Division, Multiples, Dividing by 10–200 and 2-Digit Divisors for Primary 5

Class: Primary 5
Term: 1st Term
Week: 8
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Multiplication, Decimal by Decimal, Fraction by Fraction, Squares and Roots.
Topic: DIVISION
Subject Matter: Multiples of numbers up to 50, division of whole numbers by 10, 20 up to 90, division of numbers by 100 and 200, division of whole numbers by 2-digit numbers with or without remainders, quantitative aptitude on division by 100 and 200

Specific Objectives

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

Cognitive Domain:

• Find multiples of numbers up to 50.
• Determine the number of groups of 10, 20, 30 up to 90 in a given number.
• Divide numbers by 100 and 200 using place value and decimal shifting.
• Divide whole numbers by 2-digit numbers with or without remainders.
• Solve quantitative aptitude problems involving division by 100 and 200.

Affective Domain:

• Show interest in solving division problems.
• Participate actively in class discussions and activities.
• Appreciate the importance of division in everyday life.

Psychomotor Domain:

• Accurately calculate division problems.
• Write solutions clearly and systematically.

Social Domain:

• Work cooperatively with peers to solve division tasks.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4-6 Mathematics)
• State Unified Scheme of Work for Primary Schools
• New General Mathematics for Primary Schools Book 5
• https://www.math-salamanders.com/multiples-worksheet.html
• https://www.splashlearn.com/math-vocabulary/division/multiples

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart showing multiples of numbers
• Flash cards with division problems
• Counters
• Abacus chart
• Quantitative aptitude book
• Fraction cards

Rationale for the Lesson

This lesson helps pupils to understand how numbers can be broken into equal parts or groups. It enables pupils to perform calculations involving sharing and grouping, which are useful skills in their daily lives for managing resources and solving practical problems.

Prerequisite/Previous Knowledge

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

Lesson Content/Board Summary

DIVISION

Multiples of Numbers up to 50

A multiple of a number is the result of multiplying that number by an integer (whole number). Multiples of a number are essentially its multiplication table.

To find multiples of a number, multiply it by 1, 2, 3, 4, and so on.

The following are examples of multiples:

• Multiples of 2 up to 50: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50.
• Multiples of 5 up to 50: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
• Multiples of 7 up to 50: 7, 14, 21, 28, 35, 42, 49.

Division of Whole Numbers by 10, 20, 30 up to 90

Dividing by multiples of 10 (like 10, 20, 30…90) can be done by first dividing by the non-zero digit and then adjusting for the zero or simply removing the zero from the dividend if it ends in zero.

NOTE: When dividing by 10, 20, 30, etc., we can simplify by cancelling out common zeros if both numbers end in zero. If not, we perform the division normally.

Example 1: Divide 240 by 10.

Steps:

1. Cancel out one zero from both the dividend (240) and the divisor (10).
2. 240 ÷ 10 = 24 ÷ 1 = 24.

Answer: 24

Example 2: Divide 360 by 20.

Steps:

1. Cancel out one zero from both 360 and 20. This leaves 36 ÷ 2.
2. Divide 36 by 2.
3. 36 ÷ 2 = 18.

Answer: 18

Example 3: Divide 150 by 30.

Steps:

1. Cancel out one zero from both 150 and 30. This leaves 15 ÷ 3.
2. Divide 15 by 3.
3. 15 ÷ 3 = 5.

Answer: 5

Division of Whole Numbers by 100 and 200

Dividing by 100 involves shifting the decimal point two places to the left. For whole numbers, the decimal point is at the end of the number.

Dividing by 200 can be done by first dividing by 2 and then by 100, or by shifting the decimal point two places to the left and then dividing by 2.

NOTE: When dividing by 100, move the decimal point two places to the left. If the number does not have a decimal point, assume it is at the end.

Example 1: Divide 500 by 100.

Steps:

1. Start with 500. The decimal point is after the last zero (500.).
2. Move the decimal point two places to the left.
3. 5.00

Answer: 5

Example 2: Divide 1200 by 200.

Method 1 (Cancelling zeros):

1. Cancel out two zeros from both 1200 and 200. This leaves 12 ÷ 2.
2. Divide 12 by 2.
3. 12 ÷ 2 = 6.

Method 2 (Decimal shifting then division):

1. Start with 1200. Move the decimal point two places to the left (12.00).
2. Now divide 12 by 2.
3. 12 ÷ 2 = 6.

Answer: 6

Example 3: Divide 350 by 100.

Steps:

1. Start with 350. The decimal point is after the last zero (350.).
2. Move the decimal point two places to the left.
3. 3.50

Answer: 3.5

Division of Whole Numbers by 2-Digit Numbers with or without Remainders

Long division is used to divide larger numbers by 2-digit numbers. It involves a series of steps: Divide, Multiply, Subtract, Bring down.

Example 1: Divide 156 by 12.

    13
  ____
12|156
   -12  (12 x 1)
   ---
    36
   -36  (12 x 3)
   ---
     0

Steps:

1. Divide the first part of the dividend (15) by the divisor (12). 15 ÷ 12 = 1 with a remainder. Write 1 above the 5.
2. Multiply the quotient digit (1) by the divisor (12). 1 x 12 = 12. Write 12 below 15.
3. Subtract 12 from 15. 15 – 12 = 3.
4. Bring down the next digit (6) from the dividend to form 36.
5. Divide 36 by 12. 36 ÷ 12 = 3. Write 3 next to 1 above the 6.
6. Multiply the new quotient digit (3) by the divisor (12). 3 x 12 = 36. Write 36 below 36.
7. Subtract 36 from 36. 36 – 36 = 0.

Answer: 13

Example 2: Divide 245 by 21.

    11 R 14
  _______
21|245
   -21   (21 x 1)
   ----
    35
   -21   (21 x 1)
   ----
    14

Steps:

1. Divide 24 by 21. 24 ÷ 21 = 1 with a remainder. Write 1 above the 4.
2. Multiply 1 by 21. 1 x 21 = 21. Write 21 below 24.
3. Subtract 21 from 24. 24 – 21 = 3.
4. Bring down the next digit (5) to form 35.
5. Divide 35 by 21. 35 ÷ 21 = 1 with a remainder. Write 1 next to 1 above the 5.
6. Multiply 1 by 21. 1 x 21 = 21. Write 21 below 35.
7. Subtract 21 from 35. 35 – 21 = 14. This is the remainder.

Answer: 11 remainder 14

Quantitative Aptitude on Division by 100 and 200

Quantitative aptitude problems test a pupil’s ability to apply mathematical concepts to solve real-world or abstract scenarios. For division by 100 and 200, problems often involve understanding place value and quick mental calculations.

Example 1: If 800 oranges are packed into boxes, with each box containing 100 oranges, how many boxes are needed?

Solution: Number of boxes = Total oranges ÷ Oranges per box

Number of boxes = 800 ÷ 100 = 8

Answer: 8 boxes

Example 2: A school has 1200 pupils. If they are divided into groups of 200 for an excursion, how many groups will there be?

Solution: Number of groups = Total pupils ÷ Pupils per group

Number of groups = 1200 ÷ 200 = 6

Answer: 6 groups

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson briefly. The teacher then asks pupils to recall what division means (sharing equally, grouping). The teacher introduces the topic “Division” and states the lesson objectives.
Pupils’ Activity: Pupils respond to greetings, recall previous knowledge, and listen attentively to the teacher.
Learning Point: Pupils are prepared for the new lesson and understand its purpose.

Step 2: Multiples of Numbers up to 50

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what multiples are and demonstrates how to find multiples of various numbers up to 50 using a chart or by writing on the board. The teacher asks pupils to find multiples of 3 and 6 up to 50.
Pupils’ Activity: Pupils listen to the explanation, observe the demonstrations, and find multiples of given numbers.
Learning Point: Pupils understand how to identify and list multiples of numbers.

Step 3: Division of Whole Numbers by 10, 20, 30 up to 90

Time: 7 minutes
Teaching Skill: Explanation/Guided Practice
Teacher’s Activity: The teacher explains the rule for dividing by multiples of 10, especially when both numbers end in zeros (cancelling zeros). The teacher works through examples like 240 ÷ 10 and 360 ÷ 20, guiding pupils through each step.
Pupils’ Activity: Pupils pay attention to the explanation and practice solving the examples under the teacher’s guidance.
Learning Point: Pupils learn to divide whole numbers by 10, 20, up to 90 using simplification methods.

Step 4: Division of Whole Numbers by 100 and 200

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains how to divide by 100 and 200, emphasizing the concept of shifting the decimal point or cancelling two zeros. The teacher provides examples such as 500 ÷ 100 and 1200 ÷ 200.
Pupils’ Activity: Pupils observe the examples and try to apply the rules to new problems.
Learning Point: Pupils can divide whole numbers by 100 and 200.

Step 5: Division of Whole Numbers by 2-Digit Numbers with or without Remainders

Time: 7 minutes
Teaching Skill: Demonstration/Problem-Solving
Teacher’s Activity: The teacher demonstrates the long division method for dividing by 2-digit numbers, breaking it down into “Divide, Multiply, Subtract, Bring down” steps. The teacher solves examples like 156 ÷ 12 and 245 ÷ 21.
Pupils’ Activity: Pupils follow the steps of long division and practice solving similar problems.
Learning Point: Pupils learn to perform long division by 2-digit numbers, identifying remainders where applicable.

Step 6: Quantitative Aptitude on Division by 100 and 200

Time: 5 minutes
Teaching Skill: Application/Problem-Solving
Teacher’s Activity: The teacher presents quantitative aptitude problems related to division by 100 and 200. The teacher guides pupils on how to interpret the questions and apply the learned division skills to find solutions.
Pupils’ Activity: Pupils engage in solving the word problems, applying their understanding of division.
Learning Point: Pupils apply division skills to solve practical word problems.

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. List the first five multiples of 8.
2. Divide 450 by 30.
3. What is 700 divided by 100?
4. Divide 345 by 15.
5. A farmer harvested 2000 yams. If he bundles them in groups of 200, how many bundles will he have?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of division in daily life. The teacher gives pupils homework related to the day’s topic.
Pupils’ Activity: Pupils listen to the summary and copy the homework.
Learning Point: Pupils consolidate their understanding and are given tasks to reinforce learning.

Home Task: Solve three new exercises on DIVISION. Show each step and check each answer.

Lesson Keywords

• Multiples – The result of multiplying a number by an integer.
• Division – The process of splitting a number into equal parts or groups.
• Dividend – The number being divided.
• Divisor – The number by which another number is divided.
• Quotient – The result of a division.
• Remainder – The amount left over after dividing one number by another.
• Quantitative Aptitude – Problems that test numerical ability and problem-solving skills.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more complex division problems or multi-step quantitative aptitude questions. For pupils needing extra support, the teacher will offer one-on-one guidance, simplify problems, or use more physical counters and visual aids to demonstrate the division process.

Note for teachers using this lesson plan

Ensure that pupils have a strong foundation in multiplication facts before introducing division of larger numbers. Emphasize the connection between multiplication and division. Encourage pupils to show their working steps clearly, especially for long division, to help them identify and correct errors. Use real-life examples to make the concept of division relatable and practical.