work because they preserve those place-value units while regrouping.
Represent the idea
The Math Box uses number line as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
Verify comparisons with a second representation such as a number line, common unit, or place-value expansion. A comparison is not justified by one digit or one numerator alone.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- Build one example of compare multi digit whole numbers in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Compare 1,248 and 8,635.
1248 < 8635Compare digits from the greatest place value left to right until the first difference appears.
Compare 2,365 and 9,746.
2365 < 9746Compare digits from the greatest place value left to right until the first difference appears.
Compare 1,857 and 3,174.
1857 < 3174Compare digits from the greatest place value left to right until the first difference appears.
Compare 2,968 and 4,286.
2968 < 4286Compare digits from the greatest place value left to right until the first difference appears.
Compare 4,079 and 5,397.
4079 < 5397Compare digits from the greatest place value left to right until the first difference appears.
Compare 5,184 and 6,412.
5184 < 6412Compare digits from the greatest place value left to right until the first difference appears.
Compare 6,295 and 7,524.
6295 < 7524Compare digits from the greatest place value left to right until the first difference appears.
Compare 7,316 and 8,635.
7316 < 8635Compare digits from the greatest place value left to right until the first difference appears.
Compare 8,427 and 9,746.
8427 < 9746Compare digits from the greatest place value left to right until the first difference appears.
Compare 1,857 and 9,538.
1857 < 9538Compare digits from the greatest place value left to right until the first difference appears.
Compare 1,649 and 2,968.
1649 < 2968Compare digits from the greatest place value left to right until the first difference appears.
Compare 2,751 and 4,079.
2751 < 4079Compare digits from the greatest place value left to right until the first difference appears.
Compare 3,862 and 5,184.
3862 < 5184Compare digits from the greatest place value left to right until the first difference appears.
Compare 4,973 and 6,295.
4973 < 6295Compare digits from the greatest place value left to right until the first difference appears.
Compare 6,084 and 7,316.
6084 < 7316Compare digits from the greatest place value left to right until the first difference appears.
Compare 7,195 and 8,427.
7195 < 8427Compare digits from the greatest place value left to right until the first difference appears.
Compare 8,206 and 9,538.
8206 < 9538Compare digits from the greatest place value left to right until the first difference appears.
Compare 1,649 and 9,317.
1649 < 9317Compare digits from the greatest place value left to right until the first difference appears.
Compare 1,428 and 2,751.
1428 < 2751Compare digits from the greatest place value left to right until the first difference appears.
Compare 2,539 and 3,862.
2539 < 3862Compare digits from the greatest place value left to right until the first difference appears.
Practice
Guided practice with hints
01Compare 3,641 and 4,973.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3641 < 4973
02Compare 4,752 and 6,084.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4752 < 6084
03Compare 5,863 and 7,195.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5863 < 7195
04Compare 1,248 and 8,206.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1248 < 8206
05Compare 2,365 and 9,317.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2365 < 9317
06Compare 1,428 and 3,174.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1428 < 3174
Practice
Independent practice
01Compare 2,539 and 4,286.
Answer: 2539 < 4286
02Compare 3,641 and 5,397.
Answer: 3641 < 5397
03Compare 4,752 and 6,412.
Answer: 4752 < 6412
04Compare 5,863 and 7,524.
Answer: 5863 < 7524
05Compare 1,248 and 8,635.
Answer: 1248 < 8635
06Compare 2,365 and 9,746.
Answer: 2365 < 9746
07Compare 1,857 and 3,174.
Answer: 1857 < 3174
08Compare 2,968 and 4,286.
Answer: 2968 < 4286
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use compare multi-digit whole numbers when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
Compare 4,079 and 5,397.
4079 < 5397
Compare 5,184 and 6,412.
5184 < 6412
Compare 6,295 and 7,524.
6295 < 7524
Compare 7,316 and 8,635.
7316 < 8635
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain compare multi-digit whole numbers problems accurately, then check each result with a second method.
Practice
Mastery check
01Compare 8,427 and 9,746.
Answer: 8427 < 9746
02Compare 1,857 and 9,538.
Answer: 1857 < 9538
03Compare 1,649 and 2,968.
Answer: 1649 < 2968
04Compare 2,751 and 4,079.
Answer: 2751 < 4079
05Compare 3,862 and 5,184.
Answer: 3862 < 5184
06Compare 4,973 and 6,295.
Answer: 4973 < 6295
07Compare 6,084 and 7,316.
Answer: 6084 < 7316
08Compare 7,195 and 8,427.
Answer: 7195 < 8427
Terminology
Words to know
- representation
- A diagram, model, equation, table, graph, or other form showing a mathematical idea.
- strategy
- A purposeful method chosen to solve or analyze a problem.
- estimate
- A nearby value used to judge size or reasonableness.
- verify
- To confirm a result using a second calculation, representation, or logical check.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.