Mathematics · Class 6

Active learning ideas

The Unitary Method

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

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Problem-Based Learning
• 25 min · Pairs

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.

Explain the steps involved in solving a problem using the unitary method.

Facilitation Tip

Use realistic prices and items to make the activity more relatable and engaging for students.

What to look for

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.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 20 min · Small Groups

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.

Analyse a word problem to determine when the unitary method is the appropriate strategy.

Facilitation Tip

Encourage students to write down their steps clearly, showing how they calculated the amount for one person first.

What to look for

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).

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 15 min · Individual

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.

Compare the cost of items when given bulk prices using the unitary method.

Facilitation Tip

Remind students that the first step is always to find the distance travelled in one hour.

What to look for

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.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Begin with concrete examples using real objects, like finding the cost of one pen from a packet of five. Emphasise the core logic: to find the value of one from many, we divide; to find the value of many from one, we multiply. Gradually move from simple cost-based problems to those involving distance and time, ensuring students write down each step.

Your students will soon be able to confidently solve practical word problems by mastering the simple two-step logic of the unitary method.

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Watch Out for These Misconceptions

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

  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.'

• 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).

  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.

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

  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.

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Methods used in this brief

• Problem-Based Learning