Arrays to Expressions

Overview

In this lesson, students connect arrays and equal groups to numerical multiplication expressions. They use correct vocabulary such as factors and products, and then create their own multiplication problems from pictured arrays.

Learning intentions

• Students will represent equal groups and arrays using multiplication expressions.
• Students will connect rows and columns (or group size and number of groups) to factors.
• Students will describe the meaning of a multiplication expression as a product.
• Students will create multiplication problems based on arrays and explain how they know the answer.

Success criteria

• I can count an array to write a multiplication expression that matches it.
• I can name the factors and the product in a multiplication expression.
• I can create my own multiplication problem from an array and explain my reasoning.
• I can check if my expression and product fit the array or equal groups.

Curriculum links

• Developing understanding of multiplication as equal groups and arrays
• Writing multiplication expressions and interpreting them as products
• Using multiplication facts and reasoning to solve problems with models
• Communication of mathematical thinking using words, numbers, and representations

Lesson structure (60 minutes)

1. 0–5 min: Engage with arrays

• Display two quick pictures: one array (e.g., 3 rows of 4) and one set of equal groups (e.g., 4 groups of 3).
• Ask: “How can we count these efficiently? What numbers describe how they are arranged?”

2. 5–12 min: Model from groups to numbers

• Use the array to guide students: “There are 3 rows and 4 in each row, so the number is 3 × 4.”
• Name vocabulary: “The factors tell how many rows and how many in each row. The product is the total.”
• Repeat with the equal groups model: “4 groups of 3 means 4 × 3.”

3. 12–22 min: Guided practice—match, write, explain

• Provide 4–6 class sets of cards or images (teacher prepared). Each set includes an array/equal groups picture and blank space for an expression.
• Students work with a partner to:
• Write the multiplication expression.
• Circle which numbers are the factors.
• Write the product (the total).
• Teacher checks for accurate expression and clear meaning (not just the answer).

4. 22–30 min: Whole-class discussion—common misconceptions

• Prompt students with two contrasting examples:
• A correct match: 3 rows × 4 columns → 3 × 4 = 12.
• An incorrect match (e.g., swapped placement with no explanation): ask students to critique using the model.
• Clarify that factors come from the structure of the array/equal groups, and the product is the total objects.

5. 30–45 min: Create your own problems (student production)

• Give each student a small worksheet or grid sheet:
• Part A: Draw an array with 2–6 rows and 2–6 objects per row (keep totals manageable).
• Part B: Write the matching multiplication expression.
• Part C: Label factors and product in words (e.g., “factors are ___ and ___, product is ___”).
• Encourage students to choose different arrangements (some should represent equal groups in another way).

6. 45–53 min: Gallery walk—peer check

• Students swap with a partner or rotate to view 3 classmates’ drawings.
• For each one, students write:
• The expression they think matches the array.
• Whether the proposed product fits the picture, and one sentence of evidence (e.g., “I counted 5 rows of 2, so there are 10 total.”).
• Teacher circulates, listening for correct factor/product language.

7. 53–60 min: Exit ticket—show the connection

• Exit ticket includes one array picture with blanks:
• Write one multiplication expression.
• State the factors and the product.
• Collect and sort quickly into: “meets,” “almost,” “needs support.”

Resources

• Array and equal-groups image cards (paper or projector)
• Student grid paper or dot paper for drawing arrays
• Worksheet for student problem creation (array → expression → factors/product)
• Pencil, eraser, coloured pencils for circling factors
• Exit ticket slips with one array per student
• Teacher markers and a visible board display
• Optional: counters or base-ten blocks for quick verification

Assessment

• Formative during guided practice: listen for correct expressions and factor/product explanations.
• Gallery walk feedback: check for accurate matching between pictures and expressions.
• Exit ticket: determine whether students can interpret arrays as multiplication and identify factors and product correctly.

Differentiation

• Support:
• Provide sentence frames: “There are __ rows of __, so __ × __ = __.”
• Offer a partially completed example on the worksheet (one array already drawn, students fill expression).
• Use counters or base-ten blocks for students who need concrete verification.
• Extension:
• Challenge students to create two different arrays that have the same product (e.g., 2×6 and 3×4) and explain the factors.
• EAL/SEN:
• Keep vocabulary consistent with word banks: factors, product, rows, columns, groups, total.
• Allow oral explanation or drawing-first for students who struggle with writing the expression.
• Provide simplified arrays with fewer rows/columns while still requiring correct factor/product labeling.