Ordering of fractions, changing fraction to decimal, changing decimal to fraction, conversion of fraction and decimal to percentage and vice versa Mathematics Primary 5 First Term Lesson Notes Week 6

Topic: Fractions, Decimals, and Percentages

Sub-topic: Ordering Fractions, Converting Fractions to Decimals, Converting Decimals to Fractions, Conversion of Fractions and Decimals to Percentages and Vice Versa

Duration: 2 weeks

Term: Second Term

Week: 4-5

Previous Knowledge: Students should have a basic understanding of fractions, decimals, and percentages. They should be familiar with how to add and subtract fractions and decimals.

Instructional Materials:

• Chalkboard/Whiteboard and markers
• Visual aids (fraction, decimal, and percentage charts)
• Exercise books
• Calculator (optional)
• Colored markers
• Worksheets

Reference Materials:

• Mathematics textbooks
• Workbooks
• Online resources

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

1. Order fractions from smallest to largest and vice versa.
2. Convert fractions to decimals and decimals to fractions.
3. Convert fractions and decimals to percentages and vice versa.
4. Solve real-life problems involving these conversions.

Embedded Core Skills:

• Numeracy
• Problem-solving
• Logical reasoning
• Data analysis

Learning Materials:

• Fraction strips or models
• Decimal grids or place value charts
• Percentage circles or charts
• Worksheets with exercises

 

 

Content

Ordering fractions means arranging them from smallest to largest or largest to smallest.

Let’s look at an example:

1. Comparing two fractions: 1/4 and 1/3

   We can compare them by finding a common denominator, which in this case is 12. Then, we convert both fractions to have the same denominator:

   1/4 = 3/12 1/3 = 4/12

   Now, we can see that 3/12 (1/4) is smaller than 4/12 (1/3).

2. Comparing three fractions: 1/6, 1/2, and 1/3

   First, find a common denominator, which is 6 in this case:

   1/6 = 1/6 1/2 = 3/6 1/3 = 2/6

   Now, we can arrange them from smallest to largest: 1/6, 2/6, 3/6 (1/3).

So, ordering fractions helps us know which is bigger or smaller. 🤗

Changing fractions to decimals is like changing parts into numbers with a dot.

Here’s how we do it:

1. Using division: Divide the top number (numerator) by the bottom number (denominator).

   Example: 3/4

   3 ÷ 4 = 0.75

   So, 3/4 as a decimal is 0.75.
2. Using long division: Sometimes, you can do long division to get the decimal.

   Example: 1/5

   1 ÷ 5 = 0.2

   So, 1/5 as a decimal is 0.2.

3. Knowing common fractions: Some fractions have easy decimal equivalents.

   Example: 1/2 is the same as 0.5, and 1/4 is the same as 0.25.

Changing fractions to decimals helps us work with numbers more easily. 👍

Changing decimals to fractions means turning numbers with dots into fractions. It’s like going from parts to pieces.

Here’s how you can do it:

1. Write the decimal as a fraction over 10, 100, 1000, etc.

   Example: 0.5 as a fraction is 5/10. Simplify it if needed by dividing both the top and bottom by the same number.

   5/10 can be simplified to 1/2.
2. For decimals like 0.25, write it as a fraction over 100.

   Example: 0.25 as a fraction is 25/100. Simplify it by dividing both the top and bottom by the same number.

   25/100 can be simplified to 1/4.
3. For whole number decimals, convert them to fractions over 1.

   Example: 2.0 is the same as 2. So, 2.0 as a fraction is 2/1.

Changing decimals to fractions helps us understand numbers in different

Changing Fractions to Percentages:

To change a fraction to a percentage:

1. Multiply the fraction by 100.
2. Add a ‘%’ sign.

Example: 1/4 as a percentage: 1/4 * 100 = 25% So, 1/4 as a percentage is 25%.

Changing Decimals to Percentages:

To change a decimal to a percentage:

1. Multiply the decimal by 100.
2. Add a ‘%’ sign.

Example: 0.75 as a percentage: 0.75 * 100 = 75% So, 0.75 as a percentage is 75%.

Changing Percentages to Fractions:

To change a percentage to a fraction:

1. Write the percentage over 100.
2. Simplify if possible.

Example: 25% as a fraction: 25/100 can be simplified to 1/4. So, 25% as a fraction is 1/4.

Changing Percentages to Decimals:

To change a percentage to a decimal:

1. Divide the percentage by 100.

Example: 50% as a decimal: 50 ÷ 100 = 0.50 So, 50% as a decimal is 0.50.

Changing between these helps us work with numbers in different ways! 📊📈🧮

Example 1: Changing a Fraction to a Percentage

• Fraction: 3/5
• To change it to a percentage, multiply by 100.
• 3/5 * 100 = 60%
• So, 3/5 as a percentage is 60%.

Example 2: Changing a Decimal to a Percentage

• Decimal: 0.4
• To change it to a percentage, multiply by 100.
• 0.4 * 100 = 40%
• So, 0.4 as a percentage is 40%.

Example 3: Changing a Percentage to a Fraction

• Percentage: 75%
• To change it to a fraction, write it over 100.
• 75% = 75/100
• Simplify the fraction: 75/100 = 3/4
• So, 75% as a fraction is 3/4.

Example 4: Changing a Percentage to a Decimal

• Percentage: 20%
• To change it to a decimal, divide by 100.
• 20 ÷ 100 = 0.20
• So, 20% as a decimal is 0.20.

Example 5: Changing a Fraction to a Decimal

• Fraction: 1/8
• To change it to a decimal, divide the top by the bottom.
• 1 ÷ 8 = 0.125
• So, 1/8 as a decimal is 0.125.

1. Change 3/10 to a decimal: 3/10 = ___ a) 0.3 b) 0.2 c) 3.0 d) 0.03
2. Convert 75% to a fraction: 75% = ___ a) 75/100 b) 3/4 c) 7/5 d) 15/20
3. Order these decimals from smallest to largest: 0.15, 0.3, 0.25. a) 0.15, 0.25, 0.3 b) 0.25, 0.3, 0.15 c) 0.3, 0.15, 0.25 d) 0.3, 0.25, 0.15
4. Convert 5/6 to a percentage: 5/6 = ___% a) 50% b) 83.33% c) 30% d) 62.5%
5. Change 0.4 to a fraction: 0.4 = ___ a) 4/10 b) 2/5 c) 1/4 d) 40/100
6. Change 3/4 to a decimal: 3/4 = ___ a) 0.25 b) 0.5 c) 0.75 d) 0.33
7. Order these fractions from smallest to largest: 1/5, 2/7, 3/10. a) 1/5, 2/7, 3/10 b) 3/10, 2/7, 1/5 c) 2/7, 1/5, 3/10 d) 3/10, 1/5, 2/7
8. Convert 0.6 to a fraction: 0.6 = ___ a) 3/5 b) 5/3 c) 6/10 d) 3/10
9. Change 2/3 to a percentage: 2/3 = ___% a) 33% b) 66% c) 50% d) 25%
10. Convert 0.25 to a fraction: 0.25 = ___ a) 1/25 b) 1/5 c) 25/100 d) 1/4
11. Order these decimals from smallest to largest: 0.45, 0.12, 0.7. a) 0.12, 0.45, 0.7 b) 0.45, 0.7, 0.12 c) 0.7, 0.45, 0.12 d) 0.7, 0.12, 0.45
12. Convert 40% to a fraction: 40% = ___ a) 4/10 b) 2/5 c) 40/100 d) 1/4
13. Change 5/8 to a decimal: 5/8 = ___ a) 0.625 b) 0.125 c) 0.75 d) 0.5
14. Order these fractions from largest to smallest: 3/4, 5/6, 2/3. a) 5/6, 3/4, 2/3 b) 3/4, 5/6, 2/3 c) 2/3, 3/4, 5/6 d) 2/3, 5/6, 3/4
15. Convert 0.9 to a percentage: 0.9 = ___% a) 90% b) 9% c) 9.0%

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Presentation:

Step 1: Introduction (1 day)

• Begin by revising what fractions, decimals, and percentages are.
• Discuss real-life examples of where we encounter these concepts (e.g., in recipes, measurements, discounts).
• Explain the importance of being able to convert between these forms for practical math applications.

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Step 2: Ordering Fractions (2 days)

• Show students how to find a common denominator for fractions.
• Teach them to compare and order fractions by converting them to have the same denominator.
• Use visual aids and examples to reinforce understanding.

Step 3: Converting Fractions and Decimals (2 days)

• Discuss how to change fractions to decimals by dividing the numerator by the denominator.
• Explain the reverse process, converting decimals to fractions by using place value.
• Provide plenty of practice exercises for students.

Step 4: Conversion to Percentages (2 days)

• Teach students how to convert fractions and decimals to percentages.
• Emphasize the importance of knowing common percentage equivalents.
• Discuss real-life scenarios where percentage conversion is crucial.

Step 5: Practical Application (2 days)

• Present real-life problems that require students to apply what they’ve learned.
• Encourage students to work in groups to solve these problems.
• Discuss solutions as a class to reinforce learning.

Teacher’s Activities:

• Explain concepts clearly and use visual aids.
• Demonstrate conversion techniques.
• Provide guidance and support during practice exercises.
• Create real-life scenarios for practical understanding.

Learners’ Activities:

• Participate actively in discussions.
• Practice ordering fractions, converting fractions to decimals, and vice versa.
• Complete exercises and problem-solving activities.
• Collaborate with peers during group work.

Evaluation Questions:

1. Order the following fractions from smallest to largest: 2/5, 1/3, 3/8.
2. Convert 0.625 to a fraction.
3. Change 3/4 to a decimal.
4. What is 30% as a fraction?
5. If you have 1/6 of a pizza, what percentage of the whole pizza do you have?
6. Calculate 20% of 150.

Conclusion: In this two-week lesson, students have learned how to order fractions, convert fractions to decimals, convert decimals to fractions, and perform conversions to percentages. These skills are essential in everyday life and will be further developed in the upcoming lessons. Practicing these concepts is important for mastering them and for tackling more advanced math problems. Keep up the good work!