Grade 4 · Number & Operations in Base Ten · MAT-04-NBT-007
Model Multi-Digit Multiplication
Represent and solve model multi-digit multiplication problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve model multi-digit multiplication problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for model multi-digit multiplication 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.
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
Model Multi-Digit Multiplication 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 multiplication grid 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.
Partial-Products Area Model
Decompose both factors into tens and ones. Each rectangle is one partial product.
- Build one example of model multi digit multiplication 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.
Multiply 1234 by 2.
1234 × 2 = 2468Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1251 by 3.
1251 × 3 = 3753Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1268 by 4.
1268 × 4 = 5072Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1285 by 5.
1285 × 5 = 6425Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1302 by 6.
1302 × 6 = 7812Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1319 by 7.
1319 × 7 = 9233Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1336 by 8.
1336 × 8 = 10688Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1353 by 2.
1353 × 2 = 2706Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1370 by 3.
1370 × 3 = 4110Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1387 by 4.
1387 × 4 = 5548Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1404 by 5.
1404 × 5 = 7020Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1421 by 6.
1421 × 6 = 8526Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1438 by 7.
1438 × 7 = 10066Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1455 by 8.
1455 × 8 = 11640Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1472 by 2.
1472 × 2 = 2944Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1489 by 3.
1489 × 3 = 4467Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1506 by 4.
1506 × 4 = 6024Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1523 by 5.
1523 × 5 = 7615Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1540 by 6.
1540 × 6 = 9240Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Multiply 1557 by 7.
1557 × 7 = 10899Decompose the multi-digit factor by place value, multiply each part, then recombine the partial products.
Practice
Guided practice with hints
01Multiply 1574 by 8.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1574 × 8 = 12592
02Multiply 1591 by 2.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1591 × 2 = 3182
03Multiply 1608 by 3.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1608 × 3 = 4824
04Multiply 1625 by 4.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1625 × 4 = 6500
05Multiply 1642 by 5.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1642 × 5 = 8210
06Multiply 1659 by 6.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1659 × 6 = 9954
Practice
Independent practice
01Multiply 1676 by 7.
Answer: 1676 × 7 = 11732
02Multiply 1693 by 8.
Answer: 1693 × 8 = 13544
03Multiply 1710 by 2.
Answer: 1710 × 2 = 3420
04Multiply 1727 by 3.
Answer: 1727 × 3 = 5181
05Multiply 1234 by 2.
Answer: 1234 × 2 = 2468
06Multiply 1251 by 3.
Answer: 1251 × 3 = 3753
07Multiply 1268 by 4.
Answer: 1268 × 4 = 5072
08Multiply 1285 by 5.
Answer: 1285 × 5 = 6425
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 model multi-digit multiplication 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
Multiply 1302 by 6.
1302 × 6 = 7812
Multiply 1319 by 7.
1319 × 7 = 9233
Multiply 1336 by 8.
1336 × 8 = 10688
Multiply 1353 by 2.
1353 × 2 = 2706
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain model multi-digit multiplication problems accurately, then check each result with a second method.
Practice
Mastery check
01Multiply 1370 by 3.
Answer: 1370 × 3 = 4110
02Multiply 1387 by 4.
Answer: 1387 × 4 = 5548
03Multiply 1404 by 5.
Answer: 1404 × 5 = 7020
04Multiply 1421 by 6.
Answer: 1421 × 6 = 8526
05Multiply 1438 by 7.
Answer: 1438 × 7 = 10066
06Multiply 1455 by 8.
Answer: 1455 × 8 = 11640
07Multiply 1472 by 2.
Answer: 1472 × 2 = 2944
08Multiply 1489 by 3.
Answer: 1489 × 3 = 4467
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.