HomeJSS 1MathematicsMeaning Of Fractions Types of Fractions And Mixed Numbers Mathematics JSS 1 First Term Lesson Notes Week 4

Meaning Of Fractions Types of Fractions And Mixed Numbers Mathematics JSS 1 First Term Lesson Notes Week 4

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 4
Age: 12 years

Topic: Fractions
Sub-topic: Common Fractions, Types of Fractions, Simple Conversion
Duration: 40 minutes

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

  1. Identify and describe common fractions.
  2. Distinguish between proper, improper, and mixed fractions.
  3. Convert between improper fractions and mixed fractions.

Keywords: Fraction, Numerator, Denominator, Proper Fraction, Improper Fraction, Mixed Number

Set Induction:
Start with a real-life example. Show a pizza cut into equal parts. Ask pupils, “If we have 4 slices out of 8, what fraction of the pizza is that?”

Entry Behaviour:
Pupils should already know how to count numbers and understand the concept of a whole.

Learning Resources and Materials:

  • Visual aids (slices of pizza, shapes cut into parts)
  • Fraction charts
  • Drawing board
  • Fraction strips

Building Background / Connection to Prior Knowledge:
Review the concept of whole numbers and division to link with fractions.

Embedded Core Skills:

  • Critical thinking
  • Problem-solving
  • Basic arithmetic

Learning Materials:

  • Essential Mathematics for JSS1 by AJS Oluwasanmipg
  • New General Mathematics for JSS1 by M.F. Macrae et al

Instructional Materials:

  • Visual aids (shapes, drawings)
  • Fraction strips

Content:

  1. Definition:
    A fraction is a number that represents a part of a whole. It is written as one number (numerator) divided by another (denominator). For example, 1/2 means 1 part out of 2 equal parts.
  2. Common Fractions:
    • Proper Fractions: Numerator is less than the denominator. Example: 3/4, 2/5.
    • Improper Fractions: Numerator is greater than or equal to the denominator. Example: 5/4, 7/3.
    • Mixed Numbers: Consists of a whole number and a fraction. Example: 1 1/2, 2 3/4.
  3. Simple Conversion:
    • Improper to Mixed Fractions: Divide the numerator by the denominator. Example: 7/4 = 1 3/4.
    • Mixed to Improper Fractions: Multiply the whole number by the denominator and add the numerator. Example: 2 1/3 = (2 x 3) + 1 / 3 = 7/3.

Topic: Fractions

A: Common Fractions

  1. Meaning of Fractions:
    • A fraction shows a part of a whole.
    • It is written as one number divided by another.
    • Example: 3/4 means 3 parts out of 4.
  2. General Form of a Fraction:
    • Written as a/b, where:
      • a is the numerator (the top number).
      • b is the denominator (the bottom number).
  3. Types of Fractions:

    i. Common (Vulgar) Fractions:

    • Written as one number over another.
    • Examples:
      • 9/11
      • 3/8

    ii. Decimal Fractions:

    • Written with a decimal point.
    • Example: 0.75 is a decimal fraction.

B: Types of Fractions (Common)

  1. Proper Fractions:
    • Numerator is less than the denominator.
    • Examples:
      • 4/7
      • 3/5
  2. Improper Fractions:
    • Numerator is greater than or equal to the denominator.
    • Examples:
      • 11/5
      • 4/3
  3. Mixed Numbers:
    • Contains a whole number and a fraction.
    • Examples:
      • 1 1/2 (1 whole and 1/2)
      • 2 3/4 (2 whole and 3/4)

Conversion Examples

1. Converting Improper Fractions to Mixed Numbers:

  • Method: Divide the numerator by the denominator. The quotient is the whole number, and the remainder is the numerator of the fractional part.
    • Example 1: 4/3
      • 4 divided by 3 is 1 with a remainder of 1.
      • Mixed Number: 1 1/3
    • Example 2: 57/10
      • 57 divided by 10 is 5 with a remainder of 7.
      • Mixed Number: 5 7/10
    • Example 3: 93/20
      • 93 divided by 20 is 4 with a remainder of 13.
      • Mixed Number: 4 13/20
    • Example 4: 113/3
      • 113 divided by 3 is 37 with a remainder of 2.
      • Mixed Number: 37 2/3

2. Converting Mixed Numbers to Improper Fractions:

  • Method: Multiply the whole number by the denominator and add the numerator. This result is the numerator of the improper fraction.
    • Example 1: 5 1/2
      • 5 times 2 plus 1 is 11.
      • Improper Fraction: 11/2
    • Example 2: 3 2/5
      • 3 times 5 plus 2 is 17.
      • Improper Fraction: 17/5
    • Example 3: 7 1/8
      • 7 times 8 plus 1 is 57.
      • Improper Fraction: 57/8
    • Example 4: 10 1/3
      • 10 times 3 plus 1 is 31.
      • Improper Fraction: 31/3

Evaluation

  1. Examples of Fractions:
    • List five examples each of proper fractions, improper fractions, and mixed numbers.
  2. Fractions from Figures:
    • Using provided shapes, identify and write the fraction, stating whether it is proper, improper, or mixed.

Reading Assignment

  1. Essential Mathematics for JSS1 by AJS Oluwasanmipg, pages 35-36.
  2. New General Mathematics for JSS1 by M.F. Macrae et al., pages 29-30.

Weekend Assignment

  1. Identify Proper Fractions:
    • Which of the following is not a proper fraction?
      • (a) 1/4
      • (b) 3/4
      • (c) 3/2
      • (d) 5/8
  2. Convert to Improper Fraction:
    • Express 3 1/7 as an improper fraction.
      • (a) 22/7
      • (b) 23/7
      • (c) 7/22
      • (d) 22/7
  3. Shaded Fraction:
    • What fraction of the figure shown is shaded?
      • (a) 2/11
      • (b) 3/9
      • (c) 8/3
      • (d) 4/11
  4. Convert to Mixed Fraction:
    • Express 99/5 as a mixed fraction.
      • (a) 19 4/5
      • (b) 18 4/5
      • (c) 19 5/4
      • (d) 18 5/4
  5. Figure Descriptions:
    • The figures above can best be described as:
      • (a) 2 1/2 – mixed number
      • (b) 2 3/4 – proper fraction
      • (c) 2 3/4 – improper fraction
      • (d) 2 3/4 – decimal

Theory

  1. Distinguish Fractions:
    • Describe the types of fractions and provide two examples for each.
  2. Conversion:
    • Convert 103/5 to a mixed fraction.
    • Convert 11 2/5 to an improper fraction.

Evaluation (Fill-in-the-Blank Questions):

  1. The top number in a fraction is called the _____ (a) numerator, (b) denominator, (c) fraction, (d) divisor.
  2. The bottom number in a fraction is called the _____ (a) numerator, (b) denominator, (c) fraction, (d) divisor.
  3. A fraction where the numerator is less than the denominator is called a _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
  4. The fraction 7/4 is an example of an _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
  5. The fraction 3 1/2 is a _____ number. (a) proper, (b) improper, (c) mixed, (d) decimal.
  6. Convert 9/4 to a mixed number. It is _____ (a) 2 1/4, (b) 2 3/4, (c) 1 2/4, (d) 2 2/4.
  7. Convert 4 2/5 to an improper fraction. It is _____ (a) 22/5, (b) 20/5, (c) 18/5, (d) 25/5.
  8. Which of the following is not a proper fraction? (a) 2/3, (b) 5/6, (c) 7/4, (d) 3/8.
  9. The fraction 1 1/3 can be written as _____ in improper fraction form. (a) 4/3, (b) 5/3, (c) 3/1, (d) 7/3.
  10. The mixed number 2 1/2 is equivalent to the improper fraction _____ (a) 5/2, (b) 4/2, (c) 7/2, (d) 6/2.
  11. Convert the improper fraction 8/3 to a mixed number. It is _____ (a) 2 2/3, (b) 3 1/3, (c) 2 1/3, (d) 1 2/3.
  12. The fraction 5/8 is a _____ fraction. (a) proper, (b) improper, (c) mixed, (d) decimal.
  13. The improper fraction 13/4 is a _____ number. (a) proper, (b) mixed, (c) decimal, (d) improper.
  14. To convert 5 3/4 to an improper fraction, you get _____ (a) 23/4, (b) 22/4, (c) 25/4, (d) 24/4.
  15. Which is an example of a proper fraction? (a) 4/3, (b) 2/4, (c) 5/5, (d) 7/6.

Class Activity Discussion (FAQs):

  1. What is a fraction?
    A fraction shows parts of a whole. It is written as one number over another.
  2. What is the numerator in a fraction?
    The numerator is the top number in a fraction.
  3. What is the denominator in a fraction?
    The denominator is the bottom number in a fraction.
  4. What is a proper fraction?
    A proper fraction has a numerator less than its denominator.
  5. What is an improper fraction?
    An improper fraction has a numerator greater than or equal to its denominator.
  6. How do you convert an improper fraction to a mixed number?
    Divide the numerator by the denominator. The whole number is the quotient, and the remainder becomes the numerator of the fraction part.
  7. How do you convert a mixed number to an improper fraction?
    Multiply the whole number by the denominator, then add the numerator of the fraction part.
  8. What is a mixed number?
    A mixed number consists of a whole number and a fraction.
  9. Can you give an example of a mixed number?
    An example is 2 1/2.
  10. How can you simplify a fraction?
    Divide the numerator and denominator by their greatest common factor.
  11. What is the fraction 5/4 as a mixed number?
    It is 1 1/4.
  12. How do you know if a fraction is proper or improper?
    If the numerator is less than the denominator, it’s proper; if greater, it’s improper.
  13. What is the simplest form of the fraction 8/12?
    It is 2/3.
  14. How do you compare two fractions?
    Find a common denominator or convert them to decimal form.
  15. Why do we need to learn about fractions?
    Fractions help us understand and work with parts of a whole in various real-life situations.

Presentation:

  1. Step 1: Review the previous topic of basic division and parts of a whole.
  2. Step 2: Introduce fractions by explaining numerators and denominators with visual aids.
  3. Step 3: Allow pupils to provide examples and correct them as needed.

Teacher’s Activities:

  • Use visual aids to explain fractions.
  • Demonstrate converting improper fractions to mixed numbers and vice versa.
  • Provide examples and practice problems.

Learners’ Activities:

  • Participate in discussions.
  • Solve given examples and practice problems.
  • Work in pairs to convert fractions.

Assessment:
Observe pupils’ understanding through their responses to evaluation questions and class activities.

Evaluation Questions:

  1. What is a fraction?
  2. How do you write a fraction?
  3. What is the difference between proper and improper fractions?
  4. Convert 7/3 to a mixed number.
  5. Convert 2 2/5 to an improper fraction.
  6. Identify the numerator in 3/7.
  7. Identify the denominator in 5/6.
  8. What is a mixed number?
  9. How do you simplify 12/16?
  10. Convert 8 3/4 to an improper fraction.

Conclusion:
Review the main points of the lesson and correct any misunderstandings. Mark pupils’ work and provide feedback on their performance..

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