Class VIII: Proportional Reasoning-1 Smart Lab

CLASS VIII • PROPORTIONAL REASONING-1Smart Lab: Ratios, Proportion & Rule of Three

Proportional Reasoning-1: Ratio Detective Lab

Explore why some resized images look similar, reduce ratios using HCF, test proportions, solve missing values, and apply the Rule of Three to everyday situations like lemonade, coffee, rice, speed, and maps.

Fact Sheet: Seeing Proportion

Two shapes, recipes, or quantities are proportional when both terms change by the same multiplication factor. Same difference is not enough.

Image idea: A 60 mm × 40 mm image and a 30 mm × 20 mm image look similar because width and height are both multiplied by 1/2.

Ratio language: In a : b, for every a units of the first quantity, there are b units of the second quantity.

Proportion symbol: a : b :: c : d means the two ratios are proportional.

60 : 40

÷ HCF 20

3 : 2

30 : 20

÷ HCF 10

3 : 2

Formula Hub

Ratio

Compares two quantities in order.

width : height = 60 : 40

Simplest Form

Divide both terms by their HCF.

60 : 40 = 3 : 2

Proportion Test

Ratios are proportional if simplest forms match.

3 : 2 :: 90 : 60

Cross Multiplication

For a : b :: c : d, products are equal.

a × d = b × c

Find Unknown

When a : b :: c : x.

x = (b × c) ÷ a

Rule of Three

Multiply phala by ichchhā, divide by pramāṇa.

yield = phala × ichchhā ÷ pramāṇa

a : b :: c : d ⟹ a × d = b × c

Interactive Lab: Ratio Detective

Score: 0Current Streak: 🔥 0Badge: Ratio Rookie

Activity Zone

🖼️ Similar Image Checker

Compare a base image with a new size. The lab checks whether width and height changed by the same factor.

Base width Base height
New width New height

☕ Coffee Strength Mixer

Regular coffee uses 15 mL decoction and 35 mL milk. Compare any mix.

Coffee decoction Milk

🍋 Lemonade Proportion Solver

Kesang uses 10 spoons of sugar for 6 glasses. Keep the same sweetness.

Glasses needed

🔎 Missing Term Solver

Solve a : b :: c : x using cross multiplication.

a b c

📋 Ratio Table Generator

Worksheet Generator

Generate practice on simplest form, true proportions, missing terms, and word problems.

Number of problems:

Real-World Use

Recipes: Keep the same taste by multiplying every ingredient by the same factor.

Construction: Compare wall length and cement used to judge equal strength.

Travel: If speed is constant, time and distance remain proportional after units are matched.

Maps and Models: Scale drawings use proportional lengths so shapes keep the same look.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

Explain proportional change using same multiplication factor.
Represent comparisons as ratios in the form a : b.
Reduce ratios to simplest form using HCF.
Test proportion using simplest form and cross multiplication.
Solve Rule of Three problems with correct units.

Exit Ticket Prompts

Why do 60 : 40 and 90 : 60 represent similar rectangles?
Give one example where adding the same amount does not preserve proportion.
Solve: 150 : 90 :: 240 : x and explain the unit step.

Suggested Differentiation

Use the Similar Image Checker for visual learners, the Coffee Mixer for contextual reasoning, and the Missing Term Solver for procedural fluency.