Array Multiplication

Overview

In this lesson, students explore arrays as a way to model multiplication. They create and interpret arrays using grid paper and manipulatives, then connect the rows and columns to multiplication expressions.

Learning intentions

• Students will represent multiplication as an array using rows and columns.
• Students will count the total objects in an array by using repeated groups (row by row or column by column).
• Students will describe how the dimensions (rows × columns) relate to the product.
• Students will create arrays for given multiplication facts with materials or drawings.

Success criteria

• I can draw an array that shows equal rows and equal columns.
• I can count the total objects in an array efficiently (not one-by-one).
• I can write a multiplication statement that matches my array.
• I can explain what the numbers of rows and columns mean.

Curriculum links

• Multiplication and division representations using arrays and equal groups.
• Developing strategies for understanding and applying multiplication facts through models.
• Using mathematical language to describe patterns and relationships (rows, columns, product).
• Reasoning and communicating mathematically using representations to justify answers.

Lesson structure (60 minutes)

1. 5 min – Warm-up: equal groups check Show 2–3 pictures of groups (for example, 3 groups of 4 dots, or 4 groups of 3 dots). Students turn and talk: “What multiplication could this be?” Briefly review that multiplication can represent repeated groups, and that arrays will help us see it more clearly.

2. 10 min – Teach: arrays as multiplication models Draw a 3×4 array on the board using squares (three rows and four columns). Ask:

• “How many rows?” “How many columns?”
• “If we count by rows, how many altogether?” Emphasize: the number of rows is the first factor and the number of columns is the second factor. The total is the product.

3. 5 min – Guided example with think-aloud Create a second array (e.g., 2×5). Model counting efficiently: “Two rows of five equals ten.” Write the matching multiplication sentence (as a teacher model) and underline both dimensions.

4. 25 min – Pair practice: build and record arrays Students work in pairs with base-ten blocks, counters, or array cards plus grid paper. Each pair selects or is assigned 4 multiplication facts (within 2×2 up to 5×10 depending on class readiness). For each fact, they:

• Build the array with equal rows and columns.
• Draw it on grid paper.
• Record the multiplication statement and the product. Teacher circulates, prompting with questions such as:
• “How do you know it has equal rows?”
• “Would it look different if you swapped rows and columns?”
• “What would the multiplication statement be?”

5. 10 min – Share-out: comparing arrays Invite 3–4 pairs to display different arrays. Class asks:

• “What are the dimensions?”
• “What product do you get?”
• “Is there more than one array that shows the same product?” (e.g., 3×4 vs 4×3) Reinforce that the product stays the same even if the arrangement flips.

6. 5 min – Quick check: individual exit problem Students complete one task independently: draw an array for a given multiplication fact (teacher provides one on the board, such as 4×6). Then write the multiplication sentence and product. Collect work for assessment.

7. 0 min – Transition / reset Gather materials and preview the next lesson connection: using arrays to support division facts later in the unit.

Resources

• Grid paper (blank and/or with pre-made dot or square grids)
• Counters, base-ten blocks, or physical tiles for building arrays
• Array cards showing multiplication facts (teacher-prepared)
• Board/markers and a visual display of an example array
• Mini whiteboards or scrap paper for quick check writing
• Student recording sheets: “Rows: __, Columns: __, Sentence: __, Product: __”
• Pair roles prompt cards (Builder, Recorder) to reduce off-task behaviour
• Timer for pair work

Assessment

• Observe pairs during practice: correct use of rows/columns and correct matching of multiplication sentences to arrays.
• Review the exit check: ability to draw an array with equal rows/columns and write the correct multiplication statement and product.
• Listen during share-out for mathematical communication: students explain how dimensions connect to total objects.

Differentiation

• Support: Provide starter arrays (partially drawn) and word stems: “I see __ rows of __.” Offer a smaller fact range (e.g., 2s, 3s, 4s) and more concrete manipulatives.
• Support: Allow counting by visible groups (row-by-row) with teacher coaching rather than requiring fast mental counting.
• Extension: Give facts like 6×3, 7×2, or compare arrays that share the same product; ask students to write two different multiplication statements that show the same total.
• EAL/SEN: Use sentence frames and emphasize consistent vocabulary (rows, columns, total, product). Provide visual examples and reduce language load by using diagrams heavily. Offer extra time and allow oral explanation alongside written work.