🔷 Chapter 3 – How Many Squares?
Subject: Mathematics
Main Concepts: Area, Perimeter, Squares, Rectangles, Comparing Areas
📘 Introduction
In this chapter, we learn how to compare sizes of shapes using squares. We also understand two very important ideas: Area and Perimeter.
Children are not required to memorise formulas here. Instead, they learn by counting squares, observing shapes, and doing activities.
⬛ What is a Square Grid?
A square grid is made of many equal squares. Each small square usually has a side of 1 cm.
📐 What is Area?
Area tells us how much surface a shape covers.
✔ How to find Area using squares
To find area:
- Place the shape on a square grid
- Count the number of full squares covered
If a shape covers 12 small squares, its area = 12 square cm
📏 What is Perimeter?
The length of the boundary of a shape is called its perimeter.
🟥 Rectangles with Same Area
If we use 12 equal squares, we can make many rectangles.
| Rectangle Size | Area | Perimeter |
|---|---|---|
| 1 × 12 | 12 sq cm | 26 cm |
| 2 × 6 | 12 sq cm | 16 cm |
| 3 × 4 | 12 sq cm | 14 cm |
✔ Perimeter changes
📮 Measuring Area using Stamps
We can find the area of stamps by placing them on a square grid.
If a stamp covers 12 squares, Area of the stamp = 12 sq cm
👣 How Big is My Hand or Foot?
Hands and footprints have irregular shapes. To find their area:
- Trace the hand or foot on squared paper
- Count full squares
- Join half squares to make full squares
Trace your hand and your friend’s hand. Count the squares and compare the areas.
🐾 Animal Footprints
Different animals have footprints of different areas.
✔ Shape may be different but area can be same
🔺 Try Triangles
A triangle can be formed by cutting a rectangle into two equal parts.
✏️ Complete the Shape
Sometimes only part of a shape is drawn. We complete it so that the area becomes a given value.
Can different shapes have the same area? ✔ Yes!
🧩 Puzzles with Five Squares
Using 5 equal squares, many different shapes can be made.
✔ Perimeter may be different
🎮 Game Time & Tiling
Some shapes can cover a floor completely without gaps. This is called tiling.
✔ Some shapes do not tile
✍️ Practice Questions
2) Can two shapes have the same area but different perimeters?
3) How do you find the area of an irregular shape?
4) If a rectangle has area 20 sq cm, what is the area of one half?
✅ Quick Revision
✔ Perimeter is the boundary length
✔ Same area ≠ same perimeter
✔ Counting squares helps find area
🎉 Chapter Complete
After studying this chapter, students can confidently compare areas, understand perimeters, and solve puzzles using squares.
📝 Complete Worksheet – How Many Squares?
Chapter: How Many Squares?
Focus: Area, Perimeter, Squares, Rectangles 🎯
Section A – Multiple Choice Questions (MCQs)
Q1. The length of the boundary of a shape is called:
Q2. If a shape covers 15 small squares, its area is:
Q3. Two rectangles made of 12 equal squares will always have:
Q4. Which unit is used to measure area?
✔ Q2 → (b) 15 square cm
✔ Q3 → (c) Same area
✔ Q4 → (c) square cm
Section B – Fill in the Blanks
2) A square grid helps us to find __________ of a shape.
3) Two shapes can have the same area but different __________.
4) Each small square in a grid usually represents __________ square cm.
✔ area
✔ perimeter
✔ 1
Section C – Very Short Answer Questions
1) What does area tell us?
2) What is perimeter?
3) Name the shape that tiles a floor easily.
✔ Perimeter is the length of the boundary of a shape.
✔ Square / Rectangle
Section D – Short Answer Questions
Q1. How do you find the area of an irregular shape?
Q2. Can two shapes have the same area but different perimeters? Explain.
Q3. A rectangle covers 20 squares. What is its area?
✔ Yes, area can be same but boundary length can be different.
✔ 20 square cm
Section E – Long Answer Questions
Q1. Explain with an example how rectangles of the same area can have different perimeters.
Q2. How will you find the area of your hand?
✔ Trace hand on grid, count full and half squares.
Section F – HOTS / Thinking Questions ⭐
Q1. Why do squares with the same area sometimes look different?
Q2. Why are square tiles commonly used on floors?
✔ They tile the floor completely without gaps.
🎯 Worksheet Complete
✔ Practice grid counting daily
✔ Revise area vs perimeter difference
✔ You are now exam-ready ✅