Adding and subtracting mixed numbers for Primary 4

Class: Primary 4
Term: First Term
Week: 9
Age: 9 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Basic Operations
Focal competence: Adding and subtracting proper, improper and mixed fractions
Key competencies/values: Communication; ICT and Digital Competencies
Skills:

• Identifying fraction types
• Using fraction charts or counting blocks to add and subtract fractions

Previous Lesson: Adding and subtracting proper and improper fractions
Topic: Addition And Subtraction Of Fractions: Mixed Numbers And Applications
Subject Matter: Adding and subtracting mixed numbers, applying fraction operations to everyday and quantitative problems

Specific Objectives

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

Cognitive Domain

• Identify mixed numbers and their components.
• State the steps for adding and subtracting mixed numbers.

Psychomotor Domain

• Carry out addition and subtraction of mixed numbers accurately.
• Solve word problems involving addition and subtraction of fractions in everyday life activities.
• Solve quantitative aptitude problems involving addition and subtraction of fractions.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• A suitable Primary 4 Mathematics textbook
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Fraction charts
• Flash cards showing mixed numbers
• Cardboard cut-outs representing fractions
• Number cards
• Whiteboard and markers

Rationale for the Lesson

This lesson is important as it builds on pupils’ foundational understanding of fractions, enabling them to work with more complex mixed numbers. Mastering these operations is essential for solving real-world problems involving quantities that are not whole numbers, preparing them for higher mathematical concepts and practical applications in daily life.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of proper and improper fractions, converting improper fractions to mixed numbers, and basic addition and subtraction of fractions with the same denominators.

Lesson Content/Board Summary

Addition And Subtraction Of Fractions: Mixed Numbers And Applications

Understanding Mixed Numbers

A mixed number combines a whole number and a proper fraction. For example, (2 frac{1}{4}) means 2 whole units and (frac{1}{4}) of another unit.

To perform operations on mixed numbers, it is often helpful to convert them to improper fractions first. An improper fraction has a numerator that is greater than or equal to its denominator.

Converting Mixed Numbers to Improper Fractions:

1. Multiply the whole number by the denominator.
2. Add the numerator to the result.
3. Keep the same denominator.

Example: Convert (2 frac{1}{4}) to an improper fraction.

(2 times 4 = 8)

(8 + 1 = 9)

So, (2 frac{1}{4} = frac{9}{4})

Adding Mixed Numbers

To add mixed numbers, you can follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Add the improper fractions (ensure they have the same denominator).
3. Convert the result back to a mixed number if it is an improper fraction.

Example 1 (Addition)

Question: Add (2 frac{1}{4} + 1 frac{2}{4})

Solution:

Step 1: Convert mixed numbers to improper fractions.

(2 frac{1}{4} = frac{(2 times 4) + 1}{4} = frac{8 + 1}{4} = frac{9}{4})

(1 frac{2}{4} = frac{(1 times 4) + 2}{4} = frac{4 + 2}{4} = frac{6}{4})

Step 2: Add the improper fractions.

(frac{9}{4} + frac{6}{4} = frac{9 + 6}{4} = frac{15}{4})

Step 3: Convert the improper fraction back to a mixed number.

(frac{15}{4} = 15 div 4 = 3) with a remainder of (3)

So, (frac{15}{4} = 3 frac{3}{4})

Answer: (3 frac{3}{4})

Subtracting Mixed Numbers

To subtract mixed numbers, you can follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Subtract the improper fractions (ensure they have the same denominator).
3. Convert the result back to a mixed number if it is an improper fraction.

Example 2 (Subtraction)

Question: Subtract (3 frac{3}{5} – 1 frac{1}{5})

Solution:

Step 1: Convert mixed numbers to improper fractions.

(3 frac{3}{5} = frac{(3 times 5) + 3}{5} = frac{15 + 3}{5} = frac{18}{5})

(1 frac{1}{5} = frac{(1 times 5) + 1}{5} = frac{5 + 1}{5} = frac{6}{5})

Step 2: Subtract the improper fractions.

(frac{18}{5} – frac{6}{5} = frac{18 – 6}{5} = frac{12}{5})

Step 3: Convert the improper fraction back to a mixed number.

(frac{12}{5} = 12 div 5 = 2) with a remainder of (2)

So, (frac{12}{5} = 2 frac{2}{5})

Answer: (2 frac{2}{5})

Applications of Mixed Number Operations

Mixed numbers are used to solve problems in everyday life, such as measuring ingredients for cooking, calculating distances, or sharing items.

Example 3 (Word Problem)

Question: A tailor used (3 frac{1}{2}) metres of fabric for a dress and (1 frac{1}{2}) metres for a shirt. How much fabric did the tailor use in total?

Solution:

Step 1: Identify the operation needed (addition).

Step 2: Convert mixed numbers to improper fractions.

(3 frac{1}{2} = frac{(3 times 2) + 1}{2} = frac{7}{2})

(1 frac{1}{2} = frac{(1 times 2) + 1}{2} = frac{3}{2})

Step 3: Add the improper fractions.

(frac{7}{2} + frac{3}{2} = frac{7 + 3}{2} = frac{10}{2})

Step 4: Simplify the result.

(frac{10}{2} = 5)

Answer: The tailor used 5 metres of fabric in total.

Quantitative Aptitude Problems

These problems test your ability to solve mathematical problems quickly and accurately.

Example 4 (Quantitative Aptitude)

Question: What is the value of ( (4 frac{3}{8} – 2 frac{1}{8}) + 1 frac{5}{8} )?

Solution:

Step 1: Solve the subtraction in the bracket first.

(4 frac{3}{8} – 2 frac{1}{8} = frac{35}{8} – frac{17}{8} = frac{18}{8})

Step 2: Now add the result to (1 frac{5}{8}).

(frac{18}{8} + 1 frac{5}{8} = frac{18}{8} + frac{13}{8} = frac{31}{8})

Step 3: Convert the improper fraction to a mixed number.

(frac{31}{8} = 31 div 8 = 3) with a remainder of (7)

So, (frac{31}{8} = 3 frac{7}{8})

Answer: (3 frac{7}{8})

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Reviewing/Questioning

Teacher’s Activity: The teacher begins by asking pupils to recall what fractions are and to give examples of proper and improper fractions. The teacher also asks how to convert an improper fraction to a mixed number.

Pupils’ Activity: Pupils respond to the questions and provide examples of fractions and demonstrate conversion.

Learning Point: Fraction types recap

Step 2: Introduction to Adding Mixed Numbers

Time: 7 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher introduces the concept of adding mixed numbers, explaining that it involves combining whole numbers and fractions. The teacher uses fraction charts or cardboard cut-outs to visually represent a problem like (2 frac{1}{4} + 1 frac{2}{4}).

Pupils’ Activity: Pupils observe the visual demonstration and listen to the explanation.

Learning Point: Concept of mixed number addition

Step 3: Demonstration of Adding Mixed Numbers

Time: 7 minutes

Teaching Skill: Demonstration/Modelling

Teacher’s Activity: The teacher demonstrates the step-by-step process of adding mixed numbers using the example (2 frac{1}{4} + 1 frac{2}{4}) on the board, showing conversion to improper fractions, addition, and conversion back to a mixed number.

Pupils’ Activity: Pupils pay close attention to the steps and ask questions for clarification.

Learning Point: Steps for adding mixed numbers

Step 4: Practice Adding Mixed Numbers

Time: 5 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher provides another addition problem, e.g., (1 frac{3}{5} + 2 frac{1}{5}), and guides pupils to solve it individually or in pairs, offering support as needed.

Pupils’ Activity: Pupils attempt to solve the addition problem with guidance from the teacher.

Learning Point: Practising mixed number addition

Step 5: Introduction to Subtracting Mixed Numbers

Time: 5 minutes

Teaching Skill: Explanation/Comparison

Teacher’s Activity: The teacher introduces the concept of subtracting mixed numbers, highlighting similarities and differences with addition. The teacher uses a simple sharing scenario, e.g., “If I have (3 frac{3}{5}) oranges and give away (1 frac{1}{5}) oranges, how many are left?”

Pupils’ Activity: Pupils listen and relate the concept to real-life situations.

Learning Point: Concept of mixed number subtraction

Step 6: Demonstration and Practice of Subtracting Mixed Numbers

Time: 5 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher demonstrates the subtraction of mixed numbers using the example (3 frac{3}{5} – 1 frac{1}{5}) on the board. The teacher then provides a similar problem for pupils to solve.

Pupils’ Activity: Pupils observe the demonstration and then solve a practice problem.

Learning Point: Steps for subtracting mixed numbers

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. Add (3 frac{1}{3} + 2 frac{1}{3}).
2. Subtract (4 frac{2}{7} – 1 frac{1}{7}).
3. A baker used (2 frac{1}{4}) cups of flour for a cake and (1 frac{1}{4}) cups for cookies. How much flour was used in total?
4. What is ( (5 frac{3}{10} – 2 frac{1}{10}) + 1 frac{4}{10} )?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Mixed number operations assessment

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 adding and subtracting mixed numbers and their applications into their notebooks.

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

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Consolidation

Teacher’s Activity: The teacher briefly recaps the main points of the lesson, emphasizing the importance of converting to improper fractions and applying the operations to real-life problems. The teacher encourages pupils to practice more at home.

Pupils’ Activity: Pupils listen and ask any final questions.

Learning Point: Mixed number operations consolidated

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your mathematics notebook:

1. Add: (4 frac{1}{5} + 2 frac{3}{5})
2. Subtract: (5 frac{7}{9} – 3 frac{2}{9})
3. A farmer harvested (6 frac{1}{2}) baskets of yam and sold (2 frac{1}{2}) baskets. How many baskets of yam are left?
4. Find the value of ( (7 frac{5}{6} – 3 frac{1}{6}) + 1 frac{2}{6} ).
5. Create a word problem that involves adding mixed numbers and solve it.

Lesson Keywords

• Mixed Number – A number consisting of a whole number and a proper fraction.
• Improper Fraction – A fraction where the numerator is greater than or equal to the denominator.
• Numerator – The top number in a fraction, showing how many parts are being considered.
• Denominator – The bottom number in a fraction, showing the total number of equal parts.
• Addition – The process of combining two or more numbers to find their sum.
• Subtraction – The process of taking one number away from another to find the difference.

Differentiation

Support for weaker learners: Provide pre-converted improper fractions for some problems. Use more visual aids like fraction strips or drawings to represent mixed numbers. Focus on adding/subtracting whole numbers and fractions separately before converting to improper fractions.

Extension for faster learners: Challenge them with problems involving mixed numbers with different denominators (if they have prior knowledge of finding common denominators). Ask them to create their own complex word problems involving both addition and subtraction of mixed numbers.

Suggested Lesson Videos

For further understanding, search on YouTube for: “Adding and subtracting mixed numbers Primary 4”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure all instructional materials, especially fraction charts, flashcards, and number cards, are prepared and easily accessible. Begin by reviewing basic fraction concepts to activate prior knowledge. When demonstrating addition and subtraction of mixed numbers, clearly show the conversion to improper fractions as the primary method, linking it to the visual aids. Encourage pupils to participate actively in guided practice sessions. During the note-taking step, ensure pupils copy the Board Summary accurately. Pay close attention to common errors such as incorrect conversion between mixed and improper fractions or errors in adding/subtracting the numerators. Provide individual support to pupils who struggle and offer challenging extension tasks to those who grasp the concepts quickly. Emphasize the practical applications of mixed numbers to make the learning relevant.