Ordering of Fractions Percentages and Decimals Mathematics JSS 1 First Term Lesson Notes Week 6

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 6
Age: 12 years
Topic: Fractions Continued
Sub-topic: Ordering of Fractions, Conversion of Fractions to Percentages and Vice Versa, Conversion of Fractions to Decimals and Vice Versa
Duration: 40 minutes

Behavioural Objectives

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

1. Order fractions from smallest to largest.
2. Convert fractions to percentages and percentages to fractions.
3. Convert fractions to decimals and decimals to fractions.

Keywords

Ordering, Fractions, Percentages, Decimals, Conversion

Set Induction

Begin by discussing how we often compare quantities in everyday life, such as comparing prices or amounts, and relate this to ordering fractions.

Entry Behaviour

Students should be familiar with basic fractions and their operations.

Learning Resources and Materials

1. Fraction and decimal charts
2. Whiteboard and markers
3. Worksheets with conversion exercises
4. Calculators

Building Background/Connection to Prior Knowledge

Students should recall how to perform basic fraction operations and understand decimal and percentage concepts.

Embedded Core Skills

1. Mathematical reasoning
2. Problem-solving
3. Numerical fluency

Content

1. Ordering of Fractions: Arranging fractions from smallest to largest by comparing their sizes.
   • Example: Order 1/4, 2/3, and 5/6.
   • To compare fractions, find a common denominator or convert them to decimals.
2. Conversion of Fractions to Percentages:
   • To convert a fraction to a percentage, multiply the fraction by 100.
   • Example: 3/4 = 0.75 × 100 = 75%.
3. Conversion of Percentages to Fractions:
   • To convert a percentage to a fraction, divide by 100 and simplify.
   • Example: 60% = 60/100 = 3/5.
4. Conversion of Fractions to Decimals:
   • To convert a fraction to a decimal, divide the numerator by the denominator.
   • Example: 7/8 = 0.875.
5. Conversion of Decimals to Fractions:
   • To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, etc., and simplify.
   • Example: 0.6 = 6/10 = 3/5.

Evaluation

1. Order these fractions from smallest to largest: 1/2, 3/4, 2/5.
2. Convert the following fractions to percentages: 2/5, 7/10.
3. Convert 45% to a fraction.
4. Convert 0.25 to a fraction.
5. Order these decimals from smallest to largest: 0.4, 0.75, 0.2.

Fractions

1. Ordering of Fractions

To compare fractions, it’s easier if they have the same denominator.

Example 1: Which is larger: 5/7 or 6/8?

Solution:

1. Convert to a common denominator:
   • 5/7 x 8/8 = 40/56
   • 6/8 x 7/7 = 42/56
2. 6/8 is larger than 5/7.

Examples:

Example 2: Which has the greater mass: 3054g or 3.56kg?

Solution:

1. Convert 3.56kg to grams:
   • 3.56kg = 3560g
2. Compare 3054g and 3560g:
   • 3560g is larger than 3054g.

Example 3: Which is larger?

a. 3 21/50 or 3 31/60
b. 37/45 or 19/24

Solution:

a. Convert the fractional parts to a common denominator:

• 21/50 x 6/6 = 126/300
• 31/60 x 5/5 = 155/300
• 3 31/60 is larger than 3 21/50.

b. Convert to a common denominator:

• 37/45 x 8/8 = 296/360
• 19/24 x 15/15 = 285/360
• 37/45 is larger than 19/24.

Example 4: Arrange the following fractions in ascending order: 1/3, 1/9, 5/18, 2/3, 5/6, 7/12, 3/4

Solution:

a. Convert to a common denominator:

• 1/3 = 6/18
• 1/9 = 2/18
• 5/18 is already in the same denominator.
• Ascending order: 1/9, 5/18, 1/3

b. Convert to a common denominator:

• 2/3 = 8/12
• 5/6 = 10/12
• 7/12 is already in the same denominator.
• 3/4 = 9/12
• Ascending order: 7/12, 2/3, 3/4, 5/6

Percentages

1. Converting Percentages to Fractions

To convert a percentage to a fraction, divide by 100.

Examples:

i. 30% = 30/100 = 3/10
ii. 75% = 75/100 = 3/4
iii. 7.5% = 7.5/100 = 15/200 = 3/40
iv. 13.75% = 13.75/100 = 55/400 = 11/80

2. Converting Percentages to Decimals

To convert a percentage to a decimal, divide by 100.

Examples:

i. 45% = 45/100 = 0.45
ii. 34.75% = 34.75/100 = 0.3475
iii. 5.8% = 5.8/100 = 0.058

3. Converting Fractions to Percentages

To convert a fraction to a percentage, multiply by 100.

Examples:

i. 1/4 = 25%
ii. 25/400 = 31.25%
iii. 5/8 = 62.5%

4. Converting Decimals to Percentages

To convert a decimal to a percentage, multiply by 100.

Examples:

i. 0.75 = 0.75 x 100 = 75%
ii. 0.045 = 0.045 x 100 = 4.5%

5. Finding the Percentage of a Quantity

To find the percentage of a quantity, express the percentage as a fraction and then multiply by the quantity.

Examples:

i. 4.5% of N248 = (4.5/100) x 248 = N11.16
ii. 20% of N250 = (20/100) x 250 = N50

6. Expressing One Quantity as a Percentage of Another

To express one quantity as a percentage of another, divide the first quantity by the second and multiply by 100.

Examples:

i. 8 students out of 40 did not do their assignments:

• Percentage: (8/40) x 100 = 20% did not do their assignment.
• Percentage who did their assignment: 80%

ii. What percentage of N5 is 150 kobo?

• Convert N5 to kobo: 500 kobo
• Percentage: (150/500) x 100 = 30%

iii. What percentage of 15 km is 20,000 cm?

• Convert 15 km to cm: 1,500,000 cm
• Percentage: (20,000/1,500,000) x 100 = 1.33%

Converting Fractions to Decimals

1. Terminating Decimals

When the denominator divides exactly into the numerator, it results in a terminating decimal.

Example: Change 3/4 to a decimal:

• 3/4 = 0.75

2. Recurring Decimals

When converting fractions to decimals results in repeating figures.

Examples:

i. 4/9 = 0.444…
ii. 6/11 = 0.5454…

Convert these decimals to fractions:

i. 0.4 = 4/10 = 2/5
ii. 0.067 = 67/1000

3. Addition and Subtraction of Decimals

Examples:

i. 0.6 + 1.7 = 2.3
ii. 0.59 – 0.55 = 0.44
iii. 7.5 + 1.8 = 9.3
iv. 9.3 – 6.2 = 3.1

4. Multiplication and Division of Decimals

Examples:

i. 0.08 x 0.7 = 0.056
ii. 0.5 x 7 = 3.5
iii. 0.18 ÷ 1.2 = 0.15
iv. 1.56 ÷ 1.2 = 1.3

Evaluation

1. Fractions:

   a. Which fraction is larger?

   • 2/5 or 5/7
   • 5/6 or 4/9

   b. Arrange in ascending order:

   • 3/5, 8/15, 17/30
   • 3/5, 5/8, 7/10, 13/20
2. Percentages:

   a. Calculate:

   • 5% of N500
   • 18% of 144 km
3. Converting Fractions to Decimals:

   a. Convert:

   • 4/5
   • 1 2/5

Reading Assignment

1. Essential Mathematics for JSS1 by AJS Oluwasanmi, pages 51-56
2. New General Mathematics for JSS1 by MF Macrae, pages 31-38

Evaluation:

Class Activity Discussion

1. How do you order fractions?
   • By finding a common denominator or converting them to decimals.
2. What is the process to convert fractions to percentages?
   • Multiply the fraction by 100.
3. How do you convert percentages to fractions?
   • Divide the percentage by 100 and simplify.
4. How do you convert fractions to decimals?
   • Divide the numerator by the denominator.
5. How can you convert decimals to fractions?
   • Write the decimal as a fraction with an appropriate denominator and simplify.
6. What are some real-life examples where you need to order fractions?
   • Comparing discounts, dividing amounts, etc.
7. How is understanding fractions and percentages useful?
   • For financial calculations, measurements, and comparisons.
8. How do you find a fraction equivalent to a decimal?
   • Convert the decimal to a fraction and simplify.
9. What steps do you follow to convert a percentage to a decimal?
   • Divide the percentage by 100.
10. How can you check if your fraction-to-decimal conversion is correct?
    • By performing the division and comparing results.
11. What is the easiest way to convert 0.8 to a fraction?
    • Write it as 8/10 and simplify to 4/5.
12. Why is it important to know how to convert between fractions, decimals, and percentages?
    • To solve various problems and make accurate comparisons.
13. What is the decimal equivalent of 3/5?
    • 0.6.
14. How do you simplify the fraction 24/30?
    • Divide both numerator and denominator by their greatest common divisor, 6.
15. How can you convert a repeating decimal to a fraction?
    • Use algebraic methods to solve the repeating decimal as a fraction.

Presentation

1. Step 1: Review the previous topic on equivalent fractions and their applications.
2. Step 2: Introduce ordering fractions and conversions between fractions, percentages, and decimals.
3. Step 3: Engage students in solving examples and practice problems, ensuring understanding of each concept.

Teacher’s Activities

1. Explain how to order fractions and perform conversions.
2. Demonstrate with examples and provide practice exercises.
3. Guide students through problem-solving and conversion techniques.

Learners’ Activities

1. Participate in discussions and practice exercises.
2. Solve ordering and conversion problems individually and in groups.
3. Share answers and explain reasoning.

Assessment

1. Check students’ work on ordering fractions and conversions.
2. Review problem-solving methods and provide feedback.

Evaluation Questions

1. What is the first step in ordering fractions?
2. How do you convert 1/3 to a percentage?
3. What is 80% as a fraction?
4. Convert 0.45 to a fraction.
5. Order these fractions: 5/6, 1/3, 2/5.
6. How do you convert a fraction like 4/5 to a decimal?
7. What is the decimal equivalent of 2/3?
8. How do you convert 75% to a fraction?
9. What is the fraction for the decimal 0.2?
10. Simplify the fraction 16/24.

Conclusion

The teacher will circulate to check students’ work, provide feedback, and ensure understanding of ordering fractions and conversion techniques.