Squares and Square Roots of Whole Numbers
SECOND TERM LESSON NOTE
SUBJECT: Mathematics
CLASS: Basic Four / Primary 4
TERM: Second Term
WEEK: 5
AGE: 8–9 years
TOPIC: Squares and Square Roots of Whole Numbers
Sub-topic: Understanding Squares and Square Roots
Duration: 40 minutes
Behavioral Objectives: By the end of the lesson, pupils should be able to:
- Calculate the square of numbers from 1 to 20.
- Identify perfect squares from a given set of numbers (e.g., 1–20).
- Find the square root of perfect squares up to 400.
- Solve word problems involving the square and square root of numbers.
Keywords: Square, Square Root, Perfect Squares, Numbers, Multiply
Set Induction:
Ask pupils simple multiplication questions, such as:
- “What is 2 × 2?”
- “What is 3 × 3?”
- “If I multiply a number by itself, what do we call that number?”
Relate their responses to the concept of squares and square roots to introduce the topic.
Entry Behavior:
Pupils are familiar with multiplication and can perform simple calculations involving numbers.
Learning Resources and Materials:
- Flashcards with numbers 1–100
- Cardboard for square and square root activities
- Scissors for cutting shapes or cards
- Songs or rhymes about numbers
Building Background/Connection to Prior Knowledge:
Review multiplication tables with the class and highlight the concept of repeated multiplication (e.g., 3 × 3 = 9).
Embedded Core Skills:
- Critical Thinking and Problem-Solving Skills
- Communication and Collaboration
- Creativity and Imagination
Content:
1. Definition of Squares and Square Roots
- A square is the result of multiplying a number by itself.
Example: 3 × 3 = 9, so 9 is a square number. - A square root is the number that, when multiplied by itself, gives a square.
Example: √9 = 3 because 3 × 3 = 9.
2. Examples of Square Numbers (1 to 20):
1² = 1 × 1 = 1
2² = 2 × 2 = 4
3² = 3 × 3 = 9
4² = 4 × 4 = 16
5² = 5 × 5 = 25
…
20² = 20 × 20 = 400
3. Examples of Perfect Squares:
Perfect squares from 1 to 20 are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, and 400.
4. Finding Square Roots:
The square root is the reverse of squaring a number. For example:
- √16 = 4 because 4 × 4 = 16.
- √100 = 10 because 10 × 10 = 100.
5. Solving Word Problems:
If a number represents the side of a square, its area is the square of that number.
Examples:
- A square has an area of 36 square meters. What is the length of one side? √36 = 6 meters.
- A farmer’s field has an area of 81 square meters. What is the side length of the square field? √81 = 9 meters.
Exercise 1:
Solve the following:
- Find 4² + 6²
- Subtract: 5² – 2²
- Add: 5² + 7²
- Subtract: 10² – 5²
- Find the sum: 8² + 10²
Exercise 2:
Solve these problems:
- What is the square of 12?
- Calculate the square root of 144.
- Identify the square numbers from this set: {15, 25, 36, 42}.
- What is the square root of 121?
- If one side of a square field is 13 meters, find its area.
Evaluation Questions (Fill in the Blanks):
- The square of 7 is _____.
a) 42 b) 49 c) 56 d) 63 - The square of 10 is _____.
a) 100 b) 110 c) 120 d) 130 - The square root of 16 is _____.
a) 2 b) 4 c) 6 d) 8 - The square root of 49 is _____.
a) 6 b) 7 c) 8 d) 9 - Which of these numbers is a perfect square? _____.
a) 27 b) 36 c) 43 d) 51
Answers:
- b) 49
- a) 100
- b) 4
- b) 7
- b) 36
Lesson Presentation Steps:
Step 1: Revise the previous topic (multiplication).
Step 2: Introduce the new topic (Squares and Square Roots).
Step 3: Write the definitions of squares and square roots on the board.
Step 4: Guide pupils in calculating squares of numbers 1 to 20.
Step 5: Use flashcards and activities to identify square roots of numbers from 1 to 100.
Step 6: Solve word problems with pupils.
Step 7: Allow pupils to practice solving exercises in pairs or individually.
Teacher’s Activities:
- Explain and write examples on the board.
- Use flashcards to demonstrate perfect squares.
- Guide pupils in solving exercises and word problems.
Learners’ Activities:
- Participate in class discussions and activities.
- Solve exercises in groups or individually.
- Present their answers to the class.
Assessment (Short Answer Questions):
- What is the square of 8?
- What is the square root of 64?
- Name three perfect squares.
- Find the square of 15.
- Solve: 9² – 4².
Answers:
- 64
- 8
- 1, 4, 9
- 225
- 65
Conclusion:
The teacher reviews the main points and provides additional examples. Pupils’ exercises are marked, and corrections are made where necessary. Feedback is given to improve understanding.
Theory of Numbers Prime Factors, LCM and HCF and squares of numbers
Homework
- What is the square of 7? a) 42 b) 49 c) 56 d) 63
- What is the square of 10? a) 100 b) 110 c) 120 d) 130
- What is the square root of 16? a) 2 b) 4 c) 6 d) 8
- What is the square root of 49? a) 6 b) 7 c) 8 d) 9
- Which of the following is a square number? a) 27 b) 36 c) 43 d) 51
- What is the square of 9? a) 72 b) 81 c) 90 d) 99
- What is the square of 12? a) 120 b) 132 c) 144 d) 156
- What is the square root of 25? a) 3 b) 5 c) 7 d) 9
- Which of the following is not a square number? a) 16 b) 25 c) 30 d) 36
- What is the square root of 64? a) 6 b) 7 c) 8 d) 9