Ratio – Definition, Writing, and Conversion

Grade 6 · Mathematics

Semester 2 | Period 6 | Week 31

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Subject: Mathematics

Semester: 2

Period: 6

Week: 31

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 31
Lesson Duration: 45 minutes
Week & Period: Week 31, Period 6
Topic: Ratio – Definition, Writing, and Conversion
Sub-topic: Simplifying Ratios and Real-Life Applications

Learning Objectives
By the end of the lesson, students should be able to:
Define a ratio as a comparison of two quantities using division
Write ratios in their simplest form
Convert fractions and percentages into ratios
Apply ratios to real-life situations

Previous Knowledge
Students already know fractions, percentages, and basic division.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: If there are 10 boys and 5 girls in a class, how can we compare boys to girls? Learners attempt answers, leading into the concept of ratio.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definition and Explanation

  • A ratio is a way of comparing two or more quantities of the same kind by using division.
  • Ratios show how many times one quantity is contained in another or how one quantity relates to another.
  • Written in the form a:b or as a fraction a/b.

Key Points

  1. Simplest form of a ratio:
    • Always reduce ratios to their simplest form by dividing both terms by their Greatest Common Factor (GCF).
    • Example: Ratio of 12 to 8 = 12:8.
      • GCF of 12 and 8 = 4 → Divide both by 4 → 3:2.
  1. Ratio as fractions:
    • A fraction can be written as a ratio.
    • Example: ¾ = 3:4.
  2. Ratio from percentages:
    • Any percentage can be written as a ratio over 100, then simplified.
    • Example: 60% = 60:100 = divide both by 20 → 3:5.
  3. Ratios in daily life:
    • Classroom: Boys to girls.
    • Marbles: Red to blue.
    • Cooking: Ratio of flour to sugar.
    • Maps: Ratio scale (e.g., 1:1000).

 

Worked Examples

  1. Apples and oranges: 12 apples, 8 oranges → 12:8 = 3:2.
  2. Boys to girls: 18 boys, 12 girls → 18:12 = divide by 6 = 3:2.
  3. Red to blue marbles: 15 red, 25 blue → 15:25 = divide by 5 = 3:5.
  4. Write fraction as ratio: ⅘ = 4:5.
  5. Write percentage as ratio: 75% = 75:100 = divide by 25 → 3:4.
  6. If a recipe uses 2 cups of sugar and 5 cups of flour, ratio sugar to flour = 2:5.

 

More Practice Examples (Classwork)

  • Write the following as ratios in simplest form:
  1. 9 to 15
  2. 35 boys, 21 girls
  3. 80% as a ratio
  4. ⅖ as a ratio
  5. 45 cm to 60 cm

Solutions:

  1. 9:15 = 3:5
  2. 35:21 = 5:3
  3. 80% = 80:100 = 4:5
  4. ⅖ = 2:5
  5. 45:60 = 3:4

 

Word Problem Applications

  1. A class has 25 students: 10 girls and 15 boys. Find the ratio of:
    Boys to girls
    ii. Girls to boys
    iii. Boys to total students

Solution:
i. 15:10 = 3:2
ii. 10:15 = 2:3
iii. 15:25 = 3:5

  1. A farmer has 50 goats and 30 sheep. Find the ratio of goats to sheep.
    Solution: 50:30 = 5:3.
  2. A survey shows that 40% of students like football. Write this percentage as a ratio in simplest form.
    Solution: 40:100 = 2:5.

 

Learners’ Activities (Expanded)

  • Learners count boys and girls in their own class and express as ratios.
  • Learners use real objects (books, pencils, chairs) to form ratios.
  • Learners simplify given fractions and percentages into ratios.
  • Learners create and solve their own ratio word problems in small groups.

 

Assessment Checks

  1. Write 40% as a ratio in simplest form. (Answer: 2:5)
  2. Simplify the ratio 24:36. (Answer: 2:3)
  3. If there are 8 red pens and 12 blue pens, what is the ratio of red pens to blue pens? (Answer: 2:3)
  4. Express ⅚ as a ratio. (Answer: 5:6)
  5. A school has 120 boys and 80 girls. Find the ratio of boys to total students. (Answer: 3:5)

 

Notes (Expanded & Detailed)

  • Ratios are written like fractions but use a colon (:) instead of a line.
  • Ratios can compare part-to-part (boys:girls) or part-to-whole (boys:total students).
  • Fractions and percentages can easily be written as ratios.
  • Always reduce ratios to simplest form for accuracy.
  • Ratios are widely applied in cooking, trade, maps, construction, population studies, and science experiments.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Ratios compare quantities, can be simplified, and are linked to fractions and percentages.

Evaluation Method (Expanded):
Exit slip/quiz: Simplify 24:36. Express 75% as a ratio. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):

  1. Express 2/5 as a ratio.
  2. Simplify 18:27.
  3. In a class of 20 boys and 15 girls, find the ratio of boys to girls.

Follow-up Activity:
Learners compare numbers of objects at home (spoons to plates, pens to pencils) in ratio form.

Differentiation / Inclusive Strategies
Use colored objects for learners who struggle with abstract numbers. Allow group work for peer explanation.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low