Mathematics kit use report for the activity spiral root

 

Mathematics Activity Sheet

Class: 9
Topic: Construction of Square Root Spiral
Under: PM SHRI Scheme
Using: JUMBO GEOMETRY BOX MAGNETIC — LKGM 404 Maths Kit

Aim:

To construct a Square Root Spiral (Theodorus Spiral) using geometrical tools and to understand square roots through hands-on visualization.

Kit Items Used:

• JUMBO GEOMETRY BOX MAGNETIC — LKGM 404 Maths Kit

• Magnetic ruler

• Magnetic compass

• Magnetic protractor

• Magnetic set squares

• Magnetic board

• Chalk or marker

• Pointer for demonstration

(This kit is a precision model designed for clear and accurate geometric construction, supporting interactive math learning.)

Procedure:

1. Fix the base point O on the magnetic board.

2. Draw line segment OA = 1 unit.

3. Construct a perpendicular at A using a set square.

4. With center A and radius 1 unit, mark B on the perpendicular line. OB = √2 units.

5. From B, draw the next perpendicular and mark C, making OC = √3 units.

6. Repeat this process, each time:

   • Using the last point as the center,

   • Radius = Distance from O to the last point,

   • Marking the next point.

7. Label each segment with its square root value: √2, √3, √4, √5, and so on.

8. Join all points sequentially to create the Square Root Spiral.

Observation:

• Each new line segment from O to a new point represents a square root value.

• The spiral shows how square roots grow progressively.

• It visually connects the idea of numbers with geometric length.

Conclusion:

The Square Root Spiral Activity helps students understand that square roots are real, measurable lengths and are not just abstract numbers.
This hands-on experience builds clear concepts of irrational numbers and enhances visualization skills.

Targeted Learning Outcomes:

Students will be able to:
✅ Understand the concept of square roots and their geometric representation.
✅ Accurately construct square root-based segments using the Maths Kit.
✅ Visualize the relationship between numbers and their square roots as a growing spiral.
✅ Apply this understanding to real-life math problems.
✅ Develop spatial reasoning, precision, and problem-solving skills through hands-on learning.

Teacher’s Feedback:

The Square Root Spiral Activity using the JUMBO GEOMETRY BOX MAGNETIC — LKGM 404 Maths Kit provided students with a hands-on experience that deepened their understanding of square roots and their geometric interpretation.
The PM SHRI scheme has significantly enriched mathematics learning by introducing such interactive tools, enabling students to engage deeply with concepts rather than rely on rote memorization.
The activity successfully enhanced students’ logical thinking, construction skills, and real-world application of mathematics.

Student’s Feedback:

Constructing the Square Root Spiral using the magnetic maths kit was a fun and interactive way to learn square roots!
It helped us visualize and understand square roots as actual distances rather than just numbers on paper.
We are thankful to our teacher and the PM SHRI Scheme for introducing such exciting learning methods that make math enjoyable, practical, and easy to understand.

✅ Thanks to the PM SHRI Scheme!
(For promoting hands-on, activity-based learning in Mathematics.)

 

Square Root Spiral Activity

(Using JUMBO GEOMETRY BOX MAGNETIC – LKGM 404 Maths Kit under PM SHRI Scheme)

Aim:
To construct a Square Root Spiral (also known as Theodorus Spiral) using geometrical tools, and to understand square roots through geometrical visualization.

Kit Items Used:

• JUMBO GEOMETRY BOX MAGNETIC — LKGM 404 Maths Kit

• Magnetic ruler

• Magnetic compass

• Magnetic protractor

• Magnetic set squares

• Magnetic board

• Chalk or marker

• Pointer for explanation

(This kit is a precision model designed for demonstrating accurate geometric constructions in the classroom using magnetic tools, enabling clear, hands-on learning.)

Procedure:

1. Place a magnetic board vertically or flat, and fix the base point O.

2. Using the ruler, draw a line segment OA = 1 unit.

3. At point A, construct a perpendicular using the set square.

4. With A as the center and radius 1 unit, draw an arc to cut the perpendicular at point B. Now, OB = √2 units.

5. Using B as the center and OB as the radius, draw another perpendicular and mark point C such that OC = √3 units.

6. Continue this process:

   • Each new radius equals the square root of the next natural number.

   • Join the points sequentially (O → A → B → C → D...) to create the spiral.

7. Label all the distances clearly (√2, √3, √4, √5...) along the spiral path.

Observation:

• Each new line segment represents the square root of successive natural numbers.

• The spiral visually demonstrates that square roots are real, measurable quantities — not just abstract numbers.

• The distance from the center O to any point on the spiral is √n, where n is the step number.

Conclusion:

The Square Root Spiral is an excellent geometrical representation of square roots. This activity helps students understand that square roots — including irrational numbers — can be visualized as lengths in geometry, enhancing their conceptual clarity and spatial thinking.

class 8 NCERT bridge course Answers Activity W2.3- SQUARE NUMBERS

 Activity W2.3 

The number 9 can be written as 9 = 3 × 3. 

So, it is a square number. 

This activity will make the students aware about such special numbers called square numbers. 

Material required: 

Grid sheet/graph paper/Math notebook (used in foundational stage), 

coloured sketch pens,

 square numbers cards and box. 

Preliminaries 

 Prepare number cards (of square of numbers from 1 to 8 and a few non-square numbers)

The number of cards will be equal to total number of students in the class.

 There can be multiple cards with the same square number.

Procedure

One grid sheet or graph paper or page of a Math notebook may be given to every student.

All the students may be provided opportunity to present their work in front of the whole class.

Put all the number cards in a box.

One student comes and picks a number card from the box and reads the number on it loudly.

 Colour or cross the number of boxes on the sheet equal to the number written on the chosen card.

 For example, if the number on the number card is 9, then 9 boxes should be coloured in the grid. 

Example Number Picked: Let’s assume the card shows 9.

The following process should be adopted for doing this:

 Fill or cross the adjacent boxes equally in horizontal and vertical manner (sample has been shown as under).

 Fill the boxes with different colours.

There is a possibility that students may not get equal number of filled or crossed squares horizontally and vertically for some numbers.

 Now they may observe and tell about the shape formed and write its name.

The teacher may ask questions to the presenters.

 Some sample questions are as follows: 

1. How many rows are coloured? Write in your notebook. 

ANSWER:
3 rows are coloured.

2. How many columns are coloured? Write in your notebook.

ANSWER:

3 columns are coloured.

3.Count the number of boxes coloured in total. 

ANSWER:

Total boxes coloured = 9.

4. Is there any relationship between the number of rows and columns, are coloured and the total number of boxes? 

ANSWER:

 Yes!
The total number of boxes = Number of Rows × Number of Columns
Here: 3 × 3 = 9.

5. If yes, then what is that relationship?

ANSWER:

The relationship is that both rows and columns have the same number, and their multiplication gives the total number —
This is the square of a number.

 6. What pattern have you observed in this relationship? 

ANSWER:

When the number of rows and columns are the same, the total is always a square number (e.g., 1, 4, 9, 16, 25...).

7. What is the name of shape formed by the coloured boxes? 

ANSWER:

The shape is called a Square.

8. What is the difference between shapes of the coloured boxes for numbers 16, 4, 25, 9 36 and of 8, 10, 15, 12, 30? 

ANSWER:

For 16, 4, 25, 9, 36:
The shape is always a perfect square (equal rows and columns).

For 8, 10, 15, 12, 30:
You cannot form a perfect square because these numbers are not square numbers — the rows and columns cannot be equal.

Extension Question:
How does the area of a square and square numbers relate?
→ The area of a square = side × side.
If the side is a whole number, the area is always a square number!

After discussion on above questions, teacher will conclude the class by introducing square numbers relating to the concept of multiplication. 

For example: 

1 × 1 = 1 

2 × 2 = 4 

3 × 3 = 9 

4 × 4 = 16 

5 × 5 = 25 

6 × 6 =36 And so on. 

 Teacher may discuss how the square number and the 2D square shapes are related to each other.

 Extended Learning and Exploration 

 Try the same process of filling colours in boxes for some other random numbers like 10, 15, 12, 20, etc.

 Is it possible to make the shape of square with these number of boxes? 

Answer:
→ No, it is not possible!
Because a perfect square shape always has equal rows and columns — and for numbers like 10, 15, 12, 20 there’s no whole number that can multiply by itself to reach these totals.

For example:

• √10 ≈ 3.16 (not a whole number)

• √15 ≈ 3.87 (not a whole number)

• √12 ≈ 3.46 (not a whole number)

• √20 ≈ 4.47 (not a whole number)

So these cannot form a square-shaped pattern on the grid.

 Students may be motivated to extend their learning by knowing the need of square numbers in mathematics. 

Discuss on how does the area of a square and the square numbers are related? 

Real-Life Connection:
Tiles on a floor, windows, chessboards, and fields often show square patterns — so this helps students link math with the world around them!

Participation of Special Children 

 Special children will also be able to do this activity, if the teacher pairs them with a peer buddy. 

 Some concrete objects like same size marbles or bindi can be given to the children with visual impairment so that they can count them and arrange in square shape

class 8 NCERT bridge course Answers Activity W2.3- Exploring Polygons

 Activity W2.3- Exploring Polygons 

Students may be made to explore different polygons, identify their properties, and classify them based on sides, angles, and symmetry. 

Objective:

Help students identify, classify, and understand polygons by using clues, hands-on exploration, and real-life connections.

Materials Required 

1. Pre-made polygon cutouts (triangles, quadrilaterals, pentagons, hexagons, etc.) 

2. A worksheet with clues and challenges 

3. Whiteboard and markers 

4. Straws or sticks 

How to Perform Activity 

 Warm-Up Discussion:

Show different polygon shapes and discuss sides, angles, classification and symmetry.

Ask: What do you already know about polygons?

Group Hunt:

• Hide polygon cutouts around the classroom.

• Divide students into small groups.

 Give instructions to each group with clues like: 

1. Find a shape with all 3 sides. 

2. Find a shape with 5 angles. 

3. Find a 4-sided figure with a pair of parallel side

4. Find a 4-sided figure with a pair of parallel sides. 

5. Find a 4-equal sided figure with a pair of parallel sides and 90-degree angle. 

6. Find a 4-sided figure with a pair of parallel sides and 90-degree angles. 

More such conditions can be thought of and discussed. 

 Each group searches for the correct shape and records its properties on the worksheet provided to them. 

 Each group presents one shape they found, explaining its properties. 

3. Presentation:
   Each group presents their shape, describing:

• Number of sides

• Number of angles

• Type of symmetry

• Real-world example.

ANSWER:

Clue	Expected Shape	Properties
1. Find a shape with all 3 sides.	Triangle	3 sides, 3 angles.
2. Find a shape with 5 angles.	Pentagon	5 sides, 5 angles.
3. Find a 4-sided figure with one pair of parallel sides.	Trapezium	Quadrilateral, 1 pair parallel sides.
4. Find a 4-sided figure with two pairs of parallel sides and 90° angles.	Rectangle	4 sides, opposite sides equal, all angles 90°.
5. Find a 4-sided figure with all sides equal and 90° angles.	Square	4 equal sides, all angles 90°.
6. Find a 4-sided figure with a pair of parallel sides and 90-degree angles.	Rectangle	4 sides, opposite sides equal, all angles 90°.

Extension

 Discuss real life examples of polygons (stop signs, tiles, windows, etc.). 

ANSWER:

Extension: Real-Life Polygon Examples

• Octagon → Stop signs

• Square → Tiles, windows

• Rectangle → Books, screens

• Pentagon → House-shaped signs.

Exploratory Questions Based on the Activity 

Teachers may generate a discussion on questions that require explorations.

 Here are a few examples— 

1. Is circle a polygon? 

ANSWER:

No, because a polygon must have straight sides, and a circle has a curved boundary.

2. Can we draw a polygon with 2 straight lines? 

ANSWER:

No, the minimum number of sides for a polygon is 3 (triangle).

3. Can we consider open figure as a polygon? 

ANSWER:

No, polygons must be closed shapes.

4. Can we consider square as a rectangle? If yes, then why? 

ANSWER:

Yes! A square is a special type of rectangle where all sides are equal, and all angles are 90°.

Hands on Practice 

1. Teacher may instruct students to draw a polygon using some clues, on a white board with the help of a marker. 

2. Students may also be encouraged to construct polygons with the help of straws and sticks, and given clues.

• Use straws or sticks to create polygons based on clues.

• Students can draw and label polygons on the whiteboard when the teacher gives clues.

• Assign teams to find real-world polygon examples around the school.

some clues for reference:

1. Draw a polygon with 3 sides — (Answer: Triangle)
   
2. Draw a polygon that has 4 equal sides and 4 right angles — (Answer: Square)
   
3. Draw a polygon with 4 sides, where only the opposite sides are equal and parallel — (Answer: Rectangle)
   
4. Draw a polygon with 5 sides — (Answer: Pentagon)
   
5. Draw a polygon with 6 sides — (Answer: Hexagon)
   
6. Draw a polygon with 8 equal sides — (Answer: Octagon)
   
7. Draw a polygon where no sides are equal and no angles are equal — (Answer: Scalene Quadrilateral or Scalene Triangle)
   
8. Draw a closed shape with 7 sides — (Answer: Heptagon)
9. Draw a 4-sided figure that has only one pair of parallel sides — (Answer: Trapezium)
10. Draw a regular polygon with all sides and angles equal, and more than 4 sides — (Answers: Pentagon, Hexagon, Octagon, etc., depending on the count)
11. Draw a polygon that has 4 sides, two of which are parallel but not equal.
12. Draw a polygon with 5 sides — all sides need not be equal.
13. Draw a polygon that has 6 sides, where all angles are equal.
14. Draw a 3-sided polygon where two sides are of the same length.
15. Draw a 4-sided polygon with all sides equal and all angles equal.
16. Draw a polygon that looks like a house rooftop (Hint: it's a pentagon).
17. Draw a 4-sided polygon where no sides are parallel.
18. Draw a quadrilateral where only one pair of opposite sides is parallel.
19. Draw a polygon with the least number of sides.
20. Draw a polygon that looks like a star (students can creatively connect lines, making a complex polygon).