Visual Arrays

Overview

Students learn to visualize multiplication using two models: equal groups and arrays. They connect visual representations to multiplication equations and solve simple problems within 100 using drawings and equations.

Learning intentions

• Students will be able to describe what a multiplication expression means in a real-world context (equal groups).
• Students will be able to build and interpret arrays as rows and columns.
• Students will be able to write a multiplication equation that matches an array or equal-groups picture.
• Students will be able to check whether an equation matches the model by counting.

Success criteria

• I can explain what a multiplication expression tells me using groups or rows and columns.
• I can show a multiplication problem with objects, drawings, or an array.
• I can write an equation with a multiplication symbol and a total that matches my model.
• I can use counting to verify that my equation is correct.

Curriculum links

• Operations and Algebraic Thinking: interpret products of whole numbers as total objects in equal groups.
• Operations and Algebraic Thinking: use multiplication and division with drawings and equations to solve word problems with an unknown.
• Operations and Algebraic Thinking: apply properties of operations as strategies for multiplying and dividing using commutative “either order” reasoning when helpful.
• Operations and Algebraic Thinking: determine the unknown whole number in a multiplication/division equation in simple “? ×? = total” or “? /? =?” situations.

Lesson structure (60 minutes)

1. 0–7 min · Hook with a quick picture. Teacher displays two prompts: “5 groups of 4” and an array-like sketch with 5 rows and 4 dots per row, then asks how many dots there are and how they know. Student counts using fingers or quick tally marks and explains their thinking in one sentence to the teacher.

2. 7–18 min · Mini-direct teach: equal groups. Teacher models 5 groups of 4 using counters in separate piles; then labels “5 × 4” and points out that the product is the total number of objects. Student recreates the same model with counters, writes “5 × 4 = 20,” and practices saying: “There are 5 groups of 4, so there are 20 objects.”

3. 18–30 min · Mini-direct teach: arrays. Teacher draws an array on the board (rows and columns) and guides students to count rows, count columns, then count total dots. Student builds an array (for example, 3 rows and 6 columns), writes the matching equation “3 × 6 = 18,” and states what each factor means.

4. 30–40 min · Guided practice: match model to equation. Teacher shows three pictures (two arrays and one equal-groups picture) without equations; students choose the correct multiplication sentence and justify by pointing to rows/groups and items per row/group. Student completes each item on a worksheet or paper: circle the correct equation and write one justification sentence.

5. 40–52 min · Word problem application (within 100). Teacher reads a short equal-groups problem, such as: “Jada has 4 bags with 7 stickers in each bag. How many stickers does she have?” Then asks how to show it with a drawing and equation. Student draws equal groups or an array, writes an equation “4 × 7 =?,” counts to find the total, and explains what the answer means.

6. 52–57 min · Quick “unknown” check (as a closure skill). Teacher presents one equation with a missing whole number, such as “8 ×? = 24” and offers a hint to use known multiplication facts or counting by 8s. Student solves and writes the completed equation, explaining how the model supports the answer.

7. 57–60 min · Exit ticket. Teacher shows a small 2D picture (an array or equal groups) and asks for (1) the equation and (2) a one-sentence explanation of what the factors mean. Student completes it independently, then teacher reviews for accuracy.

Resources

• Counters or small unifix cubes
• Base-ten blocks (optional) or dot cards
• Whiteboard and dry-erase markers
• Array dot grid paper (5×6 or similar)
• Printed worksheet: “Match the model to the equation” (3 items)
• Word problem card(s)
• Exit ticket sheet
• Timer or visual countdown for pacing

Assessment

• Formative checks during modeling: teacher listens for correct descriptions of factors as groups/rows and items per group/row.
• Guided practice monitoring: confirm students can match each picture to the correct multiplication equation and justify with counting.
• Exit ticket: verify the equation matches the visual model and the written explanation connects factors to meaning.

Differentiation

• Support: provide sentence starters such as “I see __ groups of __,” “Each row has __,” and “So the total is __.”
• Support: allow students to use counters and draw simple circles/dots; reduce picture complexity (e.g., at first use arrays like 2×6, 3×4).
• Extension: if ready, ask students to compare two arrays with swapped factors (e.g., 2×5 vs 5×2) and discuss why the totals match while the layout changes.
• EAL/SEN: keep language consistent (“rows,” “columns,” “groups,” “each”), and accept oral explanations recorded by the teacher if handwriting is a barrier.