NCERT Class 5 Mathematics Math-Mela: Chapter 10 — 10
This chapter, 'Designs,' from NCERT's Class 5 Mathematics Math-Mela, revisits the concept of lines of symmetry introduced in Grade 4. Students learn how to create symmetrical cutouts of letters like 'A' and 'H' by folding paper and drawing half or a quarter of the letter along the fold. The chapter explores which alphabet letters possess vertical, horizontal, or both types of symmetry. It then guides students through a practical activity to make a paper windmill (firki) by following sequential steps involving folding, cutting, and assembling. The firki activity encourages observation of rotational symmetry, prompting students to notice how the design appears after different fractions of a turn. This chapter reinforces understanding of symmetry and its application in creating patterns and objects, crucial for developing spatial reasoning skills in mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 5 |
| Subject | Mathematics |
| Book | Math-Mela |
| Chapter | Chapter 10 — 10 |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 547 |
Learning outcomes
- Understand and apply the concept of lines of symmetry to create symmetrical shapes.
- Identify letters with vertical, horizontal, and both vertical and horizontal lines of symmetry.
- Create paper cutouts of letters and designs using symmetry.
- Understand and observe rotational symmetry through a windmill activity.
- Relate symmetry concepts to practical applications like making paper crafts.
Vocabulary
| Word | Meaning |
|---|---|
| Reflection symmetry | A shape has reflection symmetry if it can be divided by a line into two parts that are mirror images of each other. |
| Lines of symmetry | The line that divides a shape into two identical halves. |
| Vertical line of symmetry | A line of symmetry that runs up and down. |
| Horizontal line of symmetry | A line of symmetry that runs from side to side. |
| Cutouts | Shapes or letters cut from paper. |
| Rotational symmetry | A shape has rotational symmetry if it looks the same after being rotated by some angle less than a full turn. |
| Firki | A pinwheel or windmill made of paper. |
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Practice questions
- Which letters from the given list (E, N, X, T, K, V, O) have a vertical line of symmetry? Answer: N, X, T, K, V
- Which letters from the given list (E, N, X, T, K, V, O) have a horizontal line of symmetry? Answer: E, X, O
- Which letters from the given list (E, N, X, T, K, V, O) have both vertical and horizontal lines of symmetry? Answer: X, O
- How can you make a cutout of the letter 'A' using a folded paper? Answer: Fold a paper in half, draw half of the letter 'A' along the fold, cut it out, and open the paper.
- What is the purpose of the pin in making the windmill firki? Answer: The pin holds the folded corners together and allows the firki to spin on a stick or straw.
Frequently asked questions
What is the main concept taught in the NCERT Class 5 Mathematics chapter 'Designs'?
The chapter focuses on lines of symmetry and how to use them to create symmetrical designs and cutouts, including letters and a paper windmill.
How can students make letter cutouts using symmetry?
Students can fold a paper in half or into quarters, draw half or a quarter of the letter along the fold, and then cut it out to reveal the full symmetrical letter when opened.
Which letters have both vertical and horizontal lines of symmetry?
Letters like 'X' and 'O' have both vertical and horizontal lines of symmetry.
What is a firki, and how is it related to symmetry?
A firki is a paper windmill. It is made using folding and cutting techniques that demonstrate rotational symmetry, as it looks the same after certain turns.
What skill does the firki activity help develop?
The firki activity helps develop observation skills related to rotational symmetry and fine motor skills through paper folding and cutting.
Where can I find the NCERT Class 5 Mathematics Math-Mela Chapter 10 PDF?
The NCERT Class 5 Mathematics Math-Mela Chapter 10 'Designs' PDF can be downloaded from the official NCERT website or other educational portals.
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NCERT Class 5 Mathematics — Math-Mela — Chapter 10 — 10. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.