Ratio Mathematics Primary 5 First Term Lesson Notes Week 8

Mathematics Primary 5 First Term Lesson Notes

Week: 8
Subject: Mathematics
Class: Primary 5
Term: First Term
Age: 10 years
Topic: Ratios
Sub-Topics:

1. Relationship Between Ratio and Fractions
2. Solving Real-Life Problems Involving Ratios
3. Quantitative Aptitude

Duration: 40 minutes

Behavioural Objectives:

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

1. Explain the meaning of a ratio.
2. Express ratios as fractions.
3. Solve real-life problems involving ratios.
4. Apply quantitative aptitude to problems related to ratios.

Keywords:

• Ratio
• Fraction
• Relationship
• Real-life problems
• Quantitative aptitude

Set Induction:
The teacher will start by discussing everyday situations where ratios are used, such as in recipes or sharing items among friends. This will introduce the concept of ratios and their practical uses.

Entry Behaviour:
Pupils should be familiar with basic fractions and simple arithmetic operations.

Learning Resources and Materials:

1. Ratio and fraction charts
2. Worksheets for practice
3. Real-life problem scenarios
4. Whiteboard and markers

Building Background/Connection to Prior Knowledge: The teacher will review fractions and discuss how ratios can be expressed as fractions.

Embedded Core Skills:

• Analytical thinking
• Problem-solving
• Application of mathematical concepts

Learning Materials:

1. Charts for ratios and fractions
2. Practice worksheets
3. Real-life problem scenarios

Reference Books:
Lagos State Scheme of Work, Primary 5 Mathematics Textbook

Instructional Materials:

1. Ratio and fraction charts
2. Worksheets
3. Whiteboard and markers

Content:

1. Relationship Between Ratio and Fractions
   • Explanation of what a ratio is.
   • How ratios can be expressed as fractions.
   • Examples and practice problems.
2. Solving Real-Life Problems Involving Ratios
   • Application of ratios in everyday situations.
   • Practice problems and examples.
3. Quantitative Aptitude
   • Using ratios in quantitative aptitude problems.
   • Practice problems and examples.

Relationship Between Ratio and Fractions

Explanation of What a Ratio Is:

• A ratio compares two or more quantities, showing how many times one quantity is compared to another. It is written as “a

  ” or “a/b.”

How Ratios Can Be Expressed as Fractions:

• A ratio can be converted to a fraction by expressing it as “a/b,” where “a” is the first quantity and “b” is the second quantity.

Examples and Practice Problems:

1. Example 1:
   • Ratio: 4:5
   • Fraction: 4/5
2. Example 2:
   • Ratio: 7:3
   • Fraction: 7/3
3. Example 3:
   • Ratio: 2:8
   • Fraction: 2/8 = 1/4
4. Example 4:
   • Ratio: 9:12
   • Fraction: 9/12 = 3/4
5. Example 5:
   • Ratio: 5:2
   • Fraction: 5/2

Class Work:

1. Convert the ratio 6:4 to a fraction.
2. Express the ratio 10:15 as a fraction in simplest form.
3. Write the ratio 8:12 as a fraction and simplify.
4. Convert the ratio 3:7 to a fraction.
5. Change the ratio 14:28 to a fraction and simplify.

Solving Real-Life Problems Involving Ratios

Application of Ratios in Everyday Situations:

• Ratios help in comparing quantities, mixing ingredients, or dividing resources in various real-life scenarios.

Examples and Practice Problems:

1. Example 1:
   • Problem: A recipe uses a ratio of 2 cups of flour to 3 cups of sugar. If you want to use 6 cups of sugar, how many cups of flour do you need?
     • Solution: Use the ratio 2:3. For 6 cups of sugar, the amount of flour needed is (2/3) × 6 = 4 cups.
2. Example 2:
   • Problem: In a classroom, the ratio of boys to girls is 4:5. If there are 20 boys, how many girls are there?
     • Solution: The ratio of boys to girls is 4:5. If there are 20 boys, the number of girls is (5/4) × 20 = 25 girls.
3. Example 3:
   • Problem: A car travels 150 miles in 3 hours. What is the ratio of miles traveled to hours?
     • Solution: The ratio is 150 miles to 3 hours, or 150:3, which simplifies to 50:1.
4. Example 4:
   • Problem: A paint mixture uses a ratio of 1 part red to 4 parts blue. If you use 8 liters of blue paint, how much red paint is needed?
     • Solution: Use the ratio 1:4. For 8 liters of blue, the red paint needed is (1/4) × 8 = 2 liters.
5. Example 5:
   • Problem: The ratio of apples to oranges in a basket is 3:2. If there are 18 apples, how many oranges are there?
     • Solution: The ratio of apples to oranges is 3:2. For 18 apples, the number of oranges is (2/3) × 18 = 12 oranges.

Class Work:

1. If a map uses a ratio of 1:50000, how many kilometers does 2 inches on the map represent?
2. In a group of 30 students, the ratio of boys to girls is 2:3. How many boys are there?
3. A fruit basket has a ratio of 5 apples to 7 oranges. If there are 35 oranges, how many apples are there?
4. Mix paint in a ratio of 3:2 red to blue. If you have 15 liters of blue paint, how much red paint do you need?
5. If the ratio of cats to dogs in a pet store is 7:4 and there are 28 dogs, how many cats are there?

Quantitative Aptitude

Using Ratios in Quantitative Aptitude Problems:

Examples and Practice Problems:

1. Example 1:
   • Problem: A company has a ratio of 3 engineers to 2 accountants. If there are 60 engineers, how many accountants are there?
     • Solution: Use the ratio 3:2. If there are 60 engineers, the number of accountants is (2/3) × 60 = 40 accountants.
2. Example 2:
   • Problem: In a school, the ratio of students who passed to those who failed is 5:1. If 150 students passed, how many students failed?
     • Solution: The ratio of passed to failed is 5:1. If 150 students passed, the number of students who failed is (1/5) × 150 = 30 students.
3. Example 3:
   • Problem: A recipe calls for a ratio of 2 parts flour to 3 parts sugar. If you use 6 kg of sugar, how much flour is needed?
     • Solution: Use the ratio 2:3. For 6 kg of sugar, the flour needed is (2/3) × 6 = 4 kg.
4. Example 4:
   • Problem: The ratio of men to women in a company is 7:5. If there are 84 men, how many women are there?
     • Solution: The ratio of men to women is 7:5. If there are 84 men, the number of women is (5/7) × 84 = 60 women.
5. Example 5:
   • Problem: A classroom has a ratio of 4 desks for every 5 chairs. If there are 40 desks, how many chairs are there?
     • Solution: Use the ratio 4:5. For 40 desks, the number of chairs is (5/4) × 40 = 50 chairs.

Class Work:

1. A recipe requires a ratio of 3:2 flour to sugar. If you have 12 kg of flour, how much sugar do you need?
2. If a team of 24 people has a ratio of 3:1 for developers to testers, how many testers are there?
3. A bag contains a ratio of 7 red marbles to 3 blue marbles. If there are 21 red marbles, how many blue marbles are there?
4. In a factory, the ratio of machines to workers is 5:7. If there are 35 machines, how many workers are there?
5. A basket has a ratio of 2 apples to 5 oranges. If there are 50 oranges, how many apples are there?

Questions Assessment

1. The ratio of 4 to 6 can be written as the fraction __________.
   a) 2/3
   b) 4/6
   c) 6/4
   d) 2/4
2. If the ratio of apples to oranges is 3:2, then there are __________ apples for every 2 oranges.
   a) 3
   b) 2
   c) 5
   d) 6
3. Express the ratio 5:10 as a fraction. The result is __________.
   a) 1/2
   b) 5/10
   c) 2/5
   d) 1/5
4. In a class of 20 students, the ratio of boys to girls is 4:1. There are __________ boys in the class.
   a) 4
   b) 16
   c) 8
   d) 5
5. The ratio of red marbles to blue marbles is 7:3. If there are 21 red marbles, there are __________ blue marbles.
   a) 9
   b) 3
   c) 7
   d) 10
6. If the ratio of the length to width of a rectangle is 5:3 and the length is 15 cm, the width is __________ cm.
   a) 9
   b) 5
   c) 10
   d) 12
7. Convert the ratio 8:4 to a fraction. The result is __________.
   a) 2/1
   b) 4/2
   c) 8/4
   d) 1/2
8. A recipe calls for a ratio of 2 cups of flour to 3 cups of sugar. If 6 cups of sugar are used, the amount of flour needed is __________ cups.
   a) 4
   b) 3
   c) 2
   d) 8
9. The ratio of cats to dogs in a pet shop is 3:7. If there are 21 dogs, there are __________ cats.
   a) 9
   b) 6
   c) 15
   d) 12
10. A bag contains red and green balls in the ratio 2:5. If there are 40 green balls, there are __________ red balls.
    a) 16
    b) 20
    c) 8
    d) 18
11. If the ratio of books to notebooks is 5:3 and there are 15 notebooks, there are __________ books.
    a) 25
    b) 10
    c) 20
    d) 8
12. The ratio of teachers to students in a school is 1:30. If there are 90 students, there are __________ teachers.
    a) 3
    b) 4
    c) 5
    d) 6
13. In a sports team, the ratio of wins to losses is 7:2. If the team has 14 wins, they have __________ losses.
    a) 4
    b) 8
    c) 7
    d) 2
14. A mixture contains a ratio of 5 parts water to 2 parts oil. If there are 20 parts of water, there are __________ parts of oil.
    a) 10
    b) 8
    c) 4
    d) 5
15. The ratio of red to blue pencils is 3:5. If there are 24 blue pencils, there are __________ red pencils.
    a) 12
    b) 9
    c) 15
    d) 8

Class Activity Discussion

1. Q: What is a ratio?
   A: A ratio is a way to compare two quantities using division.
2. Q: How can a ratio be expressed as a fraction?
   A: Divide the first quantity by the second quantity.
3. Q: What is the ratio of 10 to 5?
   A: The ratio is 2:1 or 2/1.
4. Q: How do you solve problems involving ratios?
   A: Use multiplication or division to find missing quantities based on the given ratio.
5. Q: What is the ratio of 6 to 9 simplified?
   A: The ratio is 2:3.
6. Q: How do you convert a ratio into a percentage?
   A: Divide the ratio by the total and multiply by 100.
7. Q: What is the ratio of 15 to 25 in its simplest form?
   A: The ratio is 3:5.
8. Q: How can you use ratios in real-life problems?
   A: Ratios can help solve problems related to mixing ingredients, comparing quantities, and scaling recipes.
9. Q: If a ratio is 4:5, what does it mean?
   A: It means for every 4 units of the first quantity, there are 5 units of the second quantity.
10. Q: How do you express the ratio of 8 to 12 as a fraction?
    A: The fraction is 8/12, which simplifies to 2/3.
11. Q: What is a common use for ratios?
    A: Ratios are commonly used in recipes, ratios in financial calculations, and comparing quantities.
12. Q: How do you find a missing number in a ratio?
    A: Set up a proportion and solve for the missing number.
13. Q: What is the relationship between ratios and fractions?
    A: Ratios can be written as fractions where the first number is the numerator and the second number is the denominator.
14. Q: How do you solve ratio problems with multiple quantities?
    A: Use the ratio to set up equations and solve for the unknown quantities.
15. Q: How do you check if two ratios are equivalent?
    A: Cross-multiply and compare the products. If they are equal, the ratios are equivalent.

Presentation:

Step 1: Introduce and explain the concept of ratios and their relationship to fractions.

Step 2: Demonstrate how to solve real-life problems using ratios.

Step 3: Provide practice problems and guide pupils through solving them.

Teacher’s Activities:

• Explain the concept of ratios with examples.
• Demonstrate solving real-life problems using ratios.
• Provide practice exercises and assist pupils.

Learners’ Activities:

• Participate in discussions about ratios and their applications.
• Complete practice worksheets and real-life problem scenarios.
• Solve quantitative aptitude problems related to ratios.

Assessment:

1. Convert the ratio 9:12 to a fraction.
2. If the ratio of cats to dogs is 4:5 and there are 20 dogs, how many cats are there?
3. Express the ratio 15:25 in its simplest form.
4. In a group of 30 students, the ratio of boys to girls is 2:3. How many boys are there?
5. If the ratio of red to green marbles is 7:3 and there are 28 green marbles, how many red marbles are there?
6. Convert the ratio 6:8 to a fraction.
7. In a class of 40 students, the ratio of girls to boys is 3:5. How many girls are in the class?
8. Express the ratio 10:15 as a fraction.
9. If the ratio of apples to oranges is 5:2 and there are 30 oranges, how many apples are there?
10. Convert the ratio 4:9 to a fraction.
11. In a box of 45 chocolates, the ratio of dark to milk chocolates is 2:3. How many milk chocolates are there?
12. Express the ratio 8:10 in its simplest form.
13. If the ratio of red balls to blue balls is 3:7 and there are 35 blue balls, how many red balls are there?
14. Convert the ratio 12:16 to a fraction.
15. In a recipe, the ratio of flour to sugar is 5:3. If 15 cups of sugar are used, how many cups of flour are needed?

Conclusion:

The teacher will review pupils’ answers, provide feedback, and address any misunderstandings. Pupils will discuss the importance of ratios in various real-life contexts and reflect on their learning.

More Useful Links

• Addition and Subtraction of Large Numbers Mathematics Primary 5 First Term Lesson Notes Week 3
• Identification of Odd and Even Numbers, Prime Numbers, LCM, HCF, and Quantitative Reasoning Mathematics Primary 5 First Term Lesson Notes Week 5