Grade 4 · Operations & Algebraic Thinking · MAT-04-OA-006
Generate and Use Multiples
Represent and solve generate and use multiples problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve generate and use multiples problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for generate and use multiples 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
Generate and Use Multiples describes multiplicative structure inside whole numbers. Factor relationships explain exact products and divisibility, while multiples extend repeated equal groups.
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 generate and use multiples 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.
What is the 4th positive multiple of 2?
2 × 4 = 8Positive multiples of 2 are formed by multiplying 2 by 1, 2, 3, and so on.
What is the 5th positive multiple of 3?
3 × 5 = 15Positive multiples of 3 are formed by multiplying 3 by 1, 2, 3, and so on.
What is the 6th positive multiple of 4?
4 × 6 = 24Positive multiples of 4 are formed by multiplying 4 by 1, 2, 3, and so on.
What is the 7th positive multiple of 5?
5 × 7 = 35Positive multiples of 5 are formed by multiplying 5 by 1, 2, 3, and so on.
What is the 8th positive multiple of 6?
6 × 8 = 48Positive multiples of 6 are formed by multiplying 6 by 1, 2, 3, and so on.
What is the 9th positive multiple of 7?
7 × 9 = 63Positive multiples of 7 are formed by multiplying 7 by 1, 2, 3, and so on.
What is the 10th positive multiple of 8?
8 × 10 = 80Positive multiples of 8 are formed by multiplying 8 by 1, 2, 3, and so on.
What is the 11th positive multiple of 9?
9 × 11 = 99Positive multiples of 9 are formed by multiplying 9 by 1, 2, 3, and so on.
What is the 4th positive multiple of 10?
10 × 4 = 40Positive multiples of 10 are formed by multiplying 10 by 1, 2, 3, and so on.
What is the 5th positive multiple of 11?
11 × 5 = 55Positive multiples of 11 are formed by multiplying 11 by 1, 2, 3, and so on.
What is the 6th positive multiple of 12?
12 × 6 = 72Positive multiples of 12 are formed by multiplying 12 by 1, 2, 3, and so on.
What is the 7th positive multiple of 2?
2 × 7 = 14Positive multiples of 2 are formed by multiplying 2 by 1, 2, 3, and so on.
What is the 8th positive multiple of 3?
3 × 8 = 24Positive multiples of 3 are formed by multiplying 3 by 1, 2, 3, and so on.
What is the 9th positive multiple of 4?
4 × 9 = 36Positive multiples of 4 are formed by multiplying 4 by 1, 2, 3, and so on.
What is the 10th positive multiple of 5?
5 × 10 = 50Positive multiples of 5 are formed by multiplying 5 by 1, 2, 3, and so on.
What is the 11th positive multiple of 6?
6 × 11 = 66Positive multiples of 6 are formed by multiplying 6 by 1, 2, 3, and so on.
What is the 4th positive multiple of 7?
7 × 4 = 28Positive multiples of 7 are formed by multiplying 7 by 1, 2, 3, and so on.
What is the 5th positive multiple of 8?
8 × 5 = 40Positive multiples of 8 are formed by multiplying 8 by 1, 2, 3, and so on.
What is the 6th positive multiple of 9?
9 × 6 = 54Positive multiples of 9 are formed by multiplying 9 by 1, 2, 3, and so on.
What is the 7th positive multiple of 10?
10 × 7 = 70Positive multiples of 10 are formed by multiplying 10 by 1, 2, 3, and so on.
Practice
Guided practice with hints
01What is the 8th positive multiple of 11?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 11 × 8 = 88
02What is the 9th positive multiple of 12?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 12 × 9 = 108
03What is the 10th positive multiple of 2?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2 × 10 = 20
04What is the 11th positive multiple of 3?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3 × 11 = 33
05What is the 4th positive multiple of 4?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4 × 4 = 16
06What is the 5th positive multiple of 5?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5 × 5 = 25
Practice
Independent practice
01What is the 6th positive multiple of 6?
Answer: 6 × 6 = 36
02What is the 7th positive multiple of 7?
Answer: 7 × 7 = 49
03What is the 8th positive multiple of 8?
Answer: 8 × 8 = 64
04What is the 9th positive multiple of 9?
Answer: 9 × 9 = 81
05What is the 4th positive multiple of 2?
Answer: 2 × 4 = 8
06What is the 5th positive multiple of 3?
Answer: 3 × 5 = 15
07What is the 6th positive multiple of 4?
Answer: 4 × 6 = 24
08What is the 7th positive multiple of 5?
Answer: 5 × 7 = 35
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 generate and use multiples 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
What is the 8th positive multiple of 6?
6 × 8 = 48
What is the 9th positive multiple of 7?
7 × 9 = 63
What is the 10th positive multiple of 8?
8 × 10 = 80
What is the 11th positive multiple of 9?
9 × 11 = 99
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain generate and use multiples problems accurately, then check each result with a second method.
Practice
Mastery check
01What is the 4th positive multiple of 10?
Answer: 10 × 4 = 40
02What is the 5th positive multiple of 11?
Answer: 11 × 5 = 55
03What is the 6th positive multiple of 12?
Answer: 12 × 6 = 72
04What is the 7th positive multiple of 2?
Answer: 2 × 7 = 14
05What is the 8th positive multiple of 3?
Answer: 3 × 8 = 24
06What is the 9th positive multiple of 4?
Answer: 4 × 9 = 36
07What is the 10th positive multiple of 5?
Answer: 5 × 10 = 50
08What is the 11th positive multiple of 6?
Answer: 6 × 11 = 66
Terminology
Words to know
- factor
- A whole number that divides another whole number without a remainder.
- multiple
- A product of a number and a whole number.
- prime
- A whole number greater than 1 with exactly two positive factors.
- composite
- A whole number greater than 1 with more than two positive factors.
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.