Home›Lesson Plans›Mathematics›Operations & Algebraic Thinking · Grade 3

Understanding Multiplication: Rows, Groups & the Power of ×

Students discover that multiplication is a fast way to count equal groups — building arrays, connecting them to repeated addition, and uncovering why 3 × 4 and 4 × 3 give the same answer.

Grade 3Multiplication45 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Explain multiplication as combining equal groups.
  • ✓Model a multiplication fact as an array (rows × columns).
  • ✓Connect repeated addition to a multiplication equation.
  • ✓Use the commutative property: a × b = b × a.
Essential Question

Adding the same number over and over gets slow fast. What if there were a quicker way to count equal groups — every single time?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

The Array Builder

Project this and build arrays together. Change the rows and columns, watch the equation update, and use “Flip it” to discover why order doesn’t change the product.

➕ Build an array — change the rows and columnsTry it
Rows3
In each row4

The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — The Slow Way

5 min

Write 4 + 4 + 4 + 4 + 4 + 4 on the board. Isn’t there a faster way?

👩‍🏫 Teacher Moves

  • Write a long repeated-addition string (6 fours).
  • Ask students to find the total — and a faster way to write it.
  • Introduce today’s goal: a shortcut for equal groups.

🎒 Student Actions

  • Add the repeated string and feel how slow it is.
  • Suggest a quicker way to record it.
  • Predict what “multiplication” might mean.
2

I Do — Model the Array

10 min

Teacher builds one array and names every part.

👩‍🏫 Teacher Moves

  • Draw 3 rows of 4 dots; name rows, columns, product.
  • Write 3 × 4 = 12 beside the array.
  • Show 4 + 4 + 4 = 12 to connect repeated addition.

🎒 Student Actions

  • Watch and copy the array in their notebook.
  • Label rows, columns, and the product.
  • Say the fact aloud: “3 groups of 4 equals 12.”
3

We Do — Build It Together

12 min

Class drives the Array Builder and finds a pattern.

👩‍🏫 Teacher Moves

  • Use the Array Builder to make arrays as a class.
  • Have students write the equation for each.
  • Use “Flip it” to reveal the commutative property.

🎒 Student Actions

  • Call out rows and columns to build.
  • Write the matching equation each time.
  • Notice 3 × 4 = 4 × 3 when the array flips.
4

You Do — On Your Own

13 min

Students build and solve independently.

👩‍🏫 Teacher Moves

  • Assign arrays to draw and equations to write.
  • Give 2–3 equal-group word problems.
  • Circulate and check for the array–equation link.

🎒 Student Actions

  • Draw their own arrays and write the equations.
  • Solve word problems using equal groups.
  • Check a partner’s work.
5

Close — Show What You Know

5 min

Return to the slow way — now write it the fast way.

👩‍🏫 Teacher Moves

  • Revisit the opening repeated-addition string.
  • Have students rewrite it as multiplication.
  • Hand out the exit ticket below.

🎒 Student Actions

  • Rewrite the opener as a multiplication fact.
  • Explain why multiplication is faster.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
3.OA.A.1

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

CCSS
3.OA.A.3

Use multiplication within 100 to solve word problems involving equal groups and arrays.

CCSS
3.OA.B.5

Apply properties of operations as strategies to multiply (commutative and distributive properties).

SMP
MP.7

Look for and make use of structure — students use the array’s rows and columns to see multiplication.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Physical counters to build each array before drawing.
  • Sentence frame: “___ rows of ___ equals ___.”
  • Say the array aloud together before writing the equation.

Support & Access

IEP / 504
  • Start with familiar facts (×2, ×5) and small arrays.
  • Provide pre-drawn arrays to label and count.
  • Allow counters or skip-counting instead of recall.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Explore ×10 and ×11 patterns and predict the rule.
  • Break a hard fact apart (6 × 7 = 6 × 5 + 6 × 2).
  • Write and trade two equal-group word problems.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Array Builder
  • 🔵Counters / tiles
  • 📐Grid paper
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

multiplicationa fast way to add equal groupsfactora number being multipliedproductthe answer to a multiplicationarrayobjects in equal rows and columnsrowa line going acrosscolumna line going up and downequal groupsgroups with the same amountcommutativeorder doesn’t change the product
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Write the multiplication equation for 4 equal groups of 3.
4 × 3 = 12.
QUESTION 2
An array has 5 rows with 6 dots in each row. How many dots in all, and what equation shows it?
30 dots; 5 × 6 = 30.
QUESTION 3
How can knowing 3 × 8 help you find 8 × 3?
They are equal because of the commutative property — both equal 24. Flipping the array (turning rows into columns) doesn’t change the total.

Going deeper? Build an “Array City.”

Have students design buildings on grid paper where every window array shows a multiplication fact, then label each with its equation — a math-and-art project. A printable grid-paper template is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Understanding MultiplicationFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Understanding MultiplicationQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Understanding MultiplicationPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: array, column, commutative, equal groups, factor, multiplication, product, row
  1. objects in equal rows and columns
  2. a fast way to add equal groups
  3. a line going across
  4. a line going up and down
  5. order doesn’t change the product
  6. the answer to a multiplication
  7. a number being multiplied
  8. groups with the same amount

Part B · Show what you learned

  1. Write the multiplication equation for 4 equal groups of 3.
  2. An array has 5 rows with 6 dots in each row. How many dots in all, and what equation shows it?
  3. How can knowing 3 × 8 help you find 8 × 3?
Answer key — Part A: 1) array · 2) multiplication · 3) row · 4) column · 5) commutative · 6) product · 7) factor · 8) equal groups
Part B: 1) 4 × 3 = 12. 2) 30 dots; 5 × 6 = 30. 3) They are equal because of the commutative property — both equal 24. Flipping the array (turning rows into columns) doesn’t change the total.