Using Arrays for Division

Learning Objectives

By the end of this 15-minute session, Year 2 students will:

• Understand what an array is and how it can visually represent division.
• Use arrays to divide numbers up to 100, showing equal groups.
• Explain division as sharing equally or grouping using correct mathematical language.
• Connect division with multiplication facts they know for fluency.

This lesson aligns with the New Zealand Curriculum Refresh Level 2 Mathematics and Statistics, particularly the Number and Algebra strand:

• Achievement Objective: Use multiplication and division with whole numbers, represented as arrays, and understand division as sharing or grouping.
• Key Competencies: Thinking (problem-solving with arrays), Using Language, Symbols and Texts (mathematical vocabulary of division and arrays), Relating to Others (working collaboratively).

Materials Needed

• Counters or small objects (e.g., counters, blocks) – at least 100 per group.
• Printed grid paper or whiteboards for drawing arrays.
• Large visual example of an array on a whiteboard or chart.
• Pre-prepared division problem cards with dividends up to 100.

Lesson Outline (15 minutes total)

1. Introduction to Arrays and Division (3 minutes)

• Gather students and explain: "Today we will learn how to divide numbers by making equal groups with something called an array."
• Show a simple array on the board: for example, 12 counters arranged in 3 rows and 4 columns.
• Ask: "How many counters are in each row?" and "If we share 12 counters into 3 equal groups (rows), how many are in each group?"
• Introduce vocabulary: rows, columns, groups, divide, dividend (total), divisor (number of groups), quotient (how many in each group).
• Relate this to sharing equally or grouping.

2. Demonstration with a Hands-on Example (4 minutes)

• Use counters to create an array for 20 ÷ 5.
• Arrange 20 counters in 5 rows, showing 4 in each row.
• Ask students: "How many counters are in each group? What is 20 divided by 5?"
• Demonstrate drawing the array on grid paper or whiteboard.
• Highlight how each row is an equal group and the total counters represent the dividend.

3. Student Activity: Creating and Using Arrays (6 minutes)

• Distribute counters and grid paper/whiteboards to small groups or individuals.
• Provide division problem cards, e.g., 24 ÷ 6, 30 ÷ 5, 50 ÷ 10, all up to 100 total counters.
• Students create arrays by arranging counters into equal rows and columns matching the divisor.
• They write the division equation to match their array.
• Circulate, support, and prompt students to use the correct language and check their arrays.

4. Reflection and Assessment (2 minutes)

• Invite several students/groups to show their arrays and explain how they solved their division problem.
• Ask reflective questions: "How did your array help you divide?" and "What did you notice about the rows and columns?"
• Provide quick feedback affirming correct understanding or gently correcting misconceptions.
• For an informal assessment, have students complete a quick exit slip: They draw a small array for 12 ÷ 3 and write the division sentence.

Teaching Considerations

• Focus on concrete materials and visual representations as Year 2 students learn best with hands-on activities.
• Use clear, simple language consistent with the NZ Curriculum's emphasis on mathematical vocabulary: dividend, divisor, quotient, rows, columns.
• Encourage explaining reasoning aloud to deepen understanding.
• Manage time carefully given the young age to maintain engagement.
• This learning builds foundations for multiplication and division fluency expected by the end of Year 3.

Example Division Problems (Dividends up to 100)

• 24 ÷ 6
• 36 ÷ 4
• 50 ÷ 5
• 40 ÷ 10
• 60 ÷ 3
• 90 ÷ 9

This lesson supports the NZ Curriculum refresh by integrating physical, visual, and symbolic representations for division and uses arrays as a key strategy for understanding the operation conceptually and fluently.