Multiples and Common Multiples of Numbers for Primary 4

Class: Primary 4
Term: Second Term
Week: 5
Age: 9 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Basic Operations
Focal competence: Dividing 2 -digit and 3-digit numbers by 1- digit with or without remainder and calculating the multiple of 10 up to 50
Key competencies/values: Collaboration
Skills:

• Using division charts to divide 2–3-digit numbers by a 1-digit number or multiples of 10 up to 50

Previous Lesson: Square Roots of Perfect Squares Up to 900 and Quantitative Reasoning
Topic: Division
Subject Matter: division by multiples of 10 up to 50, quantitative reasoning

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain

• Define what a multiple is.
• Identify multiples of 10 up to 50.
• Perform division of 2- or 3-digit numbers by a 1-digit number with or without remainder.
• Perform division of 2- or 3-digit numbers by multiples of 10 up to 50.
• Solve quantitative aptitude problems involving division of 1- and 2-digit numbers.

Affective Domain

• Collaborate effectively with peers in solving division problems.
• Appreciate the importance of division in everyday life.

Psychomotor Domain

• Demonstrate the process of short and long division using examples.
• Calculate quotients and remainders accurately for given division problems.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Primary Schools Book 4
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Division charts
• Flash cards (showing multiples of 10)
• Cardboard (for writing examples)
• Multimedia applications (for visual demonstrations)

Rationale for the Lesson

This lesson is important as it builds on pupils’ foundational understanding of basic operations, specifically division. Mastering division by 1-digit numbers and multiples of 10 equips pupils with essential problem-solving skills for everyday situations and quantitative reasoning. It also prepares them for more complex mathematical concepts in higher primary classes.

Prerequisite/Previous Knowledge

Pupils should have a basic understanding of multiplication facts and simple division concepts.

Lesson Content/Board Summary

Division

Meaning of Multiples

A multiple of a number is the product of that number and any other whole number. For example, multiples of 2 are 2, 4, 6, 8, …

Multiples can be generated by repeated addition or multiplication.

Generating Multiples of 10 (up to 50)

To find multiples of 10, we multiply 10 by whole numbers:

1. (10 times 1 = 10)
2. (10 times 2 = 20)
3. (10 times 3 = 30)
4. (10 times 4 = 40)
5. (10 times 5 = 50)

So, the multiples of 10 up to 50 are 10, 20, 30, 40, and 50.

Division by 1-Digit Numbers

Division is the process of sharing a number into equal parts. It can be done with or without a remainder.

Example 1: Division without Remainder

Question: Divide 72 by 3.

Solution:

Step 1: Divide the tens digit (7) by 3.

(7 div 3 = 2) remainder (1). Write 2 above the 7.

Step 2: Carry over the remainder (1) to the units digit (2) to make 12.

Step 3: Divide 12 by 3.

(12 div 3 = 4). Write 4 above the 2.

Answer: (72 div 3 = 24)

Example 2: Division with Remainder

Question: Divide 85 by 4.

Solution:

Step 1: Divide the tens digit (8) by 4.

(8 div 4 = 2). Write 2 above the 8.

Step 2: Divide the units digit (5) by 4.

(5 div 4 = 1) remainder (1). Write 1 above the 5.

Answer: (85 div 4 = 21) remainder (1)

Division by Multiples of 10 (up to 50)

When dividing by multiples of 10, we can often simplify the process by cancelling zeros if both the dividend and divisor end in zero.

Example 1: Division by 10

Question: Divide 240 by 10.

Solution:

Step 1: Write the division problem.

(240 div 10)

Step 2: Cancel one zero from both numbers.

(24 div 1)

Step 3: Perform the division.

(24 div 1 = 24)

Answer: (240 div 10 = 24)

Example 2: Division by 20

Question: Divide 360 by 20.

Solution:

Step 1: Write the division problem.

(360 div 20)

Step 2: Cancel one zero from both numbers.

(36 div 2)

Step 3: Perform the division.

(36 div 2 = 18)

Answer: (360 div 20 = 18)

Example 3: Division by 30 (Long Division)

Question: Divide 450 by 30.

Solution:

Step 1: Set up the long division.

(30 overline{smash{)} 450})

Step 2: Divide 45 by 30.

(45 div 30 = 1) remainder (15). Write 1 above the 5.

Step 3: Bring down the next digit (0) to make 150.

Step 4: Divide 150 by 30.

(150 div 30 = 5). Write 5 above the 0.

Answer: (450 div 30 = 15)

Quantitative Reasoning involving Division

Quantitative reasoning problems require applying mathematical skills to solve real-world scenarios or number puzzles.

Example

Question: If 5 pupils share 75 pencils equally, how many pencils does each pupil get?

Solution:

Step 1: Identify the total number of pencils and the number of pupils.

Total pencils = 75

Number of pupils = 5

Step 2: Perform the division.

(75 div 5)

Step 3: Calculate the answer.

(75 div 5 = 15)

Answer: Each pupil gets 15 pencils.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Problem Solving

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher greets the pupils and asks them to recall what multiplication is. The teacher then introduces division as the opposite of multiplication and a way of sharing equally.

Pupils’ Activity: Pupils respond to the teacher’s questions and listen attentively to the introduction.

Learning Point: Division concept review

Step 2: Meaning of Multiples

Time: 7 minutes

Teaching Skill: Explaining/Defining

Teacher’s Activity: The teacher explains what a multiple is, using simple examples like multiples of 2. The teacher shows how to generate multiples by repeated addition or multiplication.

Pupils’ Activity: Pupils listen, ask questions, and give examples of multiples of small numbers.

Learning Point: Meaning of multiples

Step 3: Generating Multiples of 10

Time: 7 minutes

Teaching Skill: Demonstrating/Listing

Teacher’s Activity: The teacher guides pupils to generate and list multiples of 10 up to 50 using flashcards and the division chart. The teacher emphasizes the pattern (10, 20, 30, 40, 50).

Pupils’ Activity: Pupils participate in listing multiples of 10 and observe the number pattern.

Learning Point: Multiples of ten

Step 4: Division by 1-Digit Numbers

Time: 8 minutes

Teaching Skill: Modelling/Practicing

Teacher’s Activity: The teacher models short and long division of 2- and 3-digit numbers by a 1-digit number, with and without remainders, using the division chart and cardboard for clear steps.

Pupils’ Activity: Pupils observe the teacher’s demonstration, ask questions, and solve guided practice problems on their own boards or in their notebooks.

Learning Point: Division by one-digit

Step 5: Division by Multiples of 10

Time: 8 minutes

Teaching Skill: Explaining/Applying

Teacher’s Activity: The teacher explains how to divide 2- and 3-digit numbers by multiples of 10 up to 50, demonstrating examples with and without cancelling zeros. The teacher uses the board for step-by-step solutions.

Pupils’ Activity: Pupils follow the examples, identify the patterns, and attempt similar problems guided by the teacher.

Learning Point: Division by multiples

Step 6: Quantitative Reasoning Problems

Time: 5 minutes

Teaching Skill: Problem-Solving/Guiding

Teacher’s Activity: The teacher presents simple quantitative reasoning problems involving division of 1- and 2-digit numbers. The teacher guides pupils on how to interpret the problems and apply division skills to find solutions.

Pupils’ Activity: Pupils attempt to solve the quantitative reasoning problems individually or in pairs, sharing their methods and answers.

Learning Point: Quantitative reasoning skills

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a multiple?
2. List the multiples of 10 up to 50.
3. Divide 96 by 4.
4. Divide 180 by 30.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Division concepts assessed

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils to copy the essential Board Summary notes on multiples, division by 1-digit numbers, and division by multiples of 10 into their notebooks.

Pupils’ Activity: Pupils copy the notes carefully into their notebooks.

Learning Point: Board notes copied

Step 9: Conclusion

Time: 1 minute

Teaching Skill: Summarising/Reinforcing

Teacher’s Activity: The teacher briefly reminds pupils of the importance of division in daily life and encourages them to practice regularly.

Pupils’ Activity: Pupils listen and acknowledge the importance of the lesson.

Learning Point: Division importance reinforced

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following division problems in your notebook:

1. What are the first five multiples of 10?
2. Divide 125 by 5.
3. Divide 270 by 9.
4. Divide 400 by 20.
5. A baker made 150 cookies and packed them into bags of 30. How many bags of cookies did he pack?

Lesson Keywords

• Multiple – The product of a number and any whole number.
• Division – The process of sharing equally or splitting into equal parts.
• Quotient – The result obtained by dividing one number by another.
• Remainder – The amount left over after performing a division.
• Divisor – The number by which another number is divided.
• Dividend – The number being divided.
• Quantitative Reasoning – Solving problems that involve numbers and quantities.

Differentiation

For weaker learners: Provide extra practice with flashcards for multiples of 10. Use physical manipulatives to demonstrate sharing in division. Offer simpler 2-digit by 1-digit division problems. Pair them with stronger learners for peer support.

For stronger learners: Challenge them with more complex 3-digit by 1-digit and 3-digit by multiples of 10 division problems. Introduce mental division strategies for certain problems. Provide additional quantitative reasoning word problems.

Suggested Lesson Videos

Search on YouTube for: “Primary 4 division by 1-digit numbers” or “Primary 4 division by multiples of 10”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have your division charts, flashcards for multiples of 10 (10, 20, 30, 40, 50), and a whiteboard or cardboard ready for demonstrations. Begin by reviewing basic multiplication and introducing division as sharing. Follow the instructional procedures step-by-step, modeling each type of division clearly. Pay close attention to pupils’ understanding when dividing by 1-digit numbers before moving to multiples of 10. Encourage pupils to participate actively in solving problems and discussing their methods. During Step 8, ensure pupils copy the Board Summary accurately. Provide individual support to pupils who struggle and offer extension activities for those who grasp the concepts quickly. Always check for understanding at each stage of the lesson.