Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-002
Represent Multiplication with Arrays
Represent represent multiplication with arrays with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent represent multiplication with arrays with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving represent multiplication with arrays accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Represent Multiplication with Arrays
An array arranges objects in equal rows and columns, making both factors visible.
A reliable reasoning strategy
Read rows and columns as factors; rotating the array shows the commutative relationship.
Representations that should agree
Arrays connect multiplication to area and to skip-counting by row or column. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
Interactive math lab
Change it. See what stays true.
Array Builder
Build equal rows and columns, then connect the grid to repeated addition.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
3 rows with 5 in each row. How many cells?
3 × 5 = 15Multiply the number of equal groups by the number in each group.
4 rows with 8 in each row. How many cells?
4 × 8 = 32Multiply the number of equal groups by the number in each group.
5 rows with 3 in each row. How many cells?
5 × 3 = 15Multiply the number of equal groups by the number in each group.
6 rows with 6 in each row. How many cells?
6 × 6 = 36Multiply the number of equal groups by the number in each group.
7 rows with 9 in each row. How many cells?
7 × 9 = 63Multiply the number of equal groups by the number in each group.
8 rows with 4 in each row. How many cells?
8 × 4 = 32Multiply the number of equal groups by the number in each group.
9 rows with 7 in each row. How many cells?
9 × 7 = 63Multiply the number of equal groups by the number in each group.
2 rows with 2 in each row. How many cells?
2 × 2 = 4Multiply the number of equal groups by the number in each group.
3 rows with 5 in each row. How many cells?
3 × 5 = 15Multiply the number of equal groups by the number in each group.
4 rows with 8 in each row. How many cells?
4 × 8 = 32Multiply the number of equal groups by the number in each group.
5 rows with 3 in each row. How many cells?
5 × 3 = 15Multiply the number of equal groups by the number in each group.
6 rows with 6 in each row. How many cells?
6 × 6 = 36Multiply the number of equal groups by the number in each group.
7 rows with 9 in each row. How many cells?
7 × 9 = 63Multiply the number of equal groups by the number in each group.
8 rows with 4 in each row. How many cells?
8 × 4 = 32Multiply the number of equal groups by the number in each group.
9 rows with 7 in each row. How many cells?
9 × 7 = 63Multiply the number of equal groups by the number in each group.
2 rows with 2 in each row. How many cells?
2 × 2 = 4Multiply the number of equal groups by the number in each group.
3 rows with 5 in each row. How many cells?
3 × 5 = 15Multiply the number of equal groups by the number in each group.
4 rows with 8 in each row. How many cells?
4 × 8 = 32Multiply the number of equal groups by the number in each group.
5 rows with 3 in each row. How many cells?
5 × 3 = 15Multiply the number of equal groups by the number in each group.
6 rows with 6 in each row. How many cells?
6 × 6 = 36Multiply the number of equal groups by the number in each group.
Practice
Guided practice with hints
019 rows with 7 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 63
022 rows with 2 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 4
033 rows with 5 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 15
044 rows with 8 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 32
055 rows with 3 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 15
066 rows with 6 in each row. How many cells?
Hint: Read rows and columns as factors; rotating the array shows the commutative relationship.
Answer: 36
Practice
Independent practice
015 rows with 3 in each row. How many cells?
Answer: 15
026 rows with 6 in each row. How many cells?
Answer: 36
037 rows with 9 in each row. How many cells?
Answer: 63
048 rows with 4 in each row. How many cells?
Answer: 32
059 rows with 7 in each row. How many cells?
Answer: 63
062 rows with 2 in each row. How many cells?
Answer: 4
073 rows with 5 in each row. How many cells?
Answer: 15
084 rows with 8 in each row. How many cells?
Answer: 32
Common mistakes
Learn to catch the error, not just the answer.
Name the row count and column count before finding the product.
Reconnect the answer to represent multiplication with arrays and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Plan rectangular seating, tiles, or garden plots.
- Use represent multiplication with arrays to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
9 rows with 7 in each row. How many cells?
63
2 rows with 2 in each row. How many cells?
4
3 rows with 5 in each row. How many cells?
15
4 rows with 8 in each row. How many cells?
32
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Represent Multiplication with Arrays Challenge
Solve and explain Grade 3 problems involving represent multiplication with arrays without relying on answer guessing.
Practice
Mastery check
015 rows with 3 in each row. How many cells?
Answer: 15
026 rows with 6 in each row. How many cells?
Answer: 36
037 rows with 9 in each row. How many cells?
Answer: 63
048 rows with 4 in each row. How many cells?
Answer: 32
059 rows with 7 in each row. How many cells?
Answer: 63
062 rows with 2 in each row. How many cells?
Answer: 4
073 rows with 5 in each row. How many cells?
Answer: 15
084 rows with 8 in each row. How many cells?
Answer: 32
Terminology
Words to know
- array
- An arrangement in equal rows and columns.
- row
- A horizontal group in an array.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.1
Primary standards alignment for Represent Multiplication with Arrays.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.