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Arrays

Third graders discover that arranging objects into neat rows and columns makes counting faster, and that an array is really a picture of multiplication, connecting rows, repeated addition, and the times sign.

Grade 3Arrays50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Know what an array is.
  • ✓Read rows and columns.
  • ✓Link an array to multiplication.
  • ✓See the order does not matter.
Essential Question

A box of muffins sits in 3 rows of 4. You could count one by one, or multiply. How does arranging things in equal rows turn counting into multiplication?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Explore Arrays · Interactive

Explore Arrays

Project this and open each card to explore arrays and how they connect to multiplication.

📦 Explore how arrays show multiplicationTry it

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

50 minutes, five moves

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

1

Hook — Neat Rows

5 min

A box of muffins sits in 3 rows of 4. You could count them one by one, or you could multiply. How does arranging things in equal rows make counting faster?

👩‍🏫 Teacher Moves

  • Show a muffin tin array.
  • Ask for a fast count.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Explore Arrays

12 min

Students explore what arrays are.

👩‍🏫 Teacher Moves

  • Send students to Explore Arrays.
  • Open each card.
  • Note the ideas.

🎒 Student Actions

  • Explore.
  • Read.
  • Note it.
3

Modify — Build an Array

13 min

Students make an array for a fact.

👩‍🏫 Teacher Moves

  • Pick a multiplication fact.
  • Build it as rows and columns.
  • Say the total.

🎒 Student Actions

  • Pick.
  • Build.
  • Say.
4

Create — My Array Poster

15 min

Students draw an array.

👩‍🏫 Teacher Moves

  • Draw an array of dots.
  • Write its repeated addition.
  • Write its times sentence.

🎒 Student Actions

  • Draw.
  • Write.
  • Write.
5

Reflect — Rows, Columns, Products

5 min

Students reflect on arrays.

👩‍🏫 Teacher Moves

  • How do you find the total in an array?
  • Why does 3 x 4 equal 4 x 3?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
2.OA.C.4

Use addition to find the total number of objects arranged in rectangular arrays.

CCSS
3.OA.A.1

Interpret products of whole numbers, such as 5 x 7 as the total in 5 rows of 7.

CCSS
3.OA.A.3

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

CCSS
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Array picture cards.
  • Sentence frame: “___ rows of ___ is ___ .”
  • Explore one card at a time.

Support & Access

IEP / 504
  • Start with a 2-by-3 array.
  • Build one array with tiles.
  • Explore one idea before the next.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Turn arrays to show the commutative property.
  • Split an array to show the distributive property.
  • Explain why an array equals repeated addition.
Materials

What to gather

  • 📽️Projector / board
  • 🃏Square tiles or counters
  • 💻Explore Arrays
  • 🥚An egg carton or muffin tin
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

arrayobjects arranged in equal rows and columnsrowa line of objects going acrosscolumna line of objects going up and downrepeated additionadding the same number over and overfactora number being multipliedproductthe total when you multiplycommutativethe order of factors does not change the productequal groupsgroups that each have the same amount
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
How do you find the total number of objects in an array?
Multiply the number of rows by the number in each row (or add the equal rows), such as 3 rows of 4 = 12.
QUESTION 2
Why does 3 x 4 equal 4 x 3?
Turning the array a quarter turn changes 3 rows of 4 into 4 rows of 3, and both still have 12 objects.
QUESTION 3
Write the array of 2 rows of 5 as a times sentence.
2 x 5 = 10.

Create: my array poster.

Have students draw an array of dots, write its repeated addition, and write its times sentence, so the array connects adding and multiplying. A printable arrays worksheet is in the Mathematics 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.

🃏 ArraysFlip
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Term
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Meaning
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Practice · Quiz

Check your understanding

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

📝 ArraysQuiz
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Question 1
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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.

🖨️ ArraysPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: array, column, commutative, equal groups, factor, product, repeated addition, row
  1. adding the same number over and over
  2. a number being multiplied
  3. the order of factors does not change the product
  4. groups that each have the same amount
  5. a line of objects going up and down
  6. the total when you multiply
  7. objects arranged in equal rows and columns
  8. a line of objects going across

Part B · Show what you learned

  1. How do you find the total number of objects in an array?
  2. Why does 3 x 4 equal 4 x 3?
  3. Write the array of 2 rows of 5 as a times sentence.
Answer key — Part A: 1) repeated addition · 2) factor · 3) commutative · 4) equal groups · 5) column · 6) product · 7) array · 8) row
Part B: 1) Multiply the number of rows by the number in each row (or add the equal rows), such as 3 rows of 4 = 12. 2) Turning the array a quarter turn changes 3 rows of 4 into 4 rows of 3, and both still have 12 objects. 3) 2 x 5 = 10.