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.
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.
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.
An array has 2 rows and 4 items in each row. How many items are in the array?
2 × 4 = 8Equal rows make multiplication visible: 2 rows of 4 contain 8 items.
An array has 3 rows and 5 items in each row. How many items are in the array?
3 × 5 = 15Equal rows make multiplication visible: 3 rows of 5 contain 15 items.
An array has 4 rows and 6 items in each row. How many items are in the array?
4 × 6 = 24Equal rows make multiplication visible: 4 rows of 6 contain 24 items.
An array has 5 rows and 7 items in each row. How many items are in the array?
5 × 7 = 35Equal rows make multiplication visible: 5 rows of 7 contain 35 items.
An array has 6 rows and 3 items in each row. How many items are in the array?
6 × 3 = 18Equal rows make multiplication visible: 6 rows of 3 contain 18 items.
An array has 7 rows and 4 items in each row. How many items are in the array?
7 × 4 = 28Equal rows make multiplication visible: 7 rows of 4 contain 28 items.
An array has 8 rows and 2 items in each row. How many items are in the array?
8 × 2 = 16Equal rows make multiplication visible: 8 rows of 2 contain 16 items.
An array has 9 rows and 3 items in each row. How many items are in the array?
9 × 3 = 27Equal rows make multiplication visible: 9 rows of 3 contain 27 items.
An array has 10 rows and 5 items in each row. How many items are in the array?
10 × 5 = 50Equal rows make multiplication visible: 10 rows of 5 contain 50 items.
An array has 3 rows and 8 items in each row. How many items are in the array?
3 × 8 = 24Equal rows make multiplication visible: 3 rows of 8 contain 24 items.
An array has 4 rows and 9 items in each row. How many items are in the array?
4 × 9 = 36Equal rows make multiplication visible: 4 rows of 9 contain 36 items.
An array has 5 rows and 6 items in each row. How many items are in the array?
5 × 6 = 30Equal rows make multiplication visible: 5 rows of 6 contain 30 items.
An array has 6 rows and 7 items in each row. How many items are in the array?
6 × 7 = 42Equal rows make multiplication visible: 6 rows of 7 contain 42 items.
An array has 7 rows and 5 items in each row. How many items are in the array?
7 × 5 = 35Equal rows make multiplication visible: 7 rows of 5 contain 35 items.
An array has 8 rows and 4 items in each row. How many items are in the array?
8 × 4 = 32Equal rows make multiplication visible: 8 rows of 4 contain 32 items.
An array has 9 rows and 2 items in each row. How many items are in the array?
9 × 2 = 18Equal rows make multiplication visible: 9 rows of 2 contain 18 items.
An array has 2 rows and 9 items in each row. How many items are in the array?
2 × 9 = 18Equal rows make multiplication visible: 2 rows of 9 contain 18 items.
An array has 10 rows and 3 items in each row. How many items are in the array?
10 × 3 = 30Equal rows make multiplication visible: 10 rows of 3 contain 30 items.
An array has 4 rows and 8 items in each row. How many items are in the array?
4 × 8 = 32Equal rows make multiplication visible: 4 rows of 8 contain 32 items.
An array has 5 rows and 9 items in each row. How many items are in the array?
5 × 9 = 45Equal rows make multiplication visible: 5 rows of 9 contain 45 items.
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.