Mathematics · Class 6

Active learning ideas

Solving Problems with Ratios

Have you ever wondered how to share a pizza fairly with friends, even if everyone isn't getting an equal slice? We'll explore how ratios help us divide things perfectly in real-life situations.

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

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Collaborative Problem-Solving
• 25 min · Small Groups

The Perfect Drink Recipe

Students are given a simple recipe for a drink like 'nimbu pani' in a ratio (e.g., 2 parts lemon juice, 1 part sugar, 5 parts water). They then have to calculate the exact amount of each ingredient needed to make a large jug for the whole class.

Explain how to divide a total amount between two people in a specific ratio.

Facilitation Tip

Provide measuring spoons and cups to make the abstract concept of 'parts' more tangible.

What to look for

Use an 'Exit Slip' with a single word problem, such as 'A ribbon 45 cm long is cut into two pieces in the ratio 4:5. Find the length of each piece.' This quickly assesses understanding of the core procedure.

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

Activity 02

• Collaborative Problem-Solving
• 20 min · Pairs

Pocket Money Division

In pairs, students are given a scenario: 'Divide ₹150 pocket money between two siblings, Rohan and Priya, in the ratio of their ages, 8 years and 7 years.' They must calculate how much money each sibling gets.

Analyse a problem to set up the correct ratio for comparison.

Facilitation Tip

Encourage students to first find the total number of parts by adding the terms of the ratio.

What to look for

A chapter-end test with a mix of problems: dividing quantities, finding missing terms, and more complex word problems involving ages or mixtures.

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

Activity 03

• Collaborative Problem-Solving
• 30 min · Individual

Classroom Blueprint

Students measure the length and breadth of their classroom in metres. They then have to draw a scaled-down version in their notebooks using a simple ratio like 1 metre : 2 cm, applying the ratio to their measurements.

Justify your steps when solving a word problem involving the ratio of ages or ingredients.

Facilitation Tip

Start by demonstrating how to calculate the scaled length on the board as a clear example.

What to look for

Provide students with a solved problem containing a common error. Ask them to 'Be the Teacher' and identify, explain, and correct the mistake in the solution.

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

A few notes on teaching this unit

Begin with a visual and hands-on activity, like dividing a collection of beads or counters into a given ratio. After they grasp the concept of 'parts', introduce the standard algorithm of summing the ratio terms and dividing the total. Use the 'I do, We do, You do' approach to scaffold learning from teacher-led examples to independent problem-solving.

By the end of this topic, you will be able to read any word problem and confidently use ratios to divide amounts or find missing quantities, just like a professional.

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Watch Out for These Misconceptions

• If the ratio of boys to girls is 2:3, students might think there are only 2 boys and 3 girls in total.

  Explain that a ratio is in its simplest form. The actual numbers are multiples of the ratio. So, the number of boys is 2x and girls is 3x, where 'x' is a common multiplier.

• When dividing a quantity, students might divide the total amount by each number in the ratio separately.

  Clarify that the ratio represents parts of a whole. We must first add the parts of the ratio (e.g., 2+3=5) to find the total number of shares the quantity is being divided into. Then, find the value of one share.

• Students often get the order of the ratio wrong when reading a word problem.

  Emphasise that the order matters. The quantity mentioned first in the sentence corresponds to the first number (antecedent) in the ratio, and the second quantity corresponds to the second number (consequent).

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Methods used in this brief

• Collaborative Problem-Solving