Squares and Square Roots of Whole Numbers

SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR / / PRIMARY 4

WEEK 5

TOPICS : Squares and Square Roots of Whole Numbers 

Learning Objectives

Pupils should be able to:

• calculate the square of
  numbers from 1-20
• identify the perfect
  squares in a set of
  numbers e.g.
  1,2,3,4,5,6,7,8,9,10,11,12,
  13,14,15,16,17,18,19,20.
  1, 4, 9, 16 are the perfect
  squares.
• find the square root of
  perfect squares up to 400
• solving word problems
  involving the calculation of
  square of numbers and
  square root of numbers.

Learning Objectives 

• Pupils in a group design a clock using flash
  cards where 4 represent 2, 9 represent 3.
• Pupils select perfect square numbers from a
  basket containing number cards of 1-100 and
  tell the class the square root.
• Sing songs on squares of numbers and square
  root of numbers.

Embedded Core Skills 

• Critical thinking and problem solving skills
• Communication and Collaboration
• Leadership skills and Personal Development
• Creativity and Imagination

Audio Visual Resource 

• Flash cards
• Cardboards
• Scissors

Content 

Squares and square roots are mathematical terms that help us understand how numbers work. Let me explain them to you with some examples.

A square is a number that you get when you multiply a number by itself. For example, if you multiply the number 3 by itself, you get 3 x 3 = 9. So, 9 is a square number because it’s the product of 3 x 3. Here are some more examples of square numbers:

• 1 x 1 = 1
• 2 x 2 = 4
• 3 x 3 = 9
• 4 x 4 = 16
• 5 x 5 = 25
• 6 x 6 = 36

Square roots are the opposite of squares. A square root is a number that, when multiplied by itself, gives you a square number. For example, the square root of 9 is 3 because 3 x 3 = 9. Here are some more examples of square roots:

• The square root of 1 is 1 because 1 x 1 = 1.
• The square root of 4 is 2 because 2 x 2 = 4.
• The square root of 16 is 4 because 4 x 4 = 16.
• The square root of 25 is 5 because 5 x 5 = 25.

So, to summarize, a square is the result of multiplying a number by itself, while a square root is the number that you multiply by itself to get a square. I hope this explanation helps you understand squares and square roots a little better!

SQUARES AND SQUARE ROOTS OF NUMBERS ( 1- digit and 2 – digit numbers)

Exercise 1

Find the value of:

1. 4² + 6²
2. 5² – 2²
3. 5² + 7²
4. 10² – 5²
5. 8² + 10²
6. 8² – 6²
7. 2² x 5²
8. 3² x 4²
9. 4² x 3²
10. 5² x 2²
11. 6² x2²
12. 2² x 3² x 5²
13. 2² x 3² x 5²
14. 3² x 2² x 5²

SQUARE OF 2-DIGIT NUMBER

The squares of two-digit numbers are (in short form) 102, 112, 122, 133, … 992.

To calculate the squares of two digit numbers we may use any of these methods.

a) Multiply the number by itself, i.e. using multiplication method.

b) Find the square from the square table.

c) Count the dots from the square pattern.

(This method may be too cumbersome at a later stage)

Examples

Study the workings to find 142.

Solution: (Multiplication method)

14²=14×14

(10+4)× (10+4)

10(10+4) + (10+4)

100+40+40+16

=196

Exercise

Solve each of the following:

1. 42

2. 92

3. 102

4. 122

5. 112

6. 152

7. 172

8. 162

9. 182

10. 202

Evaluation

1. What is the square of 7? a) 42 b) 49 c) 56 d) 63
2. What is the square of 10? a) 100 b) 110 c) 120 d) 130
3. What is the square root of 16? a) 2 b) 4 c) 6 d) 8
4. What is the square root of 49? a) 6 b) 7 c) 8 d) 9
5. Which of the following is a square number? a) 27 b) 36 c) 43 d) 51
6. What is the square of 9? a) 72 b) 81 c) 90 d) 99
7. What is the square of 12? a) 120 b) 132 c) 144 d) 156
8. What is the square root of 25? a) 3 b) 5 c) 7 d) 9
9. Which of the following is not a square number? a) 16 b) 25 c) 30 d) 36
10. What is the square root of 64? a) 6 b) 7 c) 8 d) 9

Lesson Presentation

Procedure:

I. Introduction (5 minutes)

• Begin the lesson by asking students if they know what squares and square roots are.
• Write the definitions of squares and square roots on the board and explain them in simple terms.
• Tell students that squares and square roots are important in many fields, including math, science, and engineering.

II. Identifying Squares and Non-Squares (15 minutes)

• Write the numbers 1-25 on the board.
• Ask students to circle the square numbers and cross out the non-square numbers.
• Discuss the answers as a group and explain why each circled number is a square and each crossed-out number is not.
• Provide additional examples if necessary.

III. Finding Square Roots (15 minutes)

• Explain how to find the square root of a number using repeated subtraction or a calculator.
• Demonstrate finding the square roots of a few simple numbers, such as 16 and 25.
• Provide practice problems for students to work on individually or in pairs.

IV. Applying Knowledge to Problem Solving (15 minutes)

• Give students word problems that involve squares and square roots.
• Have students work in pairs to solve the problems and explain their reasoning.
• Review the answers as a group and discuss any strategies that were used to solve the problems.

V. Conclusion (5 minutes)

• Summarize the key points of the lesson and ask students if they have any questions.
• Provide additional resources for students to practice their skills, such as online games or worksheets.
• Encourage students to use their knowledge of squares and square roots in their everyday lives.

Assessment:

• Evaluate students’ understanding of squares and square roots by observing their participation in class discussions and their ability to solve problems on worksheets.
• Provide feedback to students and offer additional support as needed.

Week Assessment /Test

1. The square of 5 is _____.
2. The square root of 64 is _____.
3. _____ is a non-square number.
4. The square of 9 is _____.
5. The square root of 25 is _____.
6. 49 is a _____ number.
7. The square of 12 is _____.
8. The square root of 100 is _____.
9. _____ is a square number.
10. The square root of 81 is _____.

Answers:

1. 25
2. 8
3. 3
4. 81
5. 5
6. square
7. 144
8. 10
9. 36
10. 9