Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-004
Round Multi-Digit Whole Numbers
Represent and solve round multi-digit whole numbers problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve round multi-digit whole numbers problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for round 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
Round 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
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.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- Build one example of round 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.
Round 12,345 to the nearest 10.
12,345 → 12,350The digit immediately to the right of the 10 place determines whether to round down or up.
Round 12,482 to the nearest 100.
12,482 → 12,500The digit immediately to the right of the 100 place determines whether to round down or up.
Round 12,619 to the nearest 1,000.
12,619 → 13,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 12,756 to the nearest 10.
12,756 → 12,760The digit immediately to the right of the 10 place determines whether to round down or up.
Round 12,893 to the nearest 100.
12,893 → 12,900The digit immediately to the right of the 100 place determines whether to round down or up.
Round 13,030 to the nearest 1,000.
13,030 → 13,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 13,167 to the nearest 10.
13,167 → 13,170The digit immediately to the right of the 10 place determines whether to round down or up.
Round 13,304 to the nearest 100.
13,304 → 13,300The digit immediately to the right of the 100 place determines whether to round down or up.
Round 13,441 to the nearest 1,000.
13,441 → 13,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 13,578 to the nearest 10.
13,578 → 13,580The digit immediately to the right of the 10 place determines whether to round down or up.
Round 13,715 to the nearest 100.
13,715 → 13,700The digit immediately to the right of the 100 place determines whether to round down or up.
Round 13,852 to the nearest 1,000.
13,852 → 14,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 13,989 to the nearest 10.
13,989 → 13,990The digit immediately to the right of the 10 place determines whether to round down or up.
Round 14,126 to the nearest 100.
14,126 → 14,100The digit immediately to the right of the 100 place determines whether to round down or up.
Round 14,263 to the nearest 1,000.
14,263 → 14,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 14,400 to the nearest 10.
14,400 → 14,400The digit immediately to the right of the 10 place determines whether to round down or up.
Round 14,537 to the nearest 100.
14,537 → 14,500The digit immediately to the right of the 100 place determines whether to round down or up.
Round 14,674 to the nearest 1,000.
14,674 → 15,000The digit immediately to the right of the 1,000 place determines whether to round down or up.
Round 14,811 to the nearest 10.
14,811 → 14,810The digit immediately to the right of the 10 place determines whether to round down or up.
Round 14,948 to the nearest 100.
14,948 → 14,900The digit immediately to the right of the 100 place determines whether to round down or up.
Practice
Guided practice with hints
01Round 15,085 to the nearest 1,000.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,085 → 15,000
02Round 15,222 to the nearest 10.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,222 → 15,220
03Round 15,359 to the nearest 100.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,359 → 15,400
04Round 15,496 to the nearest 1,000.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,496 → 15,000
05Round 15,633 to the nearest 10.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,633 → 15,630
06Round 15,770 to the nearest 100.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 15,770 → 15,800
Practice
Independent practice
01Round 15,907 to the nearest 1,000.
Answer: 15,907 → 16,000
02Round 16,044 to the nearest 10.
Answer: 16,044 → 16,040
03Round 16,181 to the nearest 100.
Answer: 16,181 → 16,200
04Round 16,318 to the nearest 1,000.
Answer: 16,318 → 16,000
05Round 12,345 to the nearest 10.
Answer: 12,345 → 12,350
06Round 12,482 to the nearest 100.
Answer: 12,482 → 12,500
07Round 12,619 to the nearest 1,000.
Answer: 12,619 → 13,000
08Round 12,756 to the nearest 10.
Answer: 12,756 → 12,760
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 round 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
Round 12,893 to the nearest 100.
12,893 → 12,900
Round 13,030 to the nearest 1,000.
13,030 → 13,000
Round 13,167 to the nearest 10.
13,167 → 13,170
Round 13,304 to the nearest 100.
13,304 → 13,300
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain round multi-digit whole numbers problems accurately, then check each result with a second method.
Practice
Mastery check
01Round 13,441 to the nearest 1,000.
Answer: 13,441 → 13,000
02Round 13,578 to the nearest 10.
Answer: 13,578 → 13,580
03Round 13,715 to the nearest 100.
Answer: 13,715 → 13,700
04Round 13,852 to the nearest 1,000.
Answer: 13,852 → 14,000
05Round 13,989 to the nearest 10.
Answer: 13,989 → 13,990
06Round 14,126 to the nearest 100.
Answer: 14,126 → 14,100
07Round 14,263 to the nearest 1,000.
Answer: 14,263 → 14,000
08Round 14,400 to the nearest 10.
Answer: 14,400 → 14,400
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.