Multiplication, Decimal by Decimal, Fraction by Fraction, Squares and Roots for Primary 5

Class: Primary 5
Term: 1st Term
Week: 7
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Number and Numeration
Previous Lesson: Multiplication, 3-Digit by 3-Digit, Decimals and Fractions ‘Of’.
Topic: MULTIPLICATION CONTINUED
Subject Matter: Multiplication of decimal fractions by decimal numbers, multiplication of fractions by fractions, squares of whole numbers more than 50, square roots of perfect squares greater than 400, quantitative aptitude on squares and square roots.

Specific Objectives

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

Cognitive Domain:

• Multiply decimal fractions by decimal numbers accurately.
• Multiply fractions by fractions and simplify answers to their lowest terms.
• Find the squares of whole numbers greater than 50.
• Find the square roots of perfect squares greater than 400.
• Solve quantitative aptitude problems related to squares and square roots.

Affective Domain:

• Appreciate the importance of accurate calculations in daily life.
• Develop an interest in solving mathematical problems involving multiplication, squares, and square roots.

Psychomotor Domain:

• Accurately perform multiplication operations involving decimals and fractions.
• Efficiently calculate squares and square roots of given numbers.

Social Domain:

• Participate actively in class discussions and problem-solving activities.
• Work collaboratively with peers to solve mathematical problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum for Primary 5.
• State Unified Scheme of Work for Primary 5.
• New General Mathematics for Primary Schools, Book 5.
• https://www.education.gov.ng
• https://www.nigeriancurriculum.org

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing multiplication examples.
• Flash cards with decimal and fraction multiplication problems.
• Counters.
• Abacus chart.
• Quantitative aptitude book.
• Fraction cards.

Rationale for the Lesson

This lesson helps pupils build on their understanding of multiplication by extending it to decimal and fractional numbers. Learning about squares and square roots is important as it lays the foundation for more advanced mathematical concepts and helps in solving practical problems in daily life, such as calculating areas or understanding numerical patterns.

Prerequisite/Previous Knowledge

Pupils can multiply whole numbers, understand basic concepts of fractions and decimals, and have some knowledge of basic multiplication tables.

Lesson Content/Board Summary

Multiplication Continued

Multiplication of Decimal Fractions by Decimal Numbers

To multiply decimal fractions by decimal numbers, follow these steps:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the numbers being multiplied.
3. Place the decimal point in the product by counting from the right the total number of decimal places found in step 2.

Example 1: Multiply 0.3 by 0.4

• Step 1: Multiply 3 x 4 = 12. (Multiply as whole numbers)
• Step 2: Count decimal places (0.3 has 1, 0.4 has 1; total = 2 decimal places).
• Step 3: Place the decimal point 2 places from the right in 12.
• Result = 0.12.

Example 2: Multiply 1.25 by 0.6

• Step 1: Multiply 125 x 6 = 750. (Multiply as whole numbers)
• Step 2: Count decimal places (1.25 has 2, 0.6 has 1; total = 3 decimal places).
• Step 3: Place the decimal point 3 places from the right in 750.
• Result = 0.750 or 0.75.

Multiplication of Fractions by Fractions

To multiply fractions by fractions, follow these steps:

1. Multiply the numerators (top numbers) together.
2. Multiply the denominators (bottom numbers) together.
3. Simplify the resulting fraction to its lowest terms if possible.

Example 1: Multiply 1/2 by 3/4

• Step 1: Multiply numerators: 1 x 3 = 3.
• Step 2: Multiply denominators: 2 x 4 = 8.
• Step 3: The fraction is 3/8. It cannot be simplified further.

Example 2: Multiply 2/3 by 9/10

• Step 1: Multiply numerators: 2 x 9 = 18.
• Step 2: Multiply denominators: 3 x 10 = 30.
• Step 3: The fraction is 18/30. Simplify by dividing both by 6.
• Result = 3/5.

NOTE: Cross-cancellation can be used before multiplying to simplify earlier.

Squares of Whole Numbers Greater Than 50

The square of a number is the result of multiplying the number by itself. It is written as n².

Example 1: Find the square of 52.

• Step 1: Multiply the number by itself.
• 52² = 52 x 52.
• Step 2: Perform the multiplication.
• 52 x 52 = 2704.

Example 2: Find the square of 60.

• Step 1: Multiply the number by itself.
• 60² = 60 x 60.
• Step 2: Perform the multiplication.
• 60 x 60 = 3600.

Square Roots of Perfect Squares Greater Than 400

The square root of a number is a value that, when multiplied by itself, gives the original number. It is written as √n.

To find the square root of a perfect square, look for a number that, when multiplied by itself, gives the original number.

Example 1: Find the square root of 441.

• Step 1: Look for a number that, when multiplied by itself, gives 441.
• Consider numbers ending in 1 or 9. Try 21.
• Step 2: Perform the multiplication.
• 21 x 21 = 441.
• Therefore, √441 = 21.

Example 2: Find the square root of 625.

• Step 1: Look for a number that, when multiplied by itself, gives 625.
• Consider numbers ending in 5. Try 25.
• Step 2: Perform the multiplication.
• 25 x 25 = 625.
• Therefore, √625 = 25.

Quantitative Aptitude on Squares and Square Roots

Quantitative aptitude problems test a pupil’s ability to quickly and accurately solve problems involving numbers, often requiring logical reasoning.

Example 1: If the square of a number is 64, what is the number?

• Step 1: Understand that “the square of a number is 64” means X² = 64.
• Step 2: Find the square root of 64.
• √64 = 8.
• The number is 8.

Example 2: Which number when multiplied by itself gives 900?

• Step 1: This question is asking for the square root of 900.
• Step 2: Find the square root of 900.
• √900 = 30.
• The number is 30.

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 simple multiplication. The teacher then introduces the day’s topic, “Multiplication Continued,” explaining that they will learn how to multiply different types of numbers and explore related concepts like squares and square roots.
Pupils’ Activity: Pupils respond to greetings, recall the previous lesson, and listen attentively to the introduction of the new topic.
Learning Point: Pupils are prepared for the lesson and understand the context of the day’s topic.

Step 2: Multiplication of Decimal Fractions by Decimal Numbers

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the steps for multiplying decimal fractions by decimal numbers, using the examples from the board summary. The teacher demonstrates the process clearly on the board, emphasizing counting decimal places.
Pupils’ Activity: Pupils listen, observe the examples, and ask questions for clarification. They copy the examples into their notebooks.
Learning Point: Pupils learn how to multiply decimal fractions by decimal numbers.

Step 3: Multiplication of Fractions by Fractions

Time: 10 minutes
Teaching Skill: Explanation/Guided Practice
Teacher’s Activity: The teacher explains the process of multiplying fractions by fractions, including how to simplify answers. The teacher works through examples on the board, encouraging pupils to participate in simplifying.
Pupils’ Activity: Pupils follow the teacher’s explanation, participate in solving examples, and practice multiplying fractions in their notebooks.
Learning Point: Pupils understand how to multiply fractions and simplify their answers.

Step 4: Squares of Whole Numbers Greater Than 50

Time: 5 minutes
Teaching Skill: Definition/Application
Teacher’s Activity: The teacher defines what a square of a number is and demonstrates how to find the square of numbers greater than 50 using examples like 52² and 60².
Pupils’ Activity: Pupils listen to the definition, observe the examples, and calculate squares of similar numbers.
Learning Point: Pupils learn to find the squares of whole numbers greater than 50.

Step 5: Square Roots of Perfect Squares Greater Than 400

Time: 5 minutes
Teaching Skill: Definition/Problem Solving
Teacher’s Activity: The teacher defines the square root of a number and explains how to find the square roots of perfect squares greater than 400, using examples like √441 and √625.
Pupils’ Activity: Pupils understand the concept of square roots and practice finding them for given numbers.
Learning Point: Pupils learn to find the square roots of perfect squares greater than 400.

Step 6: Quantitative Aptitude on Squares and Square Roots

Time: 5 minutes
Teaching Skill: Problem Solving/Critical Thinking
Teacher’s Activity: The teacher introduces quantitative aptitude problems related to squares and square roots. The teacher presents simple word problems and guides pupils through the logical steps to solve them.
Pupils’ Activity: Pupils attempt to solve the quantitative aptitude problems and discuss their reasoning.
Learning Point: Pupils apply their knowledge of squares and square roots to solve 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. Multiply 0.5 by 0.7.
2. Find the product of 1/3 and 2/5.
3. What is the square of 55?
4. Find the square root of 900.
5. If the square of a number is 169, what is the number?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 0 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of multiplication, squares, and square roots in mathematics. The teacher assigns homework for further practice.
Pupils’ Activity: Pupils listen to the summary and note down the homework.
Learning Point: Pupils consolidate their learning and are encouraged to practice further.

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

Lesson Keywords

• Decimal Fraction – A fraction where the denominator is a power of ten, written using a decimal point.
• 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.
• Square – The product of a number multiplied by itself (e.g., 5² = 25).
• Square Root – A number that, when multiplied by itself, gives the original number (e.g., √25 = 5).
• Quantitative Aptitude – Problems that test numerical ability and logical reasoning.

Differentiation

For pupils who are struggling, the teacher will provide additional simpler examples and use visual aids more extensively. They will be given extra practice problems with step-by-step guidance. For advanced pupils, challenging quantitative aptitude questions will be provided, and they may be asked to explore more complex square and square root problems or investigate patterns in squares of numbers.

Note for teachers using this lesson plan

Ensure that pupils have a strong foundation in basic multiplication before proceeding with decimal and fraction multiplication. Emphasize the importance of clear working steps for all calculations. Encourage mental math practice for squares of smaller numbers to build confidence. Use the instructional materials effectively to make abstract concepts more concrete. Provide ample opportunities for pupils to practice independently and in groups.