Division, Whole Numbers, Decimals, 2-Digit and 3-Digit Divisors for Primary 6

Class: Primary 6
Term: 1st Term
Week: 10
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Multiplication, 3-Digit, Decimals, Fractions and Square Roots.
Topic: DIVISION
Subject Matter: Division of whole numbers by 2-digit numbers, division of whole numbers by 3-digit numbers, division of decimals by 2-digit numbers, division of decimals by 3-digit numbers, quantitative reasoning on division of numbers

Specific Objectives

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

Cognitive Domain:

• Divide whole numbers by 2-digit numbers accurately.
• Divide whole numbers by 3-digit numbers accurately.
• Divide decimals by 2-digit numbers accurately.
• Divide decimals by 3-digit numbers accurately.
• Solve quantitative reasoning problems involving division of numbers.

Affective Domain:

• Show patience and carefulness while performing division calculations.
• Appreciate the importance of division in daily problem-solving.
• Participate actively in class discussions and problem-solving activities.

Psychomotor Domain:

• Use the long division method correctly to solve division problems.
• Write out solutions to division problems clearly and logically.

Social Domain:

• Collaborate with peers to solve quantitative reasoning problems.
• Share strategies for solving division problems with classmates.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary Mathematics)
• State Unified Scheme of Work for Primary Schools
• New General Mathematics for Primary Schools, Book 6
• https://www.mathsisfun.com/long_division.html
• https://www.splashlearn.com/math-vocabulary/division/long-division

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Multiplication charts
• Posters showing long division steps
• Workbook

Rationale for the Lesson

This lesson helps pupils to understand how to share items equally and deal with larger numbers in practical situations. It is important for daily tasks like budgeting, sharing resources, and understanding quantities, which are essential life skills.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of basic division facts, multiplication tables, place values, and simple division of numbers by single-digit numbers.

Lesson Content/Board Summary

Division

Division of Whole Numbers by 2-Digit Numbers

Division is the process of sharing a number into equal parts. When dividing a whole number by a 2-digit number, we use the long division method.

Example 1: Divide 576 by 12

Solution:

48
____
12 | 576
-48 (12 x 4 = 48; First, divide 57 by 12, which is 4. Write 4 above 7. Then, multiply 4 by 12 and write 48 below 57.)
—
96 (Subtract 48 from 57 to get 9. Bring down the next digit, 6, to make 96.)
-96 (12 x 8 = 96; Next, divide 96 by 12, which is 8. Write 8 above 6. Then, multiply 8 by 12 and write 96 below 96.)
—
0 (Subtract 96 from 96 to get 0. The remainder is 0.)

Therefore, 576 ÷ 12 = 48.

Example 2: Divide 1344 by 24

Solution:

56
____
24 | 1344
-120 (24 x 5 = 120; First, divide 134 by 24, which is 5. Write 5 above 4. Then, multiply 5 by 24 and write 120 below 134.)
—-
144 (Subtract 120 from 134 to get 14. Bring down the next digit, 4, to make 144.)
-144 (24 x 6 = 144; Next, divide 144 by 24, which is 6. Write 6 above 4. Then, multiply 6 by 24 and write 144 below 144.)
—-
0 (Subtract 144 from 144 to get 0. The remainder is 0.)

Therefore, 1344 ÷ 24 = 56.

Division of Whole Numbers by 3-Digit Numbers

The long division method is also applied when dividing whole numbers by 3-digit numbers, following the same steps.

Example 1: Divide 7245 by 105

Solution:

69
____
105 | 7245
-630 (105 x 6 = 630; First, divide 724 by 105, which is 6. Write 6 above 4. Then, multiply 6 by 105 and write 630 below 724.)
—-
945 (Subtract 630 from 724 to get 94. Bring down the next digit, 5, to make 945.)
-945 (105 x 9 = 945; Next, divide 945 by 105, which is 9. Write 9 above 5. Then, multiply 9 by 105 and write 945 below 945.)
—-
0 (Subtract 945 from 945 to get 0. The remainder is 0.)

Therefore, 7245 ÷ 105 = 69.

Example 2: Divide 15625 by 125

Solution:

125
____
125 | 15625
-125 (125 x 1 = 125; First, divide 156 by 125, which is 1. Write 1 above 5. Then, multiply 1 by 125 and write 125 below 156.)
—-
312 (Subtract 125 from 156 to get 31. Bring down the next digit, 2, to make 312.)
-250 (125 x 2 = 250; Next, divide 312 by 125, which is 2. Write 2 above 2. Then, multiply 2 by 125 and write 250 below 312.)
—-
625 (Subtract 250 from 312 to get 62. Bring down the next digit, 5, to make 625.)
-625 (125 x 5 = 625; Next, divide 625 by 125, which is 5. Write 5 above 5. Then, multiply 5 by 125 and write 625 below 625.)
—-
0 (Subtract 625 from 625 to get 0. The remainder is 0.)

Therefore, 15625 ÷ 125 = 125.

Division of Decimals by 2-Digit Numbers

When dividing decimals by whole numbers, the division process is similar to whole numbers. The decimal point in the quotient is placed directly above the decimal point in the dividend.

Example 1: Divide 7.2 by 12

Solution:

0.6
____
12 | 7.2
-0 (12 x 0 = 0; First, divide 7 by 12, which is 0. Place the decimal point in the quotient.)
—
72 (Bring down 2 to make 72.)
-72 (12 x 6 = 72; Divide 72 by 12, which is 6. Write 6 above 2.)
—
0 (Subtract 72 from 72 to get 0.)

Therefore, 7.2 ÷ 12 = 0.6.

Example 2: Divide 15.68 by 14

Solution:

1.12
____
14 | 15.68
-14 (14 x 1 = 14; First, divide 15 by 14, which is 1. Write 1 above 5. Place the decimal point.)
—
16 (Subtract 14 from 15 to get 1. Bring down 6 to make 16.)
-14 (14 x 1 = 14; Divide 16 by 14, which is 1. Write 1 above 6.)
—
28 (Subtract 14 from 16 to get 2. Bring down 8 to make 28.)
-28 (14 x 2 = 28; Divide 28 by 14, which is 2. Write 2 above 8.)
—
0 (Subtract 28 from 28 to get 0.)

Therefore, 15.68 ÷ 14 = 1.12.

Division of Decimals by 3-Digit Numbers

This follows the same rules as dividing decimals by 2-digit numbers. Align the decimal point in the quotient with that of the dividend.

Example 1: Divide 12.36 by 103

Solution:

0.12
____
103 | 12.36
-0 (103 x 0 = 0; First, divide 12 by 103, which is 0. Place the decimal point.)
—-
123 (Bring down 3 to make 123.)
-103 (103 x 1 = 103; Divide 123 by 103, which is 1. Write 1 above 3.)
—-
206 (Subtract 103 from 123 to get 20. Bring down 6 to make 206.)
-206 (103 x 2 = 206; Divide 206 by 103, which is 2. Write 2 above 6.)
—-
0 (Subtract 206 from 206 to get 0.)

Therefore, 12.36 ÷ 103 = 0.12.

Example 2: Divide 56.44 by 124

Solution:

0.455
____
124 | 56.440 (Add a zero to continue division if needed)
-0 (124 x 0 = 0; First, divide 56 by 124, which is 0. Place the decimal point.)
—-
564 (Bring down 4 to make 564.)
-496 (124 x 4 = 496; Divide 564 by 124, which is 4. Write 4 above 4.)
—-
684 (Subtract 496 from 564 to get 68. Bring down 4 to make 684.)
-620 (124 x 5 = 620; Divide 684 by 124, which is 5. Write 5 above 4.)
—-
640 (Subtract 620 from 684 to get 64. Bring down a zero to make 640.)
-620 (124 x 5 = 620; Divide 640 by 124, which is 5. Write 5 above 0.)
—-
20 (Subtract 620 from 640 to get 20. Remainder is 20.)

Therefore, 56.44 ÷ 124 ≈ 0.455 (rounded to 3 decimal places).

Quantitative Reasoning on Division of Numbers

Quantitative reasoning involves understanding numerical patterns and relationships to solve problems. These problems often require identifying the rule that links numbers in a sequence or set.

Example 1: Find the missing number in the sequence: 100, 50, ___, 12.5

Solution:

Observe the pattern: 100 ÷ 2 = 50. This means each number is divided by 2 to get the next number.

To find the missing number, divide 50 by 2:

50 ÷ 2 = 25

Check the pattern with the next number: 25 ÷ 2 = 12.5. The pattern holds.

The missing number is 25.

Example 2: If 36 ÷ 9 = 4, then 72 ÷ 18 = ___

Solution:

Observe the relationship between the first and second division problems.

The dividend 36 is doubled to 72 (36 x 2 = 72).

The divisor 9 is doubled to 18 (9 x 2 = 18).

When both the dividend and the divisor are multiplied by the same number, the quotient remains the same.

Therefore, 72 ÷ 18 = 4.

How to solve for other values in division:

In division, if some values are known, others can be found:

• To find the Dividend: Multiply the Divisor by the Quotient. (Dividend = Divisor × Quotient)
• To find the Divisor: Divide the Dividend by the Quotient. (Divisor = Dividend ÷ Quotient)

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. The teacher then asks pupils to recall what division means and gives simple examples of sharing items equally.
Pupils’ Activity: Pupils respond to greetings, recall multiplication concepts, and provide examples of division.
Learning Point: Pupils recall prior knowledge and are prepared for the new topic.

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

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the concept of dividing whole numbers by 2-digit numbers using the long division method. The teacher demonstrates Example 1 (576 ÷ 12) on the board, explaining each step clearly.
Pupils’ Activity: Pupils pay attention, listen to the explanation, and copy the example into their notebooks.
Learning Point: Pupils understand the process of dividing whole numbers by 2-digit numbers.

Step 3: Guided Practice (Whole Numbers by 2-Digit Numbers)

Time: 6 minutes
Teaching Skill: Guided Practice/Questioning
Teacher’s Activity: The teacher provides Example 2 (1344 ÷ 24) and guides pupils to solve it on their own, providing assistance where needed and checking their steps.
Pupils’ Activity: Pupils attempt to solve the example on their own, asking questions for clarification.
Learning Point: Pupils practice and apply the long division method for 2-digit divisors.

Step 4: Presentation of Division of Whole Numbers by 3-Digit Numbers

Time: 6 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains that the method for 3-digit divisors is similar to 2-digit divisors. The teacher demonstrates Example 1 (7245 ÷ 105) on the board, highlighting any differences in handling larger numbers.
Pupils’ Activity: Pupils observe the demonstration and copy the example.
Learning Point: Pupils understand how to extend the long division method to 3-digit divisors.

Step 5: Presentation of Division of Decimals by 2-Digit and 3-Digit Numbers

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher introduces the division of decimals by whole numbers. The teacher explains the rule of placing the decimal point in the quotient and demonstrates Example 1 (7.2 ÷ 12) and Example 1 (12.36 ÷ 103) from the board summary, explaining each step carefully.
Pupils’ Activity: Pupils listen, take notes, and ask questions about decimal placement.
Learning Point: Pupils learn how to divide decimals by 2-digit and 3-digit whole numbers, correctly placing the decimal point.

Step 6: Presentation of Quantitative Reasoning

Time: 6 minutes
Teaching Skill: Explanation/Problem-Solving
Teacher’s Activity: The teacher explains what quantitative reasoning is in the context of division. The teacher presents Example 1 (100, 50, ___, 12.5) and Example 2 (If 36 ÷ 9 = 4, then 72 ÷ 18 = ___) from the board summary, guiding pupils to identify the patterns and relationships.
Pupils’ Activity