Mathematics · Class 6 · Ratio and Proportion · Term 3

Introduction to Ratios

Learn how to compare two quantities of the same kind using a ratio and express it in its simplest form.

TL;DR:Let's discover a powerful mathematical tool used everywhere, from your kitchen to the cricket field, to compare anything and everything.

• CBSE Learning Outcomes
• NCERT Class 6: Chapter 12 - Ratio and Proportion

About This Topic

The introduction to ratios in Class 6 is a pivotal moment in a student's mathematical journey, serving as a bridge between arithmetic and more advanced proportional reasoning. As per the NCF guidelines, this topic must be rooted in the child's context, moving from concrete comparisons to abstract representation. Ratios extend the concept of fractions, but with a crucial distinction: while fractions are typically part-to-whole comparisons, ratios can be part-to-part (e.g., boys to girls) or part-to-whole (e.g., boys to total students). This conceptual shift is fundamental for later topics like proportions, percentages, unitary method, and even foundational concepts in physics and chemistry.

The initial focus should be on developing a strong conceptual understanding of 'comparison by division'. Students should be encouraged to use the language 'for every... there are...' before they are introduced to the formal 'a:b' notation. The curriculum intends for students to see ratios not just as a mathematical procedure but as a practical tool for making sense of the world around them, from analysing sports statistics to following a recipe. Mastering the simplification of ratios by finding the HCF is a key procedural skill that reinforces prior knowledge of factors and multiples.

Key Questions

1. Explain how a ratio is different from a fraction.
2. Identify real-life situations where ratios are used for comparison.
3. Compare the ratio of boys to girls in your class with the ratio of students to teachers.

Learning Objectives

• Define a ratio as a comparison of two quantities of the same kind by division.
• Express a comparison in the format 'a:b' and identify the antecedent and consequent.
• Calculate the simplest form of a ratio by dividing both terms by their HCF.
• Solve simple word problems involving finding and comparing ratios from real-life situations.
• Distinguish between a part-to-part and a part-to-whole comparison.

Key Vocabulary

Ratio	A comparison of two quantities of the same kind. It is written as a:b.
Antecedent	The first term in a ratio (the 'a' in a:b).
Consequent	The second term in a ratio (the 'b' in a:b).
Simplest Form	A ratio is in its simplest form when its antecedent and consequent have no common factor other than 1.
Equivalent Ratios	Ratios that represent the same comparison. For example, 1:2 and 5:10 are equivalent ratios.

Watch Out for These Misconceptions

Common Misconception

The order of the terms in a ratio does not matter. For example, the ratio of boys to girls is the same as the ratio of girls to boys.

What to Teach Instead

The order in a ratio is critical because it reflects the comparison being made. The ratio of boys to girls (boys:girls) is the inverse of the ratio of girls to boys (girls:boys), unless the numbers are equal. Always check which quantity is mentioned first.

Common Misconception

A ratio is exactly the same as a fraction.

What to Teach Instead

While a ratio can be written in a fractional form, its meaning can be different. A fraction compares a part to the whole (e.g., 5 boys out of 20 total students is 5/20). A ratio can compare a part to another part (e.g., 5 boys to 15 girls is 5:15).

Common Misconception

Ratios cannot be simplified, or they are simplified using subtraction.

What to Teach Instead

Ratios should be expressed in their simplest form, just like fractions. To simplify a ratio, you must divide both terms by their Highest Common Factor (HCF), not subtract a number.

Active Learning Ideas

Experiential Learning

Classroom Ratio Hunt

Students work in pairs to find and write down various ratios within the classroom, such as the ratio of desks to chairs, windows to doors, or notebooks to textbooks. They then simplify these ratios and share their findings with the class.

20 min·Pairs

Experiential Learning

Nimbu Paani Ratios

Provide a simple recipe for nimbu paani (lemonade), for example, 1 part lemon juice to 2 parts sugar to 8 parts water. Ask students in small groups to calculate the amount of each ingredient needed to make enough for their group, then for the whole class.

25 min·Small Groups

Experiential Learning

My Family Ratio

As a homework activity, students write down ratios from their own family, such as the ratio of adults to children, males to females, or the number of rooms to the number of people. This connects the mathematical concept to their personal lives.

15 min·Individual

Real-World Connections

• Following recipes, where the ratio of ingredients like flour to sugar determines the taste.
• Reading maps, where the scale is a ratio of the distance on the map to the actual distance on the ground.
• Mixing paints to get a specific shade, for example, the ratio of blue paint to yellow paint to make green.
• Analysing a cricketer's performance, such as the ratio of fours to sixes hit in a match.
• Comparing prices in a shop to find the best value, like the cost-to-weight ratio for two different packets of dal.

Assessment Ideas

Quick Check

Give students a picture with various objects (e.g., 5 cars, 3 bikes, 8 trees) and ask them to write three different ratios on a mini-whiteboard, such as cars to bikes.

Quick Check

A short worksheet with word problems. For example: 'In a fruit basket, there are 12 mangoes and 16 bananas. What is the ratio of mangoes to bananas in its simplest form?'

Quick Check

Students use a traffic light system (red, yellow, green) to indicate their confidence level in writing a ratio, simplifying a ratio, and solving a ratio word problem.

Frequently Asked Questions

Why do we need to learn ratios when we already know fractions?

Ratios are a special tool for comparison. They allow us to compare two parts of a group with each other (like runs scored by Virat Kohli versus Rohit Sharma), not just a part with the whole group. This is very useful in science, cooking, and everyday life.

Can a ratio have units like cm or kg?

No, a ratio is a pure number. It compares two quantities of the same kind, so the units cancel each other out. For example, the ratio of 5 kg of rice to 10 kg of wheat is 5:10 or 1:2, not 1 kg:2 kg.

Is the ratio 2:3 bigger or smaller than 3:4?

To compare ratios, we can convert them to like fractions. 2:3 is like 2/3 and 3:4 is like 3/4. To compare 2/3 and 3/4, we find a common denominator, which is 12. So we compare 8/12 and 9/12. Since 9/12 is greater, the ratio 3:4 is greater than 2:3.