Lesson Overview

This is a 60-minute Grade 3 mathematics lesson designed to introduce multiplication as a concept through array models. By the end of the lesson, students will understand multiplication as repeated addition arranged in rows and columns, and they will be able to use arrays to model and solve multiplication problems with factors up to 5.

This lesson aligns with the Grade 3 mathematics expectations found in most Canadian provincial curricula, including Ontario’s “represent and solve problems involving the multiplication of one-digit whole numbers” strand and similar expectations in British Columbia, Alberta, and the Atlantic provinces.

Learning Goal

Students will use arrays to model multiplication facts up to 5 by 5, and they will recognize the relationship between repeated addition and multiplication.

Success Criteria

By the end of this lesson, I can:

  • Build an array using counters or grid paper to represent a multiplication problem.
  • Write a multiplication sentence (like 3 x 4 = 12) and a matching repeated addition sentence (4 + 4 + 4 = 12) for the same array.
  • Explain why arranging objects in equal rows makes them easier to count.

Materials

  • Two-colour counters or unifix cubes (one set per pair of students). Free printable two-colour counters work if you do not have commercial sets.
  • 1 cm grid paper (1 sheet per student).
  • Pencils and erasers.
  • Chart paper or whiteboard for whole-class anchor chart.
  • Optional: pre-printed array task cards for centres rotation.

Open the lesson with a real-world problem. Show students an image of a baking sheet with cookies arranged in rows. Say: “I baked cookies for my family. There are 3 rows of cookies, and each row has 4 cookies. How many cookies did I make?”

Give students 2 minutes of think-pair-share time. Listen for the strategies they use. Some students will count by ones. Others will skip-count by 4s. A few might already say “12” because they recognize the pattern.

Bring the class back together and ask 2 or 3 pairs to share their thinking. Validate every strategy that arrived at 12. Then draw the cookie array on chart paper as a 3-by-4 grid of dots and circle the rows.

Tell students: “Mathematicians call this arrangement an array. Today we are going to learn how arrays help us multiply.”

Direct Instruction (15 minutes)

Build a vocabulary anchor chart together. Write and define:

  • Array: objects arranged in equal rows and equal columns.
  • Row: goes across, left to right.
  • Column: goes up and down.
  • Factor: a number being multiplied.
  • Product: the answer when you multiply.

Model building an array with counters under a document camera or by drawing on the board. Build a 2 by 5 array. Ask:

  1. “How many rows do you see?” (2)
  2. “How many counters are in each row?” (5)
  3. “How many counters total?” (10)

Write the matching sentences:

  • Repeated addition: 5 + 5 = 10
  • Multiplication: 2 x 5 = 10

Say: “We read this as ‘2 times 5 equals 10.’ The 2 tells us how many rows. The 5 tells us how many in each row. The 10 is our product.”

Repeat with one more example, a 3 by 3 array, before moving to guided practice.

Guided Practice (10 minutes)

Hand each pair a set of counters. Pose three problems for pairs to build together:

  1. “Build an array that shows 4 rows of 2.”
  2. “Build an array that shows 3 rows of 5.”
  3. “Build any array you choose, and write both the multiplication sentence and the addition sentence for it.”

Circulate. Listen for misconceptions, especially the confusion between rows and columns. Some students will count the total but struggle to identify “how many rows.” If you see this, ask them to point to one row and trace it with their finger.

Independent Practice (15 minutes)

Hand out grid paper. Students draw 4 different arrays on their grid paper and label each with both a multiplication sentence and a repeated addition sentence. They should use factors between 2 and 5.

For early finishers, extend with: “Can you find two different arrays that have the same product? Draw them both.”

Consolidation (10 minutes)

Bring the class back together. Choose 2 or 3 student examples to share under the document camera. Have the class read each array’s sentences chorally. Ask:

  • “Why is multiplying faster than adding when we have equal groups?”
  • “What did you notice about a 2 by 3 array compared to a 3 by 2 array?” (This sets up the commutative property for a future lesson.)

End with a quick exit ticket: “Draw an array that shows 3 x 4. Write the matching addition sentence and the product.” This takes 90 seconds and tells you who has the concept and who needs reinforcement tomorrow.

Differentiation

For students who need more support

Pair them with a strong partner. Use larger counters and a placemat with pre-drawn row guides. Limit the factors to 2 and 3 to start. Some students benefit from physically building the array on a 10-frame or muffin tin so the rows and columns are forced.

For students ready for extension

Introduce factors up to 9. Ask them to discover the commutative property on their own. Challenge them: “Find all the different arrays you can make for the product 12.” (1×12, 2×6, 3×4 and their commutative pairs.)

For multilingual learners

Provide the vocabulary anchor chart with a visual next to each term. Allow students to label arrays in their first language alongside English. The visual representation of an array reduces the language demand of the lesson significantly.

Assessment

The exit ticket gives you a fast snapshot. For a more formal check, collect the grid paper independent practice and assess against the success criteria. Students who consistently match the multiplication sentence to the array, and who can switch fluently between repeated addition and multiplication notation, have met the learning goal.

Follow-up Lessons

This lesson sets up the rest of the multiplication unit. Natural next steps:

  • Day 2: Commutative property (3 x 4 and 4 x 3 have the same product).
  • Day 3: Multiplication facts on a number line.
  • Day 4: Word problems that require translating between situations and multiplication sentences.
  • Day 5: Introducing factors up to 9 by 9 and building a class multiplication chart.

If you are looking for printable arrays, blank multiplication charts, and fact-practice templates, browse our Teaching Resources library. The Magic Square Generator in our tools collection makes a great Friday challenge once students are comfortable with basic multiplication facts. Canadian teachers swap classroom-tested differentiation strategies for Grade 3 math in our community forum.