Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-006
Subtract Multi-Digit Whole Numbers Fluently
Represent and solve subtract multi-digit whole numbers fluently problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve subtract multi-digit whole numbers fluently problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for subtract multi-digit whole numbers fluently 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
Subtract Multi-Digit Whole Numbers Fluently 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
Estimate before calculating, then use the inverse operation or an equivalent representation to confirm the exact result.
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 subtract multi digit whole numbers fluently 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.
Subtract 3,000 − 1,200.
3000 − 1200 = 1800Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,054 − 1,223.
3054 − 1223 = 1831Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,108 − 1,246.
3108 − 1246 = 1862Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,162 − 1,269.
3162 − 1269 = 1893Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,216 − 1,292.
3216 − 1292 = 1924Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,270 − 1,315.
3270 − 1315 = 1955Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,324 − 1,338.
3324 − 1338 = 1986Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,378 − 1,361.
3378 − 1361 = 2017Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,432 − 1,384.
3432 − 1384 = 2048Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,486 − 1,407.
3486 − 1407 = 2079Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,540 − 1,430.
3540 − 1430 = 2110Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,594 − 1,453.
3594 − 1453 = 2141Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,648 − 1,476.
3648 − 1476 = 2172Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,702 − 1,499.
3702 − 1499 = 2203Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,756 − 1,522.
3756 − 1522 = 2234Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,810 − 1,545.
3810 − 1545 = 2265Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,864 − 1,568.
3864 − 1568 = 2296Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,918 − 1,591.
3918 − 1591 = 2327Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 3,972 − 1,614.
3972 − 1614 = 2358Align place values and regroup from a greater place only when the current place does not contain enough units.
Subtract 4,026 − 1,637.
4026 − 1637 = 2389Align place values and regroup from a greater place only when the current place does not contain enough units.
Practice
Guided practice with hints
01Subtract 4,080 − 1,660.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4080 − 1660 = 2420
02Subtract 4,134 − 1,683.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4134 − 1683 = 2451
03Subtract 4,188 − 1,706.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4188 − 1706 = 2482
04Subtract 4,242 − 1,729.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4242 − 1729 = 2513
05Subtract 4,296 − 1,752.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4296 − 1752 = 2544
06Subtract 4,350 − 1,775.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4350 − 1775 = 2575
Practice
Independent practice
01Subtract 4,404 − 1,798.
Answer: 4404 − 1798 = 2606
02Subtract 4,458 − 1,821.
Answer: 4458 − 1821 = 2637
03Subtract 4,512 − 1,844.
Answer: 4512 − 1844 = 2668
04Subtract 4,566 − 1,867.
Answer: 4566 − 1867 = 2699
05Subtract 3,000 − 1,200.
Answer: 3000 − 1200 = 1800
06Subtract 3,054 − 1,223.
Answer: 3054 − 1223 = 1831
07Subtract 3,108 − 1,246.
Answer: 3108 − 1246 = 1862
08Subtract 3,162 − 1,269.
Answer: 3162 − 1269 = 1893
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 subtract multi-digit whole numbers fluently 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
Subtract 3,216 − 1,292.
3216 − 1292 = 1924
Subtract 3,270 − 1,315.
3270 − 1315 = 1955
Subtract 3,324 − 1,338.
3324 − 1338 = 1986
Subtract 3,378 − 1,361.
3378 − 1361 = 2017
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain subtract multi-digit whole numbers fluently problems accurately, then check each result with a second method.
Practice
Mastery check
01Subtract 3,432 − 1,384.
Answer: 3432 − 1384 = 2048
02Subtract 3,486 − 1,407.
Answer: 3486 − 1407 = 2079
03Subtract 3,540 − 1,430.
Answer: 3540 − 1430 = 2110
04Subtract 3,594 − 1,453.
Answer: 3594 − 1453 = 2141
05Subtract 3,648 − 1,476.
Answer: 3648 − 1476 = 2172
06Subtract 3,702 − 1,499.
Answer: 3702 − 1499 = 2203
07Subtract 3,756 − 1,522.
Answer: 3756 − 1522 = 2234
08Subtract 3,810 − 1,545.
Answer: 3810 − 1545 = 2265
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.