Mathematics · Class 6 · Ratio and Proportion · Term 3

The Unitary Method

Master a technique to first find the value of a single unit and then use it to find the value of the required number of units.

TL;DR:Unlock a powerful maths trick for everyday life, from finding the best deals at the market to planning a road trip.

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

About This Topic

The Unitary Method is a foundational arithmetic technique introduced in the middle school curriculum, aligning with the NCF's emphasis on connecting mathematics to daily life. It is a crucial stepping stone for understanding more advanced concepts like ratio, proportion, and percentages. The method involves a two-step process: first, determining the value of a single unit from the value of multiple units (using division), and second, calculating the value of the required number of units (using multiplication). This logical approach simplifies complex-looking word problems related to cost, distance, time, and capacity, making them accessible to Class 6 students.

In the Indian context, this topic holds immense practical value. Teachers can effectively contextualise problems using everyday scenarios like purchasing groceries from a local kirana store, calculating the mileage of a scooter, or scaling a recipe for a family function. Mastering the unitary method not only equips students with a problem-solving tool but also develops their logical reasoning and ability to break down problems into manageable parts. It serves as a bridge between basic arithmetic operations and their application in real-world transactional and measurement-based situations, which is a key objective of mathematics education at this level.

Key Questions

1. Explain the steps involved in solving a problem using the unitary method.
2. Analyse a word problem to determine when the unitary method is the appropriate strategy.
3. Compare the cost of items when given bulk prices using the unitary method.

Learning Objectives

• Define the unitary method as a two-step process of division then multiplication.
• Calculate the value of a single unit when given the value of multiple units.
• Solve word problems involving cost, distance, and capacity using the unitary method.
• Apply the unitary method to compare the value of items and determine the better buy.
• Articulate the steps required to solve a given problem using this method.

Key Vocabulary

Unitary Method	A method of problem-solving where we first find the value of a single unit and then find the value of the required number of units.
Unit	A single item or a standard quantity of measurement.
Value	The cost, price, or worth of something.
Quantity	The amount or number of items.
Per Unit Cost	The cost for one single item or quantity.

Watch Out for These Misconceptions

Common Misconception

Students often confuse when to multiply and when to divide. They might multiply to find the value of one unit from many.

What to Teach Instead

Explain the logic clearly: 'To find the value of one unit from many, the value must get smaller, so we divide. To find the value of many units from one, the value must get bigger, so we multiply.' Use the mantra: 'Many to one, divide. One to many, multiply.'

Common Misconception

Students try to apply the method directly to inverse proportion problems without adjusting their logic (e.g., if 10 men do a job in 6 days, they incorrectly calculate that 5 men will do it in 3 days).

What to Teach Instead

For Class 6, focus on direct proportion problems first to build a strong foundation. When introducing inverse proportion, explicitly highlight the difference: 'Here, more men means less time, so the logic is different.' This is an advanced concept that should be handled separately.

Common Misconception

Forgetting to write the units in the final answer, or using incorrect units.

What to Teach Instead

Model good practice by always writing down the units (e.g., ₹, kg, km, hours) at each step of the calculation. Remind students that the answer is incomplete without the correct unit.

Active Learning Ideas

Problem-Based Learning

Kirana Store Shopping

Provide students with mock price lists from a grocery store (e.g., '5 kg of atta for ₹180', 'a dozen bananas for ₹60'). Students work in pairs to calculate the cost of different quantities, like 2 kg of atta or 7 bananas, to find the best deals.

25 min·Pairs

Problem-Based Learning

Recipe Resizing

Give groups a simple recipe for 4 people (like for nimbu pani or a simple snack). Their task is to rewrite the recipe with the correct ingredient quantities to serve the entire class or a larger group of 20 people.

20 min·Small Groups

Problem-Based Learning

Travel Time Calculator

Present a scenario like, 'A train travels 240 km in 4 hours at a constant speed.' Ask students to calculate how far it will travel in 7 hours, or how long it will take to cover 180 km.

15 min·Individual

Real-World Connections

• Comparing prices at the supermarket to find the best deal, for example, calculating the cost per apple in a pack of 6 versus a pack of 10.
• Calculating the total cost of petrol for a road trip based on the vehicle's mileage (kilometres per litre).
• Adjusting a recipe's ingredients when cooking for more or fewer people than the recipe states.
• Figuring out how long a journey will take based on the distance covered in the first hour.
• Calculating earnings based on an hourly or daily wage.

Assessment Ideas

Exit Ticket

Use an 'exit slip'. Give students a simple word problem at the end of the class and ask them to write down only the first step: how they would find the value of one unit.

Quick Check

During group work, circulate and listen to student discussions. Note whether they are correctly identifying the two steps (finding the value of one, then finding the value of many).

Quick Check

A worksheet with 5-7 word problems of increasing difficulty, requiring students to show their complete working, including the intermediate step of finding the unit value.

Frequently Asked Questions

Why is it called the 'unitary' method?

It is called the unitary method because the first step is always to find the value of a single 'unit'. The word 'uni' means one, like in 'uniform' or 'unicycle'.

Do I always have to find the value of one unit first?

Yes, finding the value of one unit is the most reliable and universal way to solve these problems. It is a simple, two-step process that works every time, no matter what the numbers are.

Where will I use the unitary method in real life?

You use it very often! For example, when you are shopping and comparing prices of two different packets of biscuits to see which is cheaper per biscuit, or when you are calculating the petrol needed for a long trip based on your bike's mileage.