Array Division

Overview

In this lesson, students use multiplication arrays as a foundation for understanding division. They will model, represent, and solve division problems using repeated groups, then create their own division statements that match arrays.

Learning intentions

• Students will understand division as sharing into equal groups (using arrays to show groups and rows).
• Students will link multiplication facts to related division facts using the same array.
• Students will represent division with arrays, equations, and explanations.
• Students will check answers by matching the array to the equation.

Success criteria

• I can draw an array that matches a division problem and explain how it shows equal groups.
• I can write a division equation from an array and identify the divisor, quotient, and dividend.
• I can connect a multiplication fact to two related division facts using the same model.
• I can use the array to check whether my division answer is reasonable.

Curriculum links

• Develop understanding of multiplication and division, including the relationship between them.
• Use models and strategies to solve problems involving whole numbers.
• Represent and describe mathematical ideas using diagrams, words, and equations.

Lesson structure (60 minutes)

1. 0–5 min: Warm-up (retrieve multiplication links) Display 3 arrays (for example: 2×4, 3×5, 6×3). Students write one multiplication equation for each, then share one related division they think could fit.

2. 5–12 min: Mini-lesson—arrays for division Teach how an array can represent division by grouping:

• Rows or columns show equal groups.
• The number of rows is the “groups” (or the divisor), and the number in each row/column is the “size of each group.” Use one example together (e.g., an array with 3 rows and 4 columns). Show how it relates to 12 ÷ 3 = 4 and 12 ÷ 4 = 3, and how both are true because they use the same array from different directions.

3. 12–20 min: Guided practice—“What does this division mean?” Provide printed or board arrays with missing labels (no equations yet). In pairs, students decide:

• Which number is being divided (the total items).
• What the groups are (rows or columns).
• What the quotient represents (items per group). Students write one division equation and a short explanation.

4. 20–28 min: Whole-class problem solving (teacher models and students respond) Choose one class array, then ask: “If there are 18 dots and 3 equal groups, what does each group look like?” Students show the array direction using fingers or draw on mini-whiteboards. Confirm and record: 18 ÷ 3 = 6. Then rotate the array: “Same dots—how many groups if each group has 3 dots?” Record 18 ÷ 6 = 3.

5. 28–42 min: Hands-on activity—create and solve with arrays Students work in groups of 3 with dot cards, grid paper, or manipulatives. Give each group a set of division prompts such as:

• “Draw an array for 24 ÷ 6.”
• “Make an array that matches 15 ÷ 3.”
• “Create one array, then write two related division equations.” Requirements:
• Draw the array clearly (show rows and columns).
• Write the division equation(s).
• Add one multiplication equation that matches the array.

6. 42–52 min: Gallery walk—explain and check Groups post one best array. Other students use a “Does it match?” routine:

• Point to total dots (dividend).
• Point to the groups (divisor).
• Point to the number in each group (quotient). Students write one sentence feedback (for example: “Your groups are rows, so 20 ÷ 5 matches your array.”).

7. 52–60 min: Exit ticket—independent practice Students complete two tasks:

• Draw an array for a given division (e.g., 16 ÷ 4) and write the equation.
• From a given multiplication array (e.g., 3×6), write two related division equations. Collect for quick review.

Resources

• Dot cards, counters, and/or base-ten blocks
• Grid paper and pencils
• Mini-whiteboards and markers (or scrap paper) for quick responses
• Array prompt cards (division and multiplication)
• Teacher-made array visuals for the warm-up and mini-lesson
• Student sentence stems for explanations (e.g., “Each group has…”, “There are… groups.”)
• Timer for activity segments
• Exit ticket slips

Assessment

• Observe student thinking during guided practice and group work, focusing on whether they correctly interpret rows/columns as equal groups.
• Check written equations: students should correctly connect the array to division and to a related multiplication fact.
• Review exit tickets for accurate divisor/quotient identification and correct division statements.

Differentiation

• Support: Provide partially completed arrays (some rows/columns labeled) and an example bank of multiplication/division pairs to use during the hands-on activity.
• Support: Offer sentence stems and a “checklist” (total dots, number of groups, number per group) at the desk.
• Extension: Ask students to create an array for a division prompt, then generate all valid related division equations by rotating or switching how rows/columns are interpreted.
• EAL/SEN: Allow verbal explanations and diagram-only responses first; confirm meaning through one-on-one or small-group conferencing before requiring full written sentences.