Squares of one- and two-digit numbers for Primary 4

Class: Primary 4
Term: Second Term
Week: 3
Age: 9 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Basic Operations
Focal competence: Calculating square of 1- and 2- digit numbers and square root of perfect squares up to 9 00
Key competencies/values: Collaboration
Skills:

• Using mathematics square/square-root tools to solve related problems

Previous Lesson: Multiplying Fractions and Decimals by Two-Digit Numbers
Topic: Multiplication: Squares
Subject Matter: Squares of one- and two-digit numbers

Specific Objectives

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

Cognitive Domain

• Define the square of a number.
• Identify the notation for squaring a number.
• Calculate the squares of given one-digit numbers.
• Calculate the squares of given two-digit numbers.

Affective Domain

• Appreciate the importance of accurate multiplication in squaring numbers.
• Show interest in solving problems involving squares.

Psychomotor Domain

• Demonstrate the process of squaring numbers using number cards.
• Accurately write down the squares of one- and two-digit numbers.

Reference Materials

The following resources were used in planning this lesson:

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

Instructional Materials

The teacher will teach this lesson with the aid of:

• Square root charts
• Number cards
• Flash cards
• Cardboard
• Multimedia applications
• Whiteboard and markers

Rationale for the Lesson

Understanding squares of numbers is fundamental in mathematics, forming a basis for algebra, geometry, and other advanced topics. This lesson helps pupils develop their multiplication skills and introduces them to a key mathematical operation, enhancing their numerical reasoning and problem-solving abilities.

Prerequisite/Previous Knowledge

Pupils should have a good understanding of basic multiplication facts and be able to multiply two-digit numbers by one-digit numbers, and two-digit numbers by two-digit numbers.

Lesson Content/Board Summary

Multiplication: Squares of One- and Two-Digit Numbers

What is a Square of a Number?

The square of a number is the result of multiplying that number by itself. For example, the square of 3 is (3 times 3 = 9).

We can write the square of a number using a small ‘2’ above and to the right of the number. This is called an exponent or power.

For example, (3 times 3) can be written as (3^2), which is read as “3 squared”.

Squares of One-Digit Numbers

To find the square of a one-digit number, multiply the number by itself.

Example 1

Question: Find the square of 5.

Solution:

Step 1: Write the number to be squared.

(5)

Step 2: Multiply the number by itself.

(5 times 5)

Step 3: Calculate the product.

(5 times 5 = 25)

Answer: The square of 5 is (25).

Example 2

Question: Calculate (7^2).

Solution:

Step 1: Understand the notation.

(7^2) means (7 times 7)

Step 2: Multiply the numbers.

(7 times 7 = 49)

Answer: (7^2 = 49).

Squares of Two-Digit Numbers

To find the square of a two-digit number, multiply the number by itself using the standard multiplication method.

Example 1

Question: Find the square of 12.

Solution:

Step 1: Write the number to be squared.

(12)

Step 2: Multiply the number by itself.

(12 times 12)

Step 3: Perform the multiplication.

(12)

(times 12)

(—–)

(24) (This is (2 times 12))

(+ 120) (This is (10 times 12))

(—–)

(144)

Answer: The square of 12 is (144).

Example 2

Question: Calculate (15^2).

Solution:

Step 1: Understand the notation.

(15^2) means (15 times 15)

Step 2: Perform the multiplication.

(15)

(times 15)

(—–)

(75) (This is (5 times 15))

(+ 150) (This is (10 times 15))

(—–)

(225)

Answer: (15^2 = 225).

Checking Method

The best way to check your answer when calculating squares is to re-do the multiplication carefully. You can also use a calculator to verify your answer if available, but it’s important to understand the manual calculation process first.

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Activating prior knowledge

Teacher’s Activity: The teacher greets the pupils and asks them to recall what multiplication means. The teacher then introduces the idea of multiplying a number by itself.

Pupils’ Activity: Pupils respond to questions about multiplication and listen attentively.

Learning Point: Recall of multiplication

Step 2: Defining Squares

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher defines a square of a number as the number multiplied by itself. Using number cards, the teacher demonstrates simple squares like (2 times 2 = 4) and (3 times 3 = 9), explaining the notation (2^2) and (3^2).

Pupils’ Activity: Pupils observe the demonstration and repeat the definition and notation.

Learning Point: Meaning of square

Step 3: Calculating Squares of One-Digit Numbers

Time: 8 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher writes various one-digit numbers on the board (e.g., 4, 6, 8) and guides pupils through calculating their squares step-by-step, emphasizing the multiplication process. The teacher uses flashcards to show numbers and their squares.

Pupils’ Activity: Pupils participate in the calculation, providing answers and writing down the steps.

Learning Point: Squaring one-digit numbers

Step 4: Introducing Squares of Two-Digit Numbers

Time: 7 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains that the process for two-digit numbers is the same, just requiring more steps in multiplication. The teacher writes a two-digit number like 10 or 11 and sets up the multiplication problem.

Pupils’ Activity: Pupils listen and observe the setup of two-digit multiplication.

Learning Point: Concept of two-digit squares

Step 5: Worked Example for Two-Digit Numbers

Time: 7 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher demonstrates one full example of squaring a two-digit number (e.g., (12^2)) on the board, showing each step of the multiplication clearly. The teacher also shows a simple checking method by re-calculating.

Pupils’ Activity: Pupils carefully follow the steps and ask questions for clarification.

Learning Point: Calculating two-digit squares

Step 6: Practice with Two-Digit Numbers

Time: 6 minutes

Teaching Skill: Individual Practice

Teacher’s Activity: The teacher gives pupils one or two simple two-digit numbers (e.g., (13^2), (14^2)) to calculate their squares independently or in pairs. The teacher walks around to provide support.

Pupils’ Activity: Pupils work on solving the problems in their notebooks.

Learning Point: Application of squaring 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. What does it mean to find the square of a number?
2. Calculate the square of 6.
3. Find (9^2).
4. Work out the square of 11.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding number squares

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 definitions and worked examples for squares of one- and two-digit numbers, into their notebooks.

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

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Consolidation

Teacher’s Activity: The teacher briefly summarizes that squaring a number means multiplying it by itself and encourages pupils to practice more at home. The teacher praises pupils for their participation.

Pupils’ Activity: Pupils listen and acknowledge the summary.

Learning Point: Reinforcement of squares

Continuous Assessment/Further Study

Type: Homework

Instruction: Calculate the squares of the following numbers in your notebooks:

1. (4^2)
2. (8^2)
3. The square of 10
4. The square of 16
5. (19^2)

Lesson Keywords

• Square – The result of multiplying a number by itself.
• Exponent – A small number written above and to the right of a base number, indicating how many times the base number is multiplied by itself.
• Multiply – To combine numbers by repeated addition.
• One-digit number – A number from 0 to 9.
• Two-digit number – A number from 10 to 99.

Differentiation

For weaker learners: Provide additional practice with one-digit squares and simpler two-digit squares (e.g., 10, 11). Use multiplication tables to aid their recall. Pair them with stronger learners for guided practice.

For faster learners: Challenge them with squaring slightly larger two-digit numbers (e.g., 20, 25) or introduce the concept of perfect squares and how they relate to square roots, if appropriate.

Suggested Lesson Videos

For further understanding, pupils can search for “Squares of numbers for kids” or “How to find the square of a number” on YouTube.

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have all instructional materials, especially number cards and flashcards, ready to visually demonstrate the concept of squaring. Begin by reviewing basic multiplication to ensure pupils have a solid foundation. When demonstrating, clearly show the multiplication process for both one- and two-digit numbers, emphasizing that squaring is simply multiplying a number by itself. Encourage pupils to participate actively during guided practice and provide immediate feedback. During the independent practice, monitor pupils closely and offer support where needed. The Board Summary should be copied by pupils after the evaluation to ensure they have grasped the core concepts. For the homework, remind pupils to show their working clearly. Pay attention to common multiplication errors when pupils are squaring two-digit numbers.