Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-010
Divide Multi-Digit Numbers by One-Digit Divisors
Represent and solve divide multi-digit numbers by one-digit divisors problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve divide multi-digit numbers by one-digit divisors problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for divide multi-digit numbers by one-digit divisors 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
Divide Multi-Digit Numbers by One-Digit Divisors 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 equation balance 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
Check multiplication with an inverse division or a second model; check division by multiplying the quotient by the divisor and accounting for any remainder.
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.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- Build one example of divide multi digit numbers by one digit divisors 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.
Compute 48 ÷ 2.
48 ÷ 2 = 242 × 24 = 48, so multiplication verifies the quotient.
Compute 75 ÷ 3.
75 ÷ 3 = 253 × 25 = 75, so multiplication verifies the quotient.
Compute 104 ÷ 4.
104 ÷ 4 = 264 × 26 = 104, so multiplication verifies the quotient.
Compute 135 ÷ 5.
135 ÷ 5 = 275 × 27 = 135, so multiplication verifies the quotient.
Compute 168 ÷ 6.
168 ÷ 6 = 286 × 28 = 168, so multiplication verifies the quotient.
Compute 203 ÷ 7.
203 ÷ 7 = 297 × 29 = 203, so multiplication verifies the quotient.
Compute 240 ÷ 8.
240 ÷ 8 = 308 × 30 = 240, so multiplication verifies the quotient.
Compute 279 ÷ 9.
279 ÷ 9 = 319 × 31 = 279, so multiplication verifies the quotient.
Compute 64 ÷ 2.
64 ÷ 2 = 322 × 32 = 64, so multiplication verifies the quotient.
Compute 99 ÷ 3.
99 ÷ 3 = 333 × 33 = 99, so multiplication verifies the quotient.
Compute 136 ÷ 4.
136 ÷ 4 = 344 × 34 = 136, so multiplication verifies the quotient.
Compute 175 ÷ 5.
175 ÷ 5 = 355 × 35 = 175, so multiplication verifies the quotient.
Compute 216 ÷ 6.
216 ÷ 6 = 366 × 36 = 216, so multiplication verifies the quotient.
Compute 259 ÷ 7.
259 ÷ 7 = 377 × 37 = 259, so multiplication verifies the quotient.
Compute 304 ÷ 8.
304 ÷ 8 = 388 × 38 = 304, so multiplication verifies the quotient.
Compute 351 ÷ 9.
351 ÷ 9 = 399 × 39 = 351, so multiplication verifies the quotient.
Compute 80 ÷ 2.
80 ÷ 2 = 402 × 40 = 80, so multiplication verifies the quotient.
Compute 123 ÷ 3.
123 ÷ 3 = 413 × 41 = 123, so multiplication verifies the quotient.
Compute 168 ÷ 4.
168 ÷ 4 = 424 × 42 = 168, so multiplication verifies the quotient.
Compute 215 ÷ 5.
215 ÷ 5 = 435 × 43 = 215, so multiplication verifies the quotient.
Practice
Guided practice with hints
01Compute 264 ÷ 6.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 264 ÷ 6 = 44
02Compute 315 ÷ 7.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 315 ÷ 7 = 45
03Compute 368 ÷ 8.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 368 ÷ 8 = 46
04Compute 423 ÷ 9.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 423 ÷ 9 = 47
05Compute 96 ÷ 2.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 96 ÷ 2 = 48
06Compute 147 ÷ 3.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 147 ÷ 3 = 49
Practice
Independent practice
01Compute 200 ÷ 4.
Answer: 200 ÷ 4 = 50
02Compute 255 ÷ 5.
Answer: 255 ÷ 5 = 51
03Compute 312 ÷ 6.
Answer: 312 ÷ 6 = 52
04Compute 371 ÷ 7.
Answer: 371 ÷ 7 = 53
05Compute 48 ÷ 2.
Answer: 48 ÷ 2 = 24
06Compute 75 ÷ 3.
Answer: 75 ÷ 3 = 25
07Compute 104 ÷ 4.
Answer: 104 ÷ 4 = 26
08Compute 135 ÷ 5.
Answer: 135 ÷ 5 = 27
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 divide multi-digit numbers by one-digit divisors 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
Compute 168 ÷ 6.
168 ÷ 6 = 28
Compute 203 ÷ 7.
203 ÷ 7 = 29
Compute 240 ÷ 8.
240 ÷ 8 = 30
Compute 279 ÷ 9.
279 ÷ 9 = 31
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain divide multi-digit numbers by one-digit divisors problems accurately, then check each result with a second method.
Practice
Mastery check
01Compute 64 ÷ 2.
Answer: 64 ÷ 2 = 32
02Compute 99 ÷ 3.
Answer: 99 ÷ 3 = 33
03Compute 136 ÷ 4.
Answer: 136 ÷ 4 = 34
04Compute 175 ÷ 5.
Answer: 175 ÷ 5 = 35
05Compute 216 ÷ 6.
Answer: 216 ÷ 6 = 36
06Compute 259 ÷ 7.
Answer: 259 ÷ 7 = 37
07Compute 304 ÷ 8.
Answer: 304 ÷ 8 = 38
08Compute 351 ÷ 9.
Answer: 351 ÷ 9 = 39
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.