Division, Decimals by 10–200, 2-Digit Divisors and Word Problems for Primary 5

Class: Primary 5
Term: 1st Term
Week: 9
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Number and Numeration
Previous Lesson: Division, Multiples, Dividing by 10–200 and 2-Digit Divisors.
Topic: DIVISION
Subject Matter: Division of decimals by multiples of 10 up to 90, division of decimals by 100 and 200, division of whole numbers by 2-digit numbers, word problems on division of numbers, quantitative aptitude on decimals.

Specific Objectives

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

Cognitive Domain:

• Divide decimals by multiples of 10 up to 90.
• Divide decimals by 100 and 200.
• Divide 3-digit whole numbers by 2-digit numbers.
• Solve word problems involving division, including identifying quotients and remainders.
• Solve quantitative aptitude problems involving decimals.

Affective Domain:

• Appreciate the importance of accurate division in real-life situations.
• Show interest in solving various division problems.

Psychomotor Domain:

• Accurately perform division operations using appropriate methods.
• Present solutions to division problems clearly and logically.

Social Domain:

• Work cooperatively with peers to solve group division tasks.
• Engage in discussions about different approaches to solving division problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum
• State Unified Scheme of Work
• New General Mathematics for Primary Schools Book 5

Instructional Materials

The teacher will teach this lesson with the aid of:

• Sticks
• Stones
• Abacus
• Charts on division rules
• Charts on multiples of numbers

Rationale for the Lesson

This lesson helps pupils understand how to divide different types of numbers, including decimals and whole numbers, which is an important skill for everyday calculations. It enables pupils to solve practical problems they might encounter in daily life, such as sharing items or calculating quantities.

Prerequisite/Previous Knowledge

Pupils can perform basic multiplication and simple division of whole numbers. They also have an understanding of decimal place values.

Lesson Content/Board Summary

DIVISION

Division of Decimals by Multiples of 10 (up to 90)

To divide a decimal by 10, 20, 30, up to 90, we can use the method of shifting the decimal point to the left. When dividing by 10, shift the decimal point one place to the left. When dividing by 20, first divide by 2, then shift the decimal point one place to the left.

Example 1: Divide 45.6 by 10.

Steps:

1. Shift the decimal point one place to the left.
2. 45.6 becomes 4.56

Therefore, 45.6 ÷ 10 = 4.56

Example 2: Divide 123.4 by 20.

Steps:

1. First, divide 123.4 by 2: 123.4 ÷ 2 = 61.7
2. Then, divide 61.7 by 10 (shift the decimal point one place to the left): 61.7 becomes 6.17

Therefore, 123.4 ÷ 20 = 6.17

Division of Decimals by 100 and 200

To divide a decimal by 100, shift the decimal point two places to the left. To divide a decimal by 200, first divide by 2, then shift the decimal point two places to the left.

Example 1: Divide 789.2 by 100.

Steps:

1. Shift the decimal point two places to the left.
2. 789.2 becomes 7.892

Therefore, 789.2 ÷ 100 = 7.892

Example 2: Divide 345.6 by 200.

Steps:

1. First, divide 345.6 by 2: 345.6 ÷ 2 = 172.8
2. Then, divide 172.8 by 100 (shift the decimal point two places to the left): 172.8 becomes 1.728

Therefore, 345.6 ÷ 200 = 1.728

Division of Whole Numbers by 2-Digit Numbers

Division of whole numbers by 2-digit numbers usually involves long division. This method helps to systematically find the quotient and remainder.

Example 1: Divide 576 by 12.

Steps:

1. Set up the long division: 12 | 576
2. Divide the first part of the dividend (57) by the divisor (12). 12 goes into 57 four times (4 x 12 = 48).
3. Write 4 above the 7 in the dividend.
4. Subtract 48 from 57: 57 – 48 = 9.
5. Bring down the next digit (6) to make 96.
6. Divide 96 by 12. 12 goes into 96 eight times (8 x 12 = 96).
7. Write 8 above the 6 in the dividend.
8. Subtract 96 from 96: 96 – 96 = 0.

Therefore, 576 ÷ 12 = 48 with a remainder of 0.

Example 2: Divide 854 by 21.

Steps:

1. Set up the long division: 21 | 854
2. Divide 85 by 21. 21 goes into 85 four times (4 x 21 = 84).
3. Write 4 above the 5 in the dividend.
4. Subtract 84 from 85: 85 – 84 = 1.
5. Bring down the next digit (4) to make 14.
6. Divide 14 by 21. 21 goes into 14 zero times.
7. Write 0 above the 4 in the dividend.
8. Subtract 0 from 14: 14 – 0 = 14.

Therefore, 854 ÷ 21 = 40 with a remainder of 14.

Word Problems on Division of Numbers

Word problems require careful reading to identify what needs to be divided and what the divisor is. Look for keywords that indicate division.

The following are common keywords for division:

• divide
• share equally
• each
• per
• quotient
• how many in each group

Example: A baker has 750 cookies and wants to pack them into bags, with 25 cookies in each bag. How many bags will she need?

Steps to solve:

1. Identify the total number of cookies: 750
2. Identify the number of cookies per bag: 25
3. Perform the division: 750 ÷ 25
4. Using long division: 750 ÷ 25 = 30

The baker will need 30 bags.

Quantitative Aptitude on Decimals

Quantitative aptitude problems test a pupil’s ability to quickly and accurately solve numerical problems, often involving decimals, in a logical way.

Example: If 0.5 kg of sugar costs N150, what is the cost of 1 kg of sugar?

Steps:

1. Understand that 1 kg is twice 0.5 kg.
2. Alternatively, divide the cost by the quantity to find the cost per unit: N150 ÷ 0.5 kg
3. To divide by a decimal, make the divisor a whole number by multiplying both divisor and dividend by 10: (150 x 10) ÷ (0.5 x 10) = 1500 ÷ 5
4. Perform the division: 1500 ÷ 5 = 300

The cost of 1 kg of sugar is N300.

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 on multiplication of decimals. The teacher then asks pupils questions like, “If you have 10 sweets and you want to share them equally among 2 friends, how many sweets will each friend get?” This leads to the day’s topic, division.
Pupils’ Activity: Pupils respond to the teacher’s questions and recall previous knowledge.
Learning Point: Pupils are prepared for the new lesson and connect it to prior learning.

Step 2: Division of Decimals by Multiples of 10 (up to 90)

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the rule for dividing decimals by 10, 20, 30, etc., using decimal shifting. The teacher demonstrates with examples like 45.6 ÷ 10 and 123.4 ÷ 20, writing the steps clearly on the board.
Pupils’ Activity: Pupils listen attentively, observe the examples, and ask questions for clarification. They copy notes into their books.
Learning Point: Pupils understand how to divide decimals by multiples of 10 up to 90.

Step 3: Division of Decimals by 100 and 200

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher extends the concept to division by 100 and 200, explaining the two-place decimal shift. The teacher provides examples such as 789.2 ÷ 100 and 345.6 ÷ 200, ensuring pupils grasp the method.
Pupils’ Activity: Pupils follow the explanation, work through examples with the teacher, and take notes.
Learning Point: Pupils learn to divide decimals by 100 and 200.

Step 4: Division of Whole Numbers by 2-Digit Numbers

Time: 8 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher demonstrates the long division method for dividing 3-digit whole numbers by 2-digit numbers using charts and examples like 576 ÷ 12 and 854 ÷ 21. The teacher guides pupils through each step.
Pupils’ Activity: Pupils observe the demonstration, participate in guided practice, and try solving similar problems.
Learning Point: Pupils can divide whole numbers by 2-digit numbers using long division.

Step 5: Word Problems on Division of Numbers

Time: 7 minutes
Teaching Skill: Problem Solving/Application
Teacher’s Activity: The teacher presents several word problems involving division, highlighting keywords that indicate division. The teacher guides pupils on how to extract information and set up the division problem. An example like the cookie problem is solved step-by-step.
Pupils’ Activity: Pupils read the word problems, identify keywords, and work to solve them with the teacher’s guidance.
Learning Point: Pupils develop skills in solving real-life division problems.

Step 6: Quantitative Aptitude on Decimals

Time: 5 minutes
Teaching Skill: Critical Thinking/Application
Teacher’s Activity: The teacher introduces quantitative aptitude problems involving decimals, explaining that these test quick thinking and application of division concepts. The teacher provides and solves an example like finding the cost of 1 kg of sugar if 0.5 kg costs N150.
Pupils’ Activity: Pupils listen to the explanation and attempt to solve the problems presented.
Learning Point: Pupils apply decimal division in quantitative reasoning scenarios.

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. Divide 67.5 by 10.
2. Calculate 456.8 ÷ 100.
3. Perform the division: 720 ÷ 15.
4. A farmer harvested 960 oranges and packed them into crates, with 24 oranges in each crate. How many crates did he use?
5. If 0.25 litres of paint costs N500, what is the cost of 1 litre of paint?

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 different methods of division covered. The teacher assigns homework for pupils to practice division problems.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their learning and prepare for independent practice.

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

Lesson Keywords

• Division – The process of splitting a number into equal parts or groups.
• Decimal – A number that contains a decimal point, representing a fraction of a whole.
• Quotient – The result obtained when one number is divided by another.
• Remainder – The amount left over after a division when the dividend is not perfectly divisible by the divisor.
• Multiples of 10 – Numbers that can be divided by 10 without a remainder (e.g., 10, 20, 30).
• Quantitative Aptitude – The ability to solve numerical problems quickly and accurately.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more challenging multi-step division problems or problems involving larger numbers. For pupils needing extra support, the teacher will provide additional guided practice with simpler examples, use manipulatives like an abacus more extensively, and offer one-on-one assistance to reinforce understanding.

Note for teachers using this lesson plan

Ensure that pupils understand the concept of place value before introducing decimal shifting. Encourage pupils to show all their working steps for long division and word problems to help identify and correct any errors. Emphasize the practical applications of division to make the lesson relatable and engaging for pupils.