Multiplying Fractions and Decimals by Two-Digit Numbers for Primary 4

Class: Primary 4
Term: Second Term
Week: 2
Age: 9 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Basic Operations
Focal competence: Multiplying whole numbers with sum less than 50
Key competencies/values: ICT and Digital Competencies
Skills:

• Using multiplication bingo or mastery tools to solve multiplication problems

Previous Lesson: Multiplication of Whole Numbers Less Than or Equal to 50 and Quantitative Reasoning
Topic: Multiplication: Fractions And Decimals
Subject Matter: Multiplication of fractions and multiplication of decimals by 2-digit numbers

Specific Objectives

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

Cognitive Domain

• Identify the numerator and denominator in a fraction.
• Explain the process of multiplying fractions.
• State the steps for multiplying decimals by 2-digit numbers.

Affective Domain

• Appreciate the importance of accuracy in mathematical calculations.
• Show confidence in solving multiplication problems involving fractions and decimals.

Psychomotor Domain

• Perform multiplication of fractions accurately.
• Multiply decimals by 2-digit numbers correctly.
• Draw simple diagrams to represent fraction multiplication.

Social Domain

• Collaborate effectively with peers during group practice sessions.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• Essential Mathematics for Primary Schools Book 4
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing examples of fraction and decimal multiplication
• Number cards
• Flash cards with multiplication problems
• Cardboard for visual models
• Multimedia applications (if available, for interactive practice)
• Fraction strips or circles

Rationale for the Lesson

This lesson is important as it builds on pupils’ understanding of basic multiplication and fractions, extending it to more complex scenarios involving decimals and two-digit numbers. Mastering these skills is fundamental for everyday calculations, problem-solving, and further mathematical studies, preparing pupils for practical applications in real-world contexts.

Prerequisite/Previous Knowledge

Pupils should have a basic understanding of multiplication of whole numbers, the concept of fractions (numerator and denominator), and simple decimals.

Lesson Content/Board Summary

Multiplication: Fractions And Decimals

Multiplication of Fractions

To multiply fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

Fraction Notation:

1. Numerator: The top number of a fraction, which tells us how many parts of the whole we have.
2. Denominator: The bottom number of a fraction, which tells us the total number of equal parts the whole is divided into.

Visualising Fraction Multiplication:

Multiplying fractions can be thought of as finding “a fraction of a fraction”. For example, ( frac{2}{3} times frac{3}{5} ) means finding ( frac{2}{3} ) of ( frac{3}{5} ).

Imagine a rectangle divided into 5 equal parts, with 3 of them shaded to represent ( frac{3}{5} ). Then, divide the same rectangle into 3 equal parts horizontally. If you take 2 of these horizontal parts from the shaded area, you will see the result.

Formula for Multiplying Fractions

( frac{a}{b} times frac{c}{d} = frac{a times c}{b times d} )

Example 1 (Fractions)

Question: Multiply ( frac{2}{3} ) by ( frac{3}{5} ).

Solution:

Step 1: Multiply the numerators.

( 2 times 3 = 6 )

Step 2: Multiply the denominators.

( 3 times 5 = 15 )

Step 3: Write the new fraction and simplify if possible.

( frac{6}{15} )

To simplify, find a common factor for 6 and 15, which is 3.

( frac{6 div 3}{15 div 3} = frac{2}{5} )

Answer: ( frac{2}{5} )

Example 2 (Fractions)

Question: Find the product of ( frac{1}{4} ) and ( frac{2}{3} ).

Solution:

Step 1: Multiply the numerators.

( 1 times 2 = 2 )

Step 2: Multiply the denominators.

( 4 times 3 = 12 )

Step 3: Write the new fraction and simplify.

( frac{2}{12} )

Simplify by dividing both by 2.

( frac{2 div 2}{12 div 2} = frac{1}{6} )

Answer: ( frac{1}{6} )

Multiplication of Decimals by 2-Digit Numbers

To multiply a decimal by a 2-digit number, follow these steps:

1. Ignore the decimal point and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the decimal number.
3. Place the decimal point in the product so that it has the same number of decimal places as counted in step 2.

Example 1 (Decimals)

Question: Multiply ( 2.4 ) by ( 12 ).

Solution:

Step 1: Multiply the numbers as whole numbers (24 x 12).

( 24 times 12 )

( quad 24 )

( underline{times 12} )

( quad 48 quad (24 times 2) )

( underline{240 quad (24 times 10)} )

( quad 288 )

Step 2: Count the decimal places in the original decimal number.

( 2.4 ) has one decimal place.

Step 3: Place the decimal point in the product.

The product ( 288 ) needs one decimal place. So, ( 28.8 ).

Answer: ( 28.8 )

Example 2 (Decimals)

Question: Calculate ( 3.5 times 21 ).

Solution:

Step 1: Multiply ( 35 ) by ( 21 ).

( quad 35 )

( underline{times 21} )

( quad 35 quad (35 times 1) )

( underline{700 quad (35 times 20)} )

( quad 735 )

Step 2: Count decimal places.

( 3.5 ) has one decimal place.

Step 3: Place decimal point in the product.

( 73.5 )

Answer: ( 73.5 )

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher greets the pupils and asks questions about previous knowledge of fractions and multiplication of whole numbers. For example: “What is a fraction?” “What are the parts of a fraction called?” “What is 5 multiplied by 6?”

Pupils’ Activity: Pupils respond to the questions, recalling their prior knowledge.

Learning Point: Prior knowledge activation

Step 2: Introduction to Fraction Multiplication

Time: 8 minutes

Teaching Skill: Explaining/Demonstrating

Teacher’s Activity: The teacher introduces the concept of multiplying fractions. Using fraction strips or drawings on the board, the teacher demonstrates what it means to find “a fraction of a fraction” (e.g., ( frac{1}{2} ) of ( frac{1}{4} )). The teacher explains the rule: multiply numerators and denominators.

Pupils’ Activity: Pupils observe the demonstration and listen to the explanation, asking questions for clarity.

Learning Point: Fraction multiplication concept

Step 3: Worked Examples for Fractions

Time: 7 minutes

Teaching Skill: Modelling/Guiding

Teacher’s Activity: The teacher writes the formula for multiplying fractions on the board and works through Example 1 and Example 2 from the Board Summary step-by-step, explaining each stage, including simplification.

Pupils’ Activity: Pupils pay attention to the steps and copy the examples into their rough notebooks.

Learning Point: Solving fraction problems

Step 4: Introduction to Decimal Multiplication

Time: 5 minutes

Teaching Skill: Explaining/Connecting

Teacher’s Activity: The teacher introduces multiplication of decimals by 2-digit numbers. The teacher explains that it is similar to whole number multiplication but requires careful placement of the decimal point. The teacher highlights the steps involved.

Pupils’ Activity: Pupils listen to the explanation and understand the connection to whole number multiplication.

Learning Point: Decimal multiplication steps

Step 5: Worked Examples for Decimals

Time: 7 minutes

Teaching Skill: Modelling/Illustrating

Teacher’s Activity: The teacher works through Example 1 and Example 2 for decimal multiplication from the Board Summary, demonstrating how to multiply as whole numbers first and then correctly place the decimal point. The teacher emphasizes counting decimal places.

Pupils’ Activity: Pupils observe the steps and practice solving the examples in their rough notebooks.

Learning Point: Solving decimal problems

Step 6: Guided Practice

Time: 4 minutes

Teaching Skill: Facilitating/Monitoring

Teacher’s Activity: The teacher writes a few practice questions on the board (e.g., ( frac{1}{2} times frac{4}{5} ), ( 1.5 times 10 )) and guides pupils to solve them individually or in pairs. The teacher walks around to provide support and check progress.

Pupils’ Activity: Pupils attempt the practice questions, seeking help when needed.

Learning Point: Application of rules

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. Multiply ( frac{3}{4} ) by ( frac{1}{2} ).
2. What are the numerator and denominator in ( frac{5}{8} )?
3. Calculate ( 3.2 times 15 ).
4. Explain how to place the decimal point when multiplying decimals.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding multiplication processes

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, including the rules and worked examples for multiplying fractions and decimals, into their notebooks.

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

Learning Point: Recording key information

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Summarising/Consolidating

Teacher’s Activity: The teacher briefly recaps the main points of the lesson, emphasizing the importance of careful calculation and decimal point placement. The teacher encourages pupils to practice more at home.

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

Learning Point: Lesson consolidation

Continuous Assessment/Further Study

Type: Homework

Instruction: Solve the following problems in your mathematics notebook:

1. Multiply ( frac{1}{3} ) by ( frac{2}{5} ).
2. Calculate ( frac{3}{7} times frac{2}{3} ).
3. Find the product of ( 4.1 ) and ( 20 ).
4. Multiply ( 0.75 ) by ( 14 ).
5. A recipe requires ( frac{3}{4} ) cup of flour. If you want to make ( frac{1}{2} ) of the recipe, how much flour do you need?

Lesson Keywords

• Fraction – A part of a whole.
• Numerator – The top number in a fraction, showing how many parts are taken.
• Denominator – The bottom number in a fraction, showing the total number of equal parts.
• Decimal – A number that contains a decimal point, representing a part of a whole number.
• Product – The result of multiplication.

Differentiation

For weaker learners, provide additional visual aids like pre-drawn fraction models or enlarged number cards. Focus on one type of multiplication at a time (fractions first, then decimals) with simpler examples and more guided practice. For faster learners, introduce problems with mixed numbers or more complex decimal numbers, or challenge them to create their own word problems involving fraction and decimal multiplication.

Suggested Lesson Videos

For further understanding, pupils can search for “Multiplying Fractions Primary 4” or “Multiplying Decimals by 2-Digit Numbers for Kids” on YouTube.

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have all instructional materials ready, especially charts displaying fraction and decimal multiplication examples, and visual aids for fractions. Begin by reviewing basic multiplication and fraction concepts to activate prior knowledge. When teaching fraction multiplication, use visual models to illustrate the concept of “of” before introducing the formal rule. For decimal multiplication, emphasize the importance of multiplying as whole numbers first and then carefully placing the decimal point by counting decimal places. During guided practice, circulate among pupils to offer immediate feedback and support. Encourage pupils to explain their reasoning. The Board Summary should be copied by pupils after the main concepts have been taught and understood, typically during Step 8. Check for understanding frequently through questions and short exercises. Provide extra support for pupils struggling with either concept and offer challenging problems for those who grasp the concepts quickly.