Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-005
Multiply Multi-Digit Whole Numbers Fluently
Represent and solve multiply 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 multiply multi-digit whole numbers fluently problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for multiply 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
Multiply 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 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
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.
Partial-Products Area Model
Decompose both factors into tens and ones. Each rectangle is one partial product.
- Build one example of multiply 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.
Multiply 21 × 14.
21 × 14 = 294An area model or partial products separates tens and ones while preserving the complete product.
Multiply 22 × 17.
22 × 17 = 374An area model or partial products separates tens and ones while preserving the complete product.
Multiply 23 × 20.
23 × 20 = 460An area model or partial products separates tens and ones while preserving the complete product.
Multiply 24 × 23.
24 × 23 = 552An area model or partial products separates tens and ones while preserving the complete product.
Multiply 25 × 26.
25 × 26 = 650An area model or partial products separates tens and ones while preserving the complete product.
Multiply 26 × 29.
26 × 29 = 754An area model or partial products separates tens and ones while preserving the complete product.
Multiply 27 × 32.
27 × 32 = 864An area model or partial products separates tens and ones while preserving the complete product.
Multiply 28 × 35.
28 × 35 = 980An area model or partial products separates tens and ones while preserving the complete product.
Multiply 29 × 38.
29 × 38 = 1102An area model or partial products separates tens and ones while preserving the complete product.
Multiply 30 × 15.
30 × 15 = 450An area model or partial products separates tens and ones while preserving the complete product.
Multiply 31 × 18.
31 × 18 = 558An area model or partial products separates tens and ones while preserving the complete product.
Multiply 32 × 21.
32 × 21 = 672An area model or partial products separates tens and ones while preserving the complete product.
Multiply 33 × 24.
33 × 24 = 792An area model or partial products separates tens and ones while preserving the complete product.
Multiply 34 × 27.
34 × 27 = 918An area model or partial products separates tens and ones while preserving the complete product.
Multiply 35 × 30.
35 × 30 = 1050An area model or partial products separates tens and ones while preserving the complete product.
Multiply 36 × 33.
36 × 33 = 1188An area model or partial products separates tens and ones while preserving the complete product.
Multiply 37 × 36.
37 × 36 = 1332An area model or partial products separates tens and ones while preserving the complete product.
Multiply 38 × 39.
38 × 39 = 1482An area model or partial products separates tens and ones while preserving the complete product.
Multiply 39 × 16.
39 × 16 = 624An area model or partial products separates tens and ones while preserving the complete product.
Multiply 40 × 19.
40 × 19 = 760An area model or partial products separates tens and ones while preserving the complete product.
Practice
Guided practice with hints
01Multiply 41 × 22.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 41 × 22 = 902
02Multiply 42 × 25.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 42 × 25 = 1050
03Multiply 43 × 28.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 43 × 28 = 1204
04Multiply 44 × 31.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 44 × 31 = 1364
05Multiply 45 × 34.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 45 × 34 = 1530
06Multiply 46 × 37.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 46 × 37 = 1702
Practice
Independent practice
01Multiply 47 × 14.
Answer: 47 × 14 = 658
02Multiply 48 × 17.
Answer: 48 × 17 = 816
03Multiply 49 × 20.
Answer: 49 × 20 = 980
04Multiply 21 × 23.
Answer: 21 × 23 = 483
05Multiply 21 × 14.
Answer: 21 × 14 = 294
06Multiply 22 × 17.
Answer: 22 × 17 = 374
07Multiply 23 × 20.
Answer: 23 × 20 = 460
08Multiply 24 × 23.
Answer: 24 × 23 = 552
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 multiply 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
Multiply 25 × 26.
25 × 26 = 650
Multiply 26 × 29.
26 × 29 = 754
Multiply 27 × 32.
27 × 32 = 864
Multiply 28 × 35.
28 × 35 = 980
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain multiply multi-digit whole numbers fluently problems accurately, then check each result with a second method.
Practice
Mastery check
01Multiply 29 × 38.
Answer: 29 × 38 = 1102
02Multiply 30 × 15.
Answer: 30 × 15 = 450
03Multiply 31 × 18.
Answer: 31 × 18 = 558
04Multiply 32 × 21.
Answer: 32 × 21 = 672
05Multiply 33 × 24.
Answer: 33 × 24 = 792
06Multiply 34 × 27.
Answer: 34 × 27 = 918
07Multiply 35 × 30.
Answer: 35 × 30 = 1050
08Multiply 36 × 33.
Answer: 36 × 33 = 1188
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.