Ratio Mathematics Primary 5 First Term Lesson Notes Week 8

Subject: Mathematics

Class: Primary 5

Term: First Term

Week: 8

Topic: Solving Real Life Problems on Ratios

Sub-topic: Applying Ratios in Practical Scenarios

Duration: 45 minutes

Previous Knowledge: Students should have a basic understanding of what ratios are and how to write ratios.

Set Induction: Begin the lesson by asking students to think about their daily routines and how they use ratios in their lives. For example, how do they decide the ingredients for a favorite recipe or divide snacks among friends?

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

  1. Apply ratios to solve real-life problems.
  2. Calculate the cost per unit in shopping scenarios.
  3. Allocate resources fairly using ratios.

Key Vocabulary Words:

  • Ratio
  • Cost per unit
  • Allocate
  • Fair distribution

Embedded Core Skills:

  • Mathematical problem-solving
  • Critical thinking
  • Decision-making

Learning Materials:

  • Chalkboard and chalk
  • Visual aids (charts, diagrams)
  • Real-life scenarios for problem-solving

Content:

  1. Introduction (5 minutes): Explain that ratios can be used to solve practical problems in everyday life. Discuss some common scenarios where ratios are applied, such as in cooking, shopping, and sharing resources.

RATIOS:

1. Relationship between ratio and fractions:

  • A ratio is a way to compare two or more quantities. It’s like a simplified fraction.
  • Example: If you have 3 red marbles and 4 blue marbles, the ratio of red to blue marbles is 3:4. It’s similar to the fraction 3/4. 🧮

2. Solving real-life problems on ratio:

  • Ratios are used in everyday life. They help us solve problems like sharing candies, mixing ingredients, or comparing prices.
  • Example: If you need to mix 2 parts of water and 1 part of juice to make a drink, that’s a ratio. 🥤

3. Quantitative aptitude:

  • Ratios are a part of quantitative aptitude, which means being good with numbers. It’s an important skill in math and real life.
  • Example: If you want to find the best deal at the grocery store, you use ratios to compare prices and quantities. 🛒

Importance:

  • Ratios help determine fair prices and value for money in a grocery store.
  • Example: If one box of cereal costs $3 and has 500g, and another costs $4 but has 700g, you can use ratios to figure out which one gives you more cereal for your money. 🍞🥣

Understanding ratios is like having a secret code for comparing and solving real-life math problems. It’s handy when you’re shopping or sharing things with friends! 🛍️🤝📊

Using Ratios in Real Life 📊

  1. Recipe Mixing 🍰: Ratios help us get the right balance of ingredients in recipes. For example, if a cake recipe needs a 2:1 ratio of flour to sugar, you use 2 cups of flour for every 1 cup of sugar.
  2. Smart Shopping 🛒: When shopping, you can compare products by looking at their cost per unit. For instance, a larger bottle of shampoo may be a better deal if you calculate the cost per ounce.
  3. Fair Resource Sharing 🍰: In a group, ratios help divide tasks or things fairly. If there are 4 slices of pizza and 3 friends want to share them equally, you’d use a 4:3 ratio.
  4. Budget Planning 💰: Managing money is easier with ratios. If you plan to save 20% of your income, you set aside $200 if you earn $1,000.
  5. Healthy Eating 🥗: A balanced meal may need a specific ratio of nutrients. If your plate has 2 parts of vegetables and 1 part of protein, you’re following a 2:1 ratio.
  6. Construction Work 🏗️: In building, mixing concrete with the right ratio of sand to cement is crucial. For example, a 3:1 ratio means 3 parts of sand for 1 part of cement.
  7. Speed and Distance 🏃: When tracking running speed, a 10-mile run in 2 hours means a 5 miles per hour speed. It’s the ratio of distance to time.

Worked Example 1: Recipe Mixing Problem: A recipe for making lemonade calls for a ratio of 1:4 for lemon juice to water. If you have 2 cups of lemon juice, how much water should you add to maintain the ratio? Solution: You need 2 cups of lemon juice, so you should add 2 cups x 4 = 8 cups of water.

Worked Example 2: Smart Shopping Problem: You’re at a store deciding between two bottles of juice. One bottle costs $2.50 for 500 ml, and the other costs $3.00 for 750 ml. Which one is the better deal based on cost per milliliter? Solution: Calculate the cost per milliliter for each bottle. The first bottle costs $2.50 / 500 ml = $0.005 per ml, while the second bottle costs $3.00 / 750 ml = $0.004 per ml. The second bottle is the better deal.

Worked Example 3: Fair Resource Sharing Problem: You and your three friends are sharing 12 cookies. If you want to divide them equally, what’s the ratio of cookies each person should get? Solution: Divide the cookies into four equal parts. The ratio is 12 cookies divided into 4 parts, which simplifies to 3:1. Each person should get 3 cookies.

Worked Example 4: Budget Planning Problem: You earn $1,200 per month, and you want to save 15% of your income. How much should you save each month? Solution: Calculate 15% of $1,200. 15% is equivalent to the ratio 15/100. You should save (15/100) * $1,200 = $180 each month.

Worked Example 5: Construction Work Problem: To make a concrete mix with a 4:1 ratio of sand to cement, you need 100 pounds of cement. How many pounds of sand do you need? Solution: Set up a proportion: (4 parts of sand / 1 part of cement) = (x pounds of sand / 100 pounds of cement). Solve for x to find that you need 400 pounds of sand.

These examples demonstrate how ratios are applied to solve practical problems in everyday life, from cooking to shopping to resource sharing and more.

  1. In a cake recipe, the ratio of flour to sugar is 3:2. If you have 4 cups of flour, how many cups of sugar should you use? You should use ___ cups of sugar.
    • A) 2
    • B) 4
    • C) 6
    • D) 8
  2. When shopping, you can find the better deal by comparing the ___________ of products.
    • A) color
    • B) size
    • C) cost per unit
    • D) brand
  3. If there are 15 candies to be shared equally among 3 friends, the ratio of candies per friend is ___.
    • A) 5
    • B) 10
    • C) 15
    • D) 3
  4. You want to save 25% of your monthly allowance, which is $200. How much should you save? You should save ___.
    • A) $50
    • B) $100
    • C) $150
    • D) $25
  5. A balanced meal might have a ratio of 2:1 for vegetables to _______.
    • A) meat
    • B) water
    • C) dessert
    • D) fruits
  6. To create a concrete mix with a 2:1 ratio of sand to cement, if you have 60 pounds of cement, how many pounds of sand do you need? You need ___ pounds of sand.
    • A) 60
    • B) 120
    • C) 30
    • D) 90
  7. When tracking running speed, the ratio of distance to time is used to calculate ___.
    • A) distance
    • B) speed
    • C) time
    • D) shoes
  8. In a pizza, if you want to divide 8 slices equally among 4 friends, each friend should get ___ slices.
    • A) 1
    • B) 2
    • C) 4
    • D) 8
  9. If a sweater costs $30 and has 5 buttons, what is the cost per button? The cost per button is $___.
    • A) 3
    • B) 6
    • C) 5
    • D) 10
  10. To make a fruit salad, the ratio of apples to oranges is 2:3. If you have 6 apples, how many oranges should you use? You should use ___ oranges.
    • A) 4
    • B) 8
    • C) 12
    • D) 18
  11. A recipe for lemonade requires a 1:5 ratio of lemon juice to water. If you have 2 cups of lemon juice, how many cups of water should you add? You should add ___ cups of water.
    • A) 2
    • B) 4
    • C) 8
    • D) 10
  12. When planning your weekly schedule, you allocate 30% of your time for studying. If you have 24 hours in a day, how many hours should you spend studying? You should spend ___ hours studying.
    • A) 8
    • B) 6
    • C) 7.2
    • D) 9.6
  13. A carpenter uses a 3:2 ratio of nails to screws in a project. If you need 60 screws, how many nails should you use? You should use ___ nails.
    • A) 30
    • B) 45
    • C) 20
    • D) 40
  14. In a race, if you cover 12 miles in 2 hours, your speed is ___ miles per hour.
    • A) 5
    • B) 12
    • C) 2
    • D) 6
  15. When comparing the cost per unit of two products, you are looking for the _______ deal.
    • A) better
    • B) pricier
    • C) tastier
    • D) smaller
  1. Presentation (15 minutes):
    • Provide examples of real-life problems where ratios are useful. For instance, show a recipe and ask students to determine the right ratio of ingredients.
    • Explain the concept of “cost per unit” in shopping and how ratios can help find the best deal.
    • Discuss scenarios where resources need to be shared equally and how ratios can assist in fair distribution.
  2. Teacher’s Activities (10 minutes): Use the chalkboard and visual aids to work through examples with the students. Explain step by step how to use ratios in each scenario.
  3. Learners’ Activities (10 minutes): Divide the students into groups and give each group a real-life problem to solve using ratios. Encourage them to discuss and work through the problem together.
  4. Assessment (5 minutes): Ask individual students to share their solutions and explain how they used ratios to solve the problems. Evaluate their understanding and problem-solving skills.
  5. Evaluation (5 minutes): Provide feedback to the students on their performance and understanding. Clarify any misconceptions if necessary.

1. The ratio of boys to girls in a class is 3:5. If there are 18 boys, how many girls are there?

– A) 9

– B) 12

– C) 15

– D) 30

 

2. If a recipe calls for a ratio of 2 parts water to 4 parts sugar, and you need 8 cups of sugar, how much water should you use?

– A) 4 cups

– B) 6 cups

– C) 8 cups

– D) 10 cups

 

3. In a competition, the prize money of $600 is to be divided in the ratio of 1:2:3 among three winners. How much does the second winner get?

– A) $150

– B) $200

– C) $300

– D) $450

 

4. If a car travels 120 miles in 3 hours, what is the ratio of the distance traveled to the time taken?

– A) 20:1

– B) 30:2

– C) 40:3

– D) 60:4

 

5. The ratio of apples to oranges in a basket is 5:3. If there are 15 apples, how many oranges are there?

– A) 5

– B) 7

– C) 9

– D) 11

 

6. If you mix 2 liters of red paint with 3 liters of blue paint, what is the ratio of red to blue paint in the mixture?

– A) 2:3

– B) 3:2

– C) 5:6

– D) 6:5

 

7. In a classroom, the ratio of boys to girls is 4:7. If there are 28 girls, how many boys are there?

– A) 12

– B) 16

– C) 20

– D) 24

 

8. A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. What is the ratio of blue marbles to the total number of marbles?

– A) 4:8

– B) 4:12

– C) 4:12

– D) 4:11

 

9. The ratio of adults to children in a park is 5:3. If there are 30 children, how many adults are there?

– A) 15

– B) 18

– C) 20

– D) 25

 

10. A recipe for pancakes calls for 2 cups of milk and 1 cup of flour. If you want to make 12 pancakes, how much flour do you need?

– A) 6 cups

– B) 9 cups

– C) 10 cups

– D) 12 cups

 

11. If the ratio of cats to dogs in a neighborhood is 3:2, and there are 15 cats, how many dogs are there?

– A) 7

– B) 10

– C) 12

– D) 20

 

12. In a race, the ratio of the distance covered by Tom to the distance covered by Jerry is 2:3. If Tom ran 6 miles, how far did Jerry run?

– A) 4 miles

– B) 6 miles

– C) 8 miles

– D) 9 miles

 

13. A solution is made by mixing 1 part of lemon juice with 4 parts of water. If you need 500 ml of the solution, how much lemon juice should you use?

– A) 100 ml

– B) 125 ml

– C) 200 ml

– D) 400 ml

 

14. The ratio of students who like math to those who like science is 3:5. If there are 24 students who like science, how many like math?

– A) 9

– B) 12

– C) 15

– D) 18

 

15. A farmer has 20 cows and 30 sheep. What is the ratio of cows to the total number of animals?

– A) 1:2

– B) 2:5

– C) 3:5

– D) 4:5

 

  1. In a cake recipe, the ratio of flour to sugar is 3:2. If you have 4 cups of flour, how many cups of sugar should you use? You should use ___ cups of sugar.
    • A) 2
    • B) 4
    • C) 6
    • D) 8
  2. When shopping, you can find the better deal by comparing the ___________ of products.
    • A) color
    • B) size
    • C) cost per unit
    • D) brand
  3. If there are 15 candies to be shared equally among 3 friends, the ratio of candies per friend is ___.
    • A) 5
    • B) 10
    • C) 15
    • D) 3
  4. You want to save 25% of your monthly allowance, which is $200. How much should you save? You should save ___.
    • A) $50
    • B) $100
    • C) $150
    • D) $25
  5. A balanced meal might have a ratio of 2:1 for vegetables to _______.
    • A) meat
    • B) water
    • C) dessert
    • D) fruits
  6. To create a concrete mix with a 2:1 ratio of sand to cement, if you have 60 pounds of cement, how many pounds of sand do you need? You need ___ pounds of sand.
    • A) 60
    • B) 120
    • C) 30
    • D) 90
  7. When tracking running speed, the ratio of distance to time is used to calculate ___.
    • A) distance
    • B) speed
    • C) time
    • D) shoes
  8. In a pizza, if you want to divide 8 slices equally among 4 friends, each friend should get ___ slices.
    • A) 1
    • B) 2
    • C) 4
    • D) 8
  9. If a sweater costs $30 and has 5 buttons, what is the cost per button? The cost per button is $___.
    • A) 3
    • B) 6
    • C) 5
    • D) 10
  10. To make a fruit salad, the ratio of apples to oranges is 2:3. If you have 6 apples, how many oranges should you use? You should use ___ oranges.
    • A) 4
    • B) 8
    • C) 12
    • D) 18
  11. A recipe for lemonade requires a 1:5 ratio of lemon juice to water. If you have 2 cups of lemon juice, how many cups of water should you add? You should add ___ cups of water.
    • A) 2
    • B) 4
    • C) 8
    • D) 10
  12. When planning your weekly schedule, you allocate 30% of your time for studying. If you have 24 hours in a day, how many hours should you spend studying? You should spend ___ hours studying.
    • A) 8
    • B) 6
    • C) 7.2
    • D) 9.6
  13. A carpenter uses a 3:2 ratio of nails to screws in a project. If you need 60 screws, how many nails should you use? You should use ___ nails.
    • A) 30
    • B) 45
    • C) 20
    • D) 40
  14. In a race, if you cover 12 miles in 2 hours, your speed is ___ miles per hour.
    • A) 5
    • B) 12
    • C) 2
    • D) 6
  15. When comparing the cost per unit of two products, you are looking for the _______ deal.
    • A) better
    • B) pricier
    • C) tastier
    • D) smaller

Conclusion: Summarize the key points of the lesson and emphasize the practical applications of ratios in daily life.

Assignment: Assign a homework task where students need to find a real-life scenario at home where ratios can be applied. They should write a short paragraph explaining how ratios can be used to solve that problem.

By the end of this lesson, students should have a solid understanding of how ratios are used to solve real-life problems and be able to apply this knowledge in practical situations.