Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-001
Read and Write Whole Numbers to One Million
Represent and solve read and write whole numbers to one million problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve read and write whole numbers to one million problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for read and write whole numbers to one million works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
A clear representation exposes the mathematical structure before a procedure is chosen.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Read and Write Whole Numbers to One Million 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 base ten blocks 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
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
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.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- Build one example of read and write whole numbers to one million 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.
Write 1,248 in expanded form.
1000 + 200 + 40 + 8Expanded form records the value contributed by each occupied place.
Write 2,365 in expanded form.
2000 + 300 + 60 + 5Expanded form records the value contributed by each occupied place.
Write 3,174 in expanded form.
3000 + 100 + 70 + 4Expanded form records the value contributed by each occupied place.
Write 4,286 in expanded form.
4000 + 200 + 80 + 6Expanded form records the value contributed by each occupied place.
Write 5,397 in expanded form.
5000 + 300 + 90 + 7Expanded form records the value contributed by each occupied place.
Write 6,412 in expanded form.
6000 + 400 + 10 + 2Expanded form records the value contributed by each occupied place.
Write 7,524 in expanded form.
7000 + 500 + 20 + 4Expanded form records the value contributed by each occupied place.
Write 8,635 in expanded form.
8000 + 600 + 30 + 5Expanded form records the value contributed by each occupied place.
Write 9,746 in expanded form.
9000 + 700 + 40 + 6Expanded form records the value contributed by each occupied place.
Write 1,857 in expanded form.
1000 + 800 + 50 + 7Expanded form records the value contributed by each occupied place.
Write 2,968 in expanded form.
2000 + 900 + 60 + 8Expanded form records the value contributed by each occupied place.
Write 4,079 in expanded form.
4000 + 0 + 70 + 9Expanded form records the value contributed by each occupied place.
Write 5,184 in expanded form.
5000 + 100 + 80 + 4Expanded form records the value contributed by each occupied place.
Write 6,295 in expanded form.
6000 + 200 + 90 + 5Expanded form records the value contributed by each occupied place.
Write 7,316 in expanded form.
7000 + 300 + 10 + 6Expanded form records the value contributed by each occupied place.
Write 8,427 in expanded form.
8000 + 400 + 20 + 7Expanded form records the value contributed by each occupied place.
Write 9,538 in expanded form.
9000 + 500 + 30 + 8Expanded form records the value contributed by each occupied place.
Write 1,649 in expanded form.
1000 + 600 + 40 + 9Expanded form records the value contributed by each occupied place.
Write 2,751 in expanded form.
2000 + 700 + 50 + 1Expanded form records the value contributed by each occupied place.
Write 3,862 in expanded form.
3000 + 800 + 60 + 2Expanded form records the value contributed by each occupied place.
Practice
Guided practice with hints
01Write 4,973 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4000 + 900 + 70 + 3
02Write 6,084 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6000 + 0 + 80 + 4
03Write 7,195 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 7000 + 100 + 90 + 5
04Write 8,206 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 8000 + 200 + 0 + 6
05Write 9,317 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 9000 + 300 + 10 + 7
06Write 1,428 in expanded form.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1000 + 400 + 20 + 8
Practice
Independent practice
01Write 2,539 in expanded form.
Answer: 2000 + 500 + 30 + 9
02Write 3,641 in expanded form.
Answer: 3000 + 600 + 40 + 1
03Write 4,752 in expanded form.
Answer: 4000 + 700 + 50 + 2
04Write 5,863 in expanded form.
Answer: 5000 + 800 + 60 + 3
05Write 1,248 in expanded form.
Answer: 1000 + 200 + 40 + 8
06Write 2,365 in expanded form.
Answer: 2000 + 300 + 60 + 5
07Write 3,174 in expanded form.
Answer: 3000 + 100 + 70 + 4
08Write 4,286 in expanded form.
Answer: 4000 + 200 + 80 + 6
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 read and write whole numbers to one million 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
Write 5,397 in expanded form.
5000 + 300 + 90 + 7
Write 6,412 in expanded form.
6000 + 400 + 10 + 2
Write 7,524 in expanded form.
7000 + 500 + 20 + 4
Write 8,635 in expanded form.
8000 + 600 + 30 + 5
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain read and write whole numbers to one million problems accurately, then check each result with a second method.
Practice
Mastery check
01Write 9,746 in expanded form.
Answer: 9000 + 700 + 40 + 6
02Write 1,857 in expanded form.
Answer: 1000 + 800 + 50 + 7
03Write 2,968 in expanded form.
Answer: 2000 + 900 + 60 + 8
04Write 4,079 in expanded form.
Answer: 4000 + 0 + 70 + 9
05Write 5,184 in expanded form.
Answer: 5000 + 100 + 80 + 4
06Write 6,295 in expanded form.
Answer: 6000 + 200 + 90 + 5
07Write 7,316 in expanded form.
Answer: 7000 + 300 + 10 + 6
08Write 8,427 in expanded form.
Answer: 8000 + 400 + 20 + 7
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.