Arrays and Problem-Solving

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Subject: Mathematics

Semester: 1

Period: 2

Week: 11

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School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 11
Lesson Duration: 45 minutes
Week & Period: Week 11, Period 2
Topic: Arrays and Problem-Solving
Sub-topic: Applying Arrays in Multiplication and Division

Learning Objectives
By the end of the lesson, students should be able to:

1. Define arrays and show how they represent multiplication and division.
2. Use arrays to show square numbers and factors.
3. Solve word problems using arrays.

Previous Knowledge
Students already know multiplication and division facts.

Instructional Materials
Square paper, counters, chart of arrays

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher draws a 3 × 4 array and asks: How many dots are there?

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

✅ Definition:

An array is a systematic arrangement of objects, symbols, or numbers in rows and columns. Arrays help us visualize and understand multiplication, division, and square numbers by showing the repeated grouping of quantities.

• Rows: Horizontal lines of objects
• Columns: Vertical lines of objects

 

🔢 Key Concept:

• Multiplication using arrays:
  Multiplication can be seen as repeated addition. An array helps represent this visually.
  For example:
  3 × 4 = 12 means 3 rows of 4 objects each.
  ✅ It can also mean 4 rows of 3 – both give the same result but show commutative property.
• Division using arrays:
  Arrays help divide objects evenly into rows or columns.
  For example:
  If 24 apples are placed in 6 rows, we can ask: How many in each row?
  → 24 ÷ 6 = 4
• Square numbers using arrays:
  Square numbers are perfect arrays with the same number of rows and columns.
  Example:
  5² = 25 → 5 rows and 5 columns (5 × 5 array)

 

🔍 Examples (Visual & Text):

1. 3 × 4 = 12
   Array:

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2. 6 × 2 = 12
   Array:

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• ●
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• ●

3. Square number: 4² = 16

• ● ● ●
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4. Division example: 20 ÷ 5 = 4
   → Arrange 20 counters in 5 rows → each row has 4 counters

 

✏️ Word Problems:

1. A farmer arranges 24 eggs in 4 rows. How many eggs are in each row?
   → Use an array to divide: 24 ÷ 4 = 6 eggs per row
2. A garden has 6 rows of flowers with 8 in each row. How many flowers are there?
   → 6 × 8 = 48 flowers
3. A school arranges chairs in 5 rows with 7 chairs in each row. How many chairs are there?
   → 5 × 7 = 35 chairs
4. There are 36 students. If 6 students are seated in each row, how many rows are needed?
   → 36 ÷ 6 = 6 rows

 

🎯 Learners’ Activities (Expanded):

1. Hands-On with Counters or Cubes:
   • Learners use counters to physically build arrays for different multiplication facts (e.g., 3 × 5, 4 × 6).
2. Graph Paper Arrays:
   • Pairs draw rectangles on graph paper to represent arrays. Label rows, columns, and total number.
3. Create Your Own Word Problem:
   • In small groups, students create real-life multiplication or division problems using arrays and share with the class.
4. Square Number Challenge:
   • Learners form square arrays (e.g., 4 × 4, 5 × 5) and write down which number it represents.
5. Matching Game:
   • Match multiplication equations to drawn arrays (cards or pictures).

 

✅ Assessment Checks (Formative):

1. Teacher Questions (Oral/Written):
   • “Show 7 × 6 with an array. How many rows? How many columns?”
   • “Use an array to show 36 ÷ 6.”
   • “Is 5 × 5 a square number? Can you show it as an array?”
2. Quick Practice:
   • Draw an array for:
     a) 3 × 3
     b) 2 × 6
     c) 4 × 5
     d) 6 ÷ 2 (division array)
3. Exit Ticket:
   • Provide a blank grid. Ask students to shade and label an array that represents 4 × 7.

 

📘 Notes (Expanded & Detailed):

• Arrays are a visual strategy that support students' understanding of:
• Multiplication as repeated addition
• Division as equal grouping or sharing
• Square numbers as special cases
• Arrays also connect with:
• Area models in geometry
• Factor pairs (e.g., 12 = 3 × 4 = 2 × 6)
• Commutative property (3 × 4 = 4 × 3)
• Real-life examples:
• Egg trays, chocolate boxes, tile arrangements, chair setups

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews arrays and their application in problem-solving.

Evaluation Method (Expanded):
Exit slip/quiz: Draw an array for 4 × 9.

Assignment (Expanded):
Learners create posters showing arrays for different multiplication tables.

Follow-up Activity:
Students use arrays to solve homework multiplication problems.

Differentiation / Inclusive Strategies
Provide real counters for weaker learners.

Teacher’s Reflection (After Class)
• What worked well? ___________________________________________
• What needs improvement? ____________________________________
• Students’ engagement level: ☑ High ☑ Medium ☑ Low