Class: Primary 4
Term: 1st Term
Week: 9
Age: 9 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Addition and Subtraction, Fractions, Decimals and Reasoning.
Topic: MULTIPLICATION
Subject Matter: Squares of 1-digit, 2-digit and 3-digit numbers, square roots of perfect squares up to 400 using square chart and factor method, quantitative reasoning on squares and square roots, multiplication of decimals by 2-digit numbers, quantitative reasoning on multiplication.

Specific Objectives

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

Cognitive Domain:

Define multiplication and the square of a number.
Multiply 2-digit and 3-digit whole numbers by 2-digit whole numbers.
Multiply decimals by 2-digit numbers.
Find the squares of 1-digit, 2-digit, and 3-digit numbers using a square chart.
Define the square root of a number.
Find the square roots of perfect squares up to 400 using a square chart.
Calculate square roots of perfect squares using the factor method.
Solve quantitative reasoning problems involving multiplication, squares, and square roots.

Affective Domain:

Participate actively in class discussions.
Develop an interest in solving problems involving squares and square roots.

Psychomotor Domain:

Accurately perform multiplication operations.
Correctly use a square chart to find squares and square roots.
Demonstrate the steps of the factor method for square roots.

Work cooperatively in groups to solve problems.

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 4

Instructional Materials

The teacher will teach this lesson with the aid of:

Square multiplication table
Textbook
Chart showing examples of squares and square roots
Objects with square faces (e.g., dice, building blocks)

Rationale for the Lesson

This lesson helps pupils understand how to perform multiplication with larger numbers and decimals, which is a basic skill for everyday calculations. It also introduces them to squares and square roots, which are fundamental concepts in higher mathematics and geometry.

Prerequisite/Previous Knowledge

Pupils have learned basic multiplication tables and concepts of whole numbers.

Lesson Content/Board Summary

Multiplication, Squares, and Square Roots

Multiplication of Whole Numbers

Multiplication is a repeated addition of a number to itself a certain number of times. For example, 3 x 4 means 3 added to itself 4 times (3 + 3 + 3 + 3).

To multiply larger whole numbers (e.g., 2-digit or 3-digit numbers by 2-digit numbers), arrange the numbers vertically and multiply each digit, carrying over when necessary.

Multiplication of Decimals by 2-digit Numbers

To multiply a decimal number by a 2-digit whole number:

Multiply the numbers as if they were whole numbers, ignoring the decimal point.
Count the total number of decimal places in the decimal number.
Place the decimal point in the product so that it has the same number of decimal places as counted in the previous step.

Squares of Numbers

The square of a number is the result of multiplying the number by itself. It is written with a small ‘2’ above the number (e.g., 5²).

Examples:

2² = 2 x 2 = 4
10² = 10 x 10 = 100
15² = 15 x 15 = 225

Squares of numbers can be found using a square chart or by direct multiplication. Objects with perfect square faces include dice, Rubik’s cubes, and some building blocks.

Square Roots of Perfect Squares

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

Examples:

√4 = 2 (because 2 x 2 = 4)
√100 = 10 (because 10 x 10 = 100)

Square roots of perfect squares up to 400 can be found using a square chart.

The factor method for finding square roots involves:

Breaking down the number into its prime factors.
Grouping identical prime factors in pairs.
Multiplying one factor from each pair to get the square root.

Example: To find √36

Prime factors of 36 are 2 x 2 x 3 x 3.
Group pairs: (2 x 2) x (3 x 3).
Take one from each pair: 2 x 3 = 6. So, √36 = 6.

Quantitative Reasoning on Multiplication, Squares, and Square Roots

Quantitative reasoning involves solving problems using mathematical concepts and logical thinking. These problems often present patterns or relationships that require pupils to apply their knowledge of multiplication, squares, and square roots to find missing numbers or solutions.

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, checks attendance, and reviews the previous lesson on basic multiplication. The teacher then introduces the topic by asking pupils to state what they know about multiplying numbers and what happens when a number is multiplied by itself.
Pupils’ Activity: Pupils respond to greetings, answer questions about multiplication, and listen attentively.
Learning Point: Pupils recall prior knowledge of multiplication and are prepared for the new topic.

Step 2: Revision of Multiplication of Whole Numbers

Time: 5 minutes
Teaching Skill: Explaining/Recall
Teacher’s Activity: The teacher guides pupils to revise multiplication of 2-digit numbers by 1-digit numbers using a few examples on the board.
Pupils’ Activity: Pupils solve revision problems on their slates and participate in discussions.
Learning Point: Pupils refresh their understanding of basic multiplication principles.

Step 3: Multiplication of Larger Whole Numbers and Decimals

Time: 9 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher demonstrates how to multiply 2-digit and 3-digit whole numbers by 2-digit whole numbers with clear examples. The teacher then explains and demonstrates how to multiply decimals by 2-digit numbers, emphasizing decimal point placement.
Pupils’ Activity: Pupils observe the teacher’s demonstrations, ask questions, and practice solving similar problems in their notebooks.
Learning Point: Pupils learn to multiply larger whole numbers and decimals accurately.

Step 4: Introduction to Squares of Numbers

Time: 5 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher introduces the concept of squares of numbers by defining what a square of a number is (a number multiplied by itself). The teacher shows how to write it (e.g., 4²) and provides simple examples like 2² and 3². The teacher also asks pupils to identify objects with perfect square faces.
Pupils’ Activity: Pupils listen, define a square of a number, and identify objects with square faces around the classroom.
Learning Point: Pupils understand the concept and notation of squares of numbers.

Step 5: Finding Squares and Square Roots

Time: 9 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher uses a square chart to demonstrate how to find squares of 1-digit, 2-digit, and 3-digit numbers. The teacher then introduces square roots, explains the symbol (√), and demonstrates how to find square roots of perfect squares up to 400 using the square chart. The teacher further explains and demonstrates the factor method for finding square roots with an example like √36.
Pupils’ Activity: Pupils observe the use of the square chart, practice finding squares and square roots, and follow the steps of the factor method.
Learning Point: Pupils learn practical methods for calculating squares and square roots.

Step 6: Quantitative Reasoning

Time: 6 minutes
Teaching Skill: Problem-solving/Application
Teacher’s Activity: The teacher presents various quantitative reasoning problems involving multiplication, squares, and square roots on the board. The teacher guides pupils through solving these problems, encouraging logical thinking and application of learned concepts.
Pupils’ Activity: Pupils attempt to solve the quantitative reasoning problems individually or in small groups, sharing their approaches and solutions.
Learning Point: Pupils apply their knowledge to solve practical and reasoning-based 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:

What is the square of a number?
Multiply 125 by 23.
Find 0.45 multiplied by 15.
What is the square root of 225?
Explain how to find the square root of 64 using the factor method.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the importance of accurate calculations in multiplication, squares, and square roots. The teacher gives pupils homework to practice.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their learning and are assigned further practice.

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

Lesson Keywords

Multiplication – A mathematical operation where a number is added to itself a certain number of times.
Decimal – A number that contains a decimal point, separating the whole number part from the fractional part.
Square – The result of multiplying a number by itself.
Square Root – A number that, when multiplied by itself, gives the original number.
Perfect Square – A number that is the square of an integer (e.g., 4, 9, 16).
Factor Method – A method of finding the square root of a number by breaking it down into its prime factors.
Quantitative Reasoning – Solving problems using numerical and logical skills.

Differentiation

For struggling learners, the teacher will provide additional guided practice with simpler multiplication problems and focus on using the square chart for squares and square roots. Advanced learners will be given more complex quantitative reasoning problems and challenged to find square roots of larger numbers or explore patterns in squares.

Note for teachers using this lesson plan

Ensure pupils have a good grasp of basic multiplication tables before introducing larger numbers and decimals. Provide ample opportunities for practice, both individually and in groups. Encourage pupils to explain their reasoning when solving problems, especially in quantitative reasoning. Use visual aids like the square chart effectively throughout the lesson.