Subtraction of Numbers and Fractions, Decimals, Mixed Numbers and Word Problems for Primary 5

Class: Primary 5
Term: First Term
Week: 5
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Number and Numeration
Previous Lesson: Addition of Numbers and Fractions, Decimals, Mixed Numbers and Word Problems.
Topic: SUBTRACTION OF NUMBERS AND FRACTIONS.
Subject Matter: Subtraction of numbers involving three or more digits, subtraction of decimal fractions, subtraction of mixed fractions and mixed numbers, word problems on subtraction of numbers and fractions, quantitative aptitude on subtraction of numbers.

Specific Objectives

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

Cognitive Domain:

• Subtract numbers involving three or more digits accurately.
• Subtract decimal numbers correctly by aligning decimal points.
• Subtract mixed fractions and mixed numbers using appropriate methods (e.g., LCM, borrowing).
• Solve word problems involving the subtraction of numbers, decimals, and fractions.
• Solve quantitative aptitude problems related to subtraction of numbers.

Affective Domain:

• Appreciate the importance of accurate subtraction in everyday calculations.
• Develop patience and precision when solving mathematical problems.

Psychomotor Domain:

• Demonstrate the correct steps for subtracting various types of numbers and fractions.
• Accurately write down solutions to subtraction problems in their notebooks.

Social Domain:

• Work cooperatively in groups to solve subtraction challenges.
• Communicate their mathematical ideas clearly to peers and the teacher.

Reference Materials

The following resources were used in planning this lesson:

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

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart showing subtraction steps for different number types
• Flash cards with subtraction problems
• Counters for illustrating subtraction concepts
• Subtraction chart
• Quantitative aptitude book
• Fraction cards

Rationale for the Lesson

This lesson helps pupils understand how to subtract different types of numbers, which is an important skill for daily life. It enables pupils to manage money, calculate differences, and solve practical problems involving quantities. Mastering subtraction builds a strong foundation for more advanced mathematical concepts.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic subtraction of two-digit numbers, addition of numbers and fractions, and understanding of place values.

Lesson Content/Board Summary

SUBTRACTION OF NUMBERS AND FRACTIONS

Subtraction of Numbers Involving Three or More Digits

Subtraction of numbers with three or more digits involves taking away one number from another, often requiring borrowing from higher place values.

Example 1: Subtract 543 from 876.

Solution:
Step 1: Write the numbers vertically, aligning digits by place value.
876
– 543
—–
Step 2: Subtract the units column (6 – 3 = 3).
876
– 543
—–
3
Step 3: Subtract the tens column (7 – 4 = 3).
876
– 543
—–
33
Step 4: Subtract the hundreds column (8 – 5 = 3).
876
– 543
—–
333
Therefore, 876 – 543 = 333.

Example 2: Subtract 3456 from 7895.

Solution:
Step 1: Write the numbers vertically, aligning digits by place value.
7895
– 3456
—–
Step 2: Subtract the units column. Since 5 is less than 6, borrow 1 ten (10 units) from the tens column. The 9 in the tens column becomes 8, and the 5 in the units column becomes 15.
78⁸9¹⁵5
– 3456
—–
9 (15 – 6 = 9)
Step 3: Subtract the tens column (8 – 5 = 3).
78⁸9¹⁵5
– 3456
—–
39
Step 4: Subtract the hundreds column (8 – 4 = 4).
78⁸9¹⁵5
– 3456
—–
439
Step 5: Subtract the thousands column (7 – 3 = 4).
78⁸9¹⁵5
– 3456
—–
4439
Therefore, 7895 – 3456 = 4439.

How to find a missing number in a subtraction problem:
If A – B = C:

• To find the minuend (A) when the subtrahend (B) and difference (C) are known: A = C + B
• To find the subtrahend (B) when the minuend (A) and difference (C) are known: B = A – C

Subtraction of Decimal Fractions

To subtract decimal fractions, align the decimal points and then subtract as with whole numbers. Add zeros to the end of decimals if necessary to make the number of decimal places equal.

Example 1: Subtract 2.30 from 5.75.

Solution:
Step 1: Write the numbers vertically, aligning the decimal points.
5.75
– 2.30
—–
Step 2: Subtract the hundredths column (5 – 0 = 5).
5.75
– 2.30
—–
.05
Step 3: Subtract the tenths column (7 – 3 = 4).
5.75
– 2.30
—–
.45
Step 4: Subtract the whole number part (5 – 2 = 3).
5.75
– 2.30
—–
3.45
Therefore, 5.75 – 2.30 = 3.45.

Example 2: Subtract 3.75 from 12.5.

Solution:
Step 1: Write the numbers vertically, aligning decimal points. Add a zero to 12.5 to make the decimal places equal.
12.50
– 3.75
—–
Step 2: Subtract the hundredths column. Since 0 is less than 5, borrow 1 tenth (10 hundredths) from the tenths column. The 5 in the tenths column becomes 4, and the 0 in the hundredths column becomes 10.
12.⁴5¹⁰0
– 3.75
—–
5 (10 – 5 = 5)
Step 3: Subtract the tenths column. Since 4 is less than 7, borrow 1 whole (10 tenths) from the units column. The 2 in the units column becomes 1, and the 4 in the tenths column becomes 14.
1¹2.¹⁴5¹⁰0
– 3.75
—–
.75 (14 – 7 = 7)
Step 4: Subtract the units column. Since 1 is less than 3, borrow 1 ten (10 units) from the tens column. The 1 in the tens column becomes 0, and the 1 in the units column becomes 11.
1⁰¹¹2.¹⁴5¹⁰0
– 3.75
—–
8.75 (11 – 3 = 8)
Therefore, 12.5 – 3.75 = 8.75.

Subtraction of Mixed Fractions and Mixed Numbers

To subtract mixed fractions, convert them to improper fractions, find a common denominator (LCM), subtract the numerators, and then convert back to a mixed number if needed. Alternatively, subtract the whole numbers and fractional parts separately, borrowing from the whole number if the first fraction is smaller.

Example 1: Subtract 1 1/4 from 3 1/2.

Solution (Method 1: Convert to Improper Fractions):
Step 1: Convert mixed fractions to improper fractions.
3 1/2 = (3 × 2 + 1)/2 = 7/2
1 1/4 = (1 × 4 + 1)/4 = 5/4
Step 2: Find the Least Common Multiple (LCM) of the denominators (2 and 4). The LCM is 4.
Step 3: Convert the fractions to equivalent fractions with the common denominator.
7/2 = (7 × 2)/(2 × 2) = 14/4
5/4 remains 5/4
Step 4: Subtract the improper fractions.
14/4 – 5/4 = (14 – 5)/4 = 9/4
Step 5: Convert the improper fraction back to a mixed number.
9 ÷ 4 = 2 remainder 1. So, 9/4 = 2 1/4.
Therefore, 3 1/2 – 1 1/4 = 2 1/4.

Solution (Method 2: Subtract Whole Numbers and Fractions Separately):
Step 1: Write the fractions vertically.
3 1/2
– 1 1/4
Step 2: Find the LCM of the fractional denominators (2 and 4), which is 4. Convert fractions to equivalent fractions.
1/2 = 2/4
1/4 remains 1/4
The problem becomes:
3 2/4
– 1 1/4
Step 3: Subtract the fractional parts: 2/4 – 1/4 = 1/4.
Step 4: Subtract the whole number parts: 3 – 1 = 2.
Step 5: Combine the results.
2 1/4.
Therefore, 3 1/2 – 1 1/4 = 2 1/4.

Example 2: Subtract 2 2/3 from 5 1/3.

Solution (Method with Borrowing):
Step 1: Write the fractions vertically.
5 1/3
– 2 2/3
Step 2: Observe that 1/3 is less than 2/3. We need to borrow from the whole number. Borrow 1 whole from 5 (making it 4) and convert it into a fraction with the same denominator as 1/3, which is 3/3. Add this to the existing fraction.
5 1/3 becomes 4 + (3/3 + 1/3) = 4 4/3.
The problem becomes:
4 4/3
– 2 2/3
Step 3: Subtract the fractional parts: 4/3 – 2/3 = 2/3.
Step 4: Subtract the whole number parts: 4 – 2 = 2.
Step 5: Combine the results.
2 2/3.
Therefore, 5 1/3 – 2 2/3 = 2 2/3.

Word Problems on Subtraction of Numbers and Fractions

Word problems require careful reading to identify the quantities involved and the need for subtraction. Look for keywords such as “difference,” “how many left,” “how much more/less,” or “take away.”

Example 1: A farmer had 5,472 oranges. He sold 2,150 oranges. How many oranges are left?

Solution:
Number of oranges the farmer had = 5,472
Number of oranges sold = 2,150
Number of oranges left = 5,472 – 2,150
5472
– 2150
—–
3322
Therefore, 3,322 oranges are left.

Example 2: A tailor bought 7 1/2 metres of fabric. He used 3 1/4 metres to sew a dress. How much fabric is remaining?

Solution:
Total fabric bought = 7 1/2 metres
Fabric used = 3 1/4 metres
Fabric remaining = 7 1/2 – 3 1/4
Step 1: Convert to improper fractions.
7 1/2 = 15/2
3 1/4 = 13/4
Step 2: Find LCM of 2 and 4, which is 4.
15/2 = 30/4
Step 3: Subtract.
30/4 – 13/4 = 17/4
Step 4: Convert back to a mixed number.
17 ÷ 4 = 4 remainder 1. So, 4 1/4.
Therefore, 4 1/4 metres of fabric are remaining.

Quantitative Aptitude on Subtraction of Numbers

Quantitative aptitude problems on subtraction often involve identifying patterns, finding missing numbers, or solving mental math challenges.

Example 1: Find the missing number in the sequence: 50, 45, 40, ___, 30.

Solution:
Observe the pattern: 50 – 45 = 5; 45 – 40 = 5.
The pattern is subtracting 5 each time.
So, 40 – 5 = 35.
The missing number is 35.

Example 2: What number should replace the question mark?
87
– ?5
—–
42

Solution:
Step 1: Look at the units column: 7 – 5 = 2. This is correct.
Step 2: Look at the tens column: 8 – ? = 4.
To find the missing number, we subtract the difference from the minuend: 8 – 4 = 4.
So, the missing digit is 4.
The number to replace ?5 is 45.
87
– 45
—–
42

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 subtraction means and gives a simple subtraction problem (e.g., “If you have 10 sweets and eat 3, how many are left?”). The teacher introduces the topic: “Today, we will learn about subtracting numbers and fractions, including bigger numbers, decimals, and mixed fractions.”

Pupils’ Activity: Pupils respond to greetings, answer review questions, and listen attentively to the introduction of the new topic.

Learning Point: Pupils recall basic subtraction and are prepared for the new lesson.

Step 2: Subtraction of Numbers Involving Three or More Digits

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains how to subtract numbers with three or more digits, emphasizing place value alignment and the concept of borrowing. The teacher works through Example 1 (876 – 543) and Example 2 (7895 – 3456) from the board summary, step-by-step, on the board or using a chart. The teacher provides a simple problem for pupils to try.

Pupils’ Activity: Pupils observe the examples, ask questions for clarification, and attempt the practice problem in their notebooks.

Learning Point: Pupils understand and practice subtracting multi-digit numbers, including borrowing.

Step 3: Subtraction of Decimal Fractions

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains the rule for subtracting decimals: aligning decimal points. The teacher demonstrates Example 1 (5.75 – 2.30) and Example 2 (12.5 – 3.75), showing how to add zeros to equalize decimal places and borrow when necessary. The teacher provides another practice problem for the pupils.

Pupils’ Activity: Pupils pay attention to the alignment of decimal points and borrowing techniques, and solve practice problems.

Learning Point: Pupils learn to subtract decimal fractions accurately by aligning decimal points and handling borrowing.

Step 4: Subtraction of Mixed Fractions and Mixed Numbers

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains two methods for subtracting mixed fractions: converting to improper fractions and finding LCM, or subtracting whole numbers and fractions separately with borrowing. The teacher demonstrates Example 1 (3 1/2 – 1 1/4) and Example 2 (5 1/3 – 2 2/3) using the methods. Pupils are guided to choose a method and solve a practice problem.

Pupils’ Activity: Pupils observe the different methods, ask questions about LCM and borrowing, and practice solving mixed fraction subtraction problems.

Learning Point: Pupils understand and apply methods for subtracting mixed fractions, including finding LCM and borrowing.

Step 5: Word Problems on Subtraction of Numbers and Fractions

Time: 6 minutes

Teaching Skill: Problem Solving/Application

Teacher’s Activity: The teacher explains how to identify subtraction in word problems by looking for keywords. The teacher guides pupils through Example 1 (oranges problem) and Example 2 (fabric problem) from the board summary, emphasizing how to extract information and set up the subtraction. Pupils are given a similar word problem to solve individually or in pairs.

Pupils’ Activity: Pupils identify keywords, set up and solve word problems, and discuss their solutions with peers.

Learning Point: Pupils can translate real-life scenarios into subtraction problems and solve them.

Step 6: Quantitative Aptitude on Subtraction of Numbers

Time: 5 minutes

Teaching Skill: Critical Thinking

Teacher’s Activity: The teacher introduces quantitative aptitude problems related to subtraction, focusing on patterns and missing numbers. The teacher works through Example 1 (sequence) and Example 2 (missing digit) from the board summary. The teacher then presents a short quantitative aptitude problem for pupils to attempt.

Pupils’ Activity: Pupils analyze the problems, identify patterns or missing values, and apply their subtraction skills to solve them.

Learning Point: Pupils develop critical thinking skills by solving subtraction-based quantitative aptitude 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. Define subtraction in your own words.
2. Subtract 7,421 from 9,875.
3. Calculate the difference between 15.6 and 8.92.
4. Solve: 6 3/5 – 2 1/10.
5. A baker made 500 loaves of bread and sold 385. How many loaves are left?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes

Teaching Skill: Summarization

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of aligning numbers correctly, finding common denominators for fractions, and identifying subtraction in word problems. The teacher assigns homework which includes a mix of subtraction problems covered in the lesson.

Pupils’ Activity: Pupils listen to the summary, ask any final questions, and copy down the homework assignment.

Learning Point: Pupils consolidate their understanding and are prepared for independent practice.

Home Task: Solve three new exercises on SUBTRACTION OF NUMBERS AND FRACTIONS. Show each step and check each answer.

Lesson Keywords

• Subtraction – The process of taking one number or quantity away from another.
• Decimal – A number that uses a decimal point to represent parts of a whole