class 8 NCERT bridge course Answers Activity W2.2: A Mathematical Tambola

 Activity W2.2: A Mathematical Tambola

Each student gets a tambola ticket with 15 numbers randomly selected from 1 to 90. 

 Instead of directly calling out numbers, the host will give a math-based clue for each number. 

For example, instead of saying 2, it may be said ‘An even prime number’. 

 Players are required to solve the clue to mark the correct number on their ticket. 

 Winning rules: 

1. Early five: first to mark any 5 numbers. 

2. Top row/middle row/bottom row: First to mark all numbers in a row. 

3. Full house: first to mark all 15 numbers. 

4. Students will mark question numbers on each strike out for later verification

Some Sample Clues 

S.No.                         Clue                                 Number 

1.                                 3²                                         9 

2. The sum of intirior angles in a triangle             180 

3.                                     Half of 130                     65 

Suggestions for the Teacher 

 You can create more such clues based on basic arithmetic, geometry, prime numbers, factors, multiples, etc. 

 Teacher can give questions in written or can announce as per convenience. 

 Teacher may change the difficulty level of the clues as per students’ comprehension level.

Instructions for Students:

• Each student will receive a Tambola ticket.

• When the teacher announces a math clue, solve it and mark the correct number on your ticket.

• Winning categories: Early Five, Top Row, Middle Row, Bottom Row, Full House. 

Sample Tambola Ticket:

                                    

12	9	65	40	33
75	7	36	15	2
42	5	90	8	50

Host's Clue Sheet:

S.No.	Clue Description	Answer
1	3 squared	9
2	Sum of interior angles in a triangle	180
3	Half of 130	65
4	Smallest even prime number	2
5	8 times 5	40
6	A dozen	12
7	Number of sides in a pentagon	5
8	7 times 6	42
9	Square root of 81	9
10	Sum of first five natural numbers	15
11	Perimeter of a square with side 10	40
12	Product of 9 and 4	36
13	Total days in a week	7
14	A century minus a quarter century	75
15	11 times 3	33

12	9	65	40	33
75	7	36	15	2
42	5	90	8	50

Reflection Questions:

1. Which type of clues did you find easiest?

2. Were there any clues you solved using a shortcut?

3. How do patterns and numbers help in everyday life?

Teacher's Note:

• Adjust the difficulty of clues based on student understanding.

• Allow discussions after each round for reinforcement.

• Special children can use a buddy system for support.

Happy Learning! 🌟🥇

class 8 NCERT bridge course Answers Activity W2.1: Let us Brainstorm

 Activities for Week 2 

Activity W2.1: Let us Brainstorm

 Students may be given these puzzles to solve. 

They may do it individually or in pairs. 

They may be asked to justify their answers. 

A. Determine the missing value in the puzzle below

☆❒☆❒☆❒☆❒ = 16

☆❒☆❒☆❒☆ = 13

☆❒☆❒ = 8

☆☆☆❒❒❒ = ?

SOLUTION
Let:

• ☆ = x

  
  

• ❒= y

4 stars + 4 squares = 16
4x + 4y = 16
Divide both sides by 4:
x + y = 4 — (Equation 1)

4 stars + 3 squares = 13
4x + 3y = 13 — (Equation 2)

Subtract Equation 1 from Equation 2:
(4x + 3y) - (4x + 4y) = 13 - 16
4x + 3y - 4x - 4y = -3
Simplifies to:
-y = -3
So:
y = 3 (Square = 3)
Substitute into Equation 1:
x + 3 = 4
So:
x = 1 (Star = 1)
 Now solve the last expression:
☆ + ☆ + ☆ + ❒ + ❒ + ❒
= 3x + 3y
= 3(1) + 3(3)
= 3 + 9 = 12

FINAL ANSWER 

☆☆☆❒❒❒ = 12

a) x² - 1 - ( x² + 1) 

= 6² - 1 - (5² +1)

= 36 - 1 - (25 +1)

= 35 - 26
= 9

b) x² - 1 + ( x² + 1) 

= 8² - 1 + (5² +1)

= 64 - 1 + (25 +1)

= 63 + 26
= 89

class 8 NCERT bridge course Answers Activity 1W1.5: Pattern Observation

 Activity W1.5: Pattern Observation 

In this activity, students explore, identify and generalise patterns using physical movements. 

They, then, connect it to number patterns. 

Step 1: Students may be asked to perform a simple body movement sequence without explaining the pattern. 

💡 Example 1: Clap, Clap, Clap, Clap...

Q1: What do you notice about the movement?
ANSWER

 The same action (clap) is repeated again and again without changing. It’s a simple, repeating pattern.

Q2: Can you predict what comes next? Why?
ANSWER

The next movement will be a clap — the pattern never changes, so it will always be a clap.

Q3: If I stop at the 7th movement, what should the 8th movement be?
ANSWER

The 8th movement will also be a clap, because the same action is repeated.

 Step 2: Change the movements to 

💡 Example 2: Clap, Clap, Jump, Clap, Clap, Jump...

Possible questions could be— 

Q1: How is this different from movements in Example 1?

ANSWER
 In this pattern, there are two claps followed by a jump, so the actions change. It’s not just repeating the same movement like in Example 1.

Q2: Can you describe the rule?
ANSWER

 The rule is: After every two claps, there is one jump. The pattern repeats this sequence: Clap, Clap, Jump.

Q3: If the first jump is at 3, the second jump is at 6; then at what number do we get the third jump?
ANSWER

The jumps happen every 3rd move. So the third jump will be at 9.

 Many such different body movements can be thought of 

Questions followed by discussions should be done. 

Step 3: Connecting to numbers 

💡 Example 3: Clap, clap clap, clap clap clap, clap clap clap, clap, … 

We may write the corresponding sequence of numbers as 1, 2, 3, 4 … 

Q: What sequence of numbers can we assign to Example 2?

ANSWER 

If Clap = 1, 2 and Jump = 0, the number sequence is: 1, 2, 0, 1, 2, 0, 1, 2, 0...

 Students may be given a number sequence, such as 1, 3, 5, 7,… and may be asked to assign corresponding body movements that justify this pattern. 

We may ask students to assign their own numbers and create a sequence of numbers.

 This is an odd number sequence. Students could choose a movement like:

• Jump for odd numbers (1, 3, 5, 7…)

• Clap for even numbers (if extended to 2, 4, 6, 8...)
  In this case, the pattern only shows odd numbers, so maybe only jumping is used.

 Step 4: Students may think of many such movements and their corresponding number patterns. 

Examples of Movements and Corresponding Number Patterns

Example 1:

Movement Pattern:
Tap, Tap, Snap, Tap, Tap, Snap...

Number Pattern:
1, 2, 0, 1, 2, 0, 1, 2, 0, ...

Explanation:

• Tap is represented by 1, 2.

• Snap is represented by 0.

• The pattern repeats every 3 moves.

Example 2:

Movement Pattern:
Jump, Clap, Jump, Clap, Jump, Clap...

Number Pattern:
0, 1, 0, 1, 0, 1, ...

Explanation:

• Jump = 0

• Clap = 1

• Alternates between the two actions.

Example 3:

Movement Pattern:
Clap, Jump, Spin, Clap, Jump, Spin...

Number Pattern:
1, 2, 3, 1, 2, 3, ...

Explanation:

• Clap = 1

• Jump = 2

• Spin = 3

• Repeats every 3 steps.

Example 4:

Movement Pattern:
Step forward, Step backward, Step forward, Step backward...

Number Pattern:
1, -1, 1, -1, 1, -1, ...

Explanation:

• Step forward = 1

• Step backward = -1

• Alternates like a simple plus-minus pattern.

Example 5:

Movement Pattern:
Clap, Clap, Jump, Jump, Clap, Clap, Jump, Jump...

Number Pattern:
1, 1, 0, 0, 1, 1, 0, 0, ...

Explanation:

• Clap = 1

• Jump = 0

• Two claps, two jumps, repeating.

Example 6:

Movement Pattern:
Touch head, Touch shoulders, Touch knees, Touch toes...

Number Pattern:
1, 2, 3, 4, 1, 2, 3, 4, ...

Explanation:

• Each action is numbered from 1 to 4 in a cycle.

• Helps connect actions with counting sequences.

Students to invent their own movement patterns like:
👉 spin, stomp, wave
👉 blink, clap, nod
and match them to any number sequence want!

Reflections on the Activity

 Discussion may be held on questions, such as: 

Q: How do patterns help us make predictions?

ANSWER:

Patterns show regularity and repetition, so once we recognize the rule, we can guess what comes next without seeing the full sequence.

Q: Where do we see patterns like this in real life?

ANSWER:

 Patterns are everywhere!

• Days of the week (Monday, Tuesday...)

• Traffic lights (Red, Yellow, Green)

• Music beats and dance steps

• Shapes in tiles or floor designs

• Plant growth (leaf arrangement)

• Numbers like even/odd, multiplication tables.

Participation of Special Children- ADAPTATION 

 Instead of requiring physical movement (for example, clapping, jumping), allow students with mobility disabilities to use gestures, verbal cues, or assistive devices.

 Provide alternative options, such as— 

• Hand tapping or finger snapping instead of clapping. 
• Nodding, blinking, or pointing instead of jumping.
•  Using small objects (counters, flashcards, or digital tools) to represent movements. 
• Pair students with physical disabilities with a peer buddy who can perform the movements on their behalf while they identify, predict, and describe the pattern

class 8 NCERT bridge course Answers Activity 1W1.4: Recreational Puzzles

 Activity W1.4: Recreational Puzzle

Bridge Programme for Grade 8

 Students may be asked to play this game either individually or in pairs. 

1. Locate the following mathematical terms in the above grid. 

2. Encircle them in the grid. 

3. These could be found vertically, horizontally or diagonally. 

4. Time may be allotted for doing this. 

5. Marks may be decided accordingly. 

Words are: 

Circle, 

Octagon,

 Square, 

Parallelogram, 

Star, 

Hexagon, 

 Quadrilateral, 

Triangle, 

Kite and 

Rectangle.

class 8 NCERT bridge course Answers Activity 1W1.3: Recreational Puzzles

 Activity W1.3: Recreational Puzzles 

Students may be asked to play this game either individually or in pairs. 

They may be motivated to disclose their strategy before the class. 

Fill in the missing numbers

 1. The missing values are the whole numbers between 1 and 9. 

2. Each number is used only once.

3. Each row is an arithmetic equation. 

4. Each column is an arithmetic equation. 

5. Remember that multiplication and division are performed before addition and subtraction

Solve the 2nd Column

The equation is:  4 − A +3=2    

-A = 2-7

A = 5

Automatically the 2nd Row solved 

2 x 5 + 8 = 18

Solve the 1st column

A + 2 + B = 15

Solve the 3rd column

C + 8 - D = 0

C - D = -8

The numbers C and D must differ by -8. Possible pairs (from 1-9 without repeats):

• $\mathrm{<br>}$

• $A=2,C=10$ (from 1-9 without repeats so not possible)

• $\mathrm{A=}\mathrm{<span\; class="base"><span\; class="strut"></span><span\; class="mpunct">0,C</span><span\; class="mrel">=8 \; </span><span\; style="font-family:\; "Times\; New\; Roman";\; font-size:\; medium;">(from\; 1-9\; without\; repeats\; so\; not\; possible)</span></span>}$

• So only possible answer is C=1,D=9

Solve the 1st Row

A - 4 - C = 1

A - C = 1 +4

A - C = 5

The numbers $\mathrm{A\; and\; C\; must\; differ\; by\; 5.\; Possible\; pairs\; (from\; 1-9\; without\; repeats):}$

• 
  $A = 6, B = 1$

Solve the 3rd Row

B - 3 X D = -20

D = 9

B - 3 x 9 = - 20

B - 27 = -20

B = -20 + 27

B = 7

Solution for the puzzle

class 8 NCERT bridge course Answers Activity 1W1.2: Dice Math Challenge

 Activity W1.2 Dice Math Challenge 

 Material Required:

• Two large dice (these can be made using cubical cardboard boxes)

Instructions for the Teacher:

• Divide the class into two teams. You can choose creative team names (e.g., “The Math Wizards” and “The Number Ninjas”).
• Draw a line to split the blackboard into two sections and write the team names on each side.
• Each student will take turns throwing the dice for their team.

Steps to Play:

• A student from Team A throws the dice and announces the number that appears on the top.

• The team will multiply the number by itself 3 times (i.e., calculate $number \times number \times number$) and the result will be written under Team A's column on the board.

• A student from Team B takes their turn, following the same steps.

• After each throw, both teams add their new result to their team’s total score on the board.

• Continue until each team has had the set number of turns (e.g., 10 or 12 turns).

• The team whose total score is closest to the target number (500 or 1000, as decided) at the end wins!

                            

SL NO	TEAM A	CUBE	TEAM B	CUBE
1	5	125	2	8
2	1	1	6	216
3	6	216	4	64
4	4	64	3	27
5	2	8	1	1
6	5	125	2	8
7	6	216	5	125
8	3	27	3	27
9	3	27	5	125
10	4	64	5	125
11	1	1	6	216
12	2	8	1	1
13	4	64	2	8
14	3	27	1	1
15	4	64	3	27
	TOTAL	1037	TOTAL	979

TEAM A IS THE WINNER

Based on the above activity, 

Some reflective questions may be discussed, such as: 

1. Number Observation:
   Look at the scores written on the board. Try to find numbers other than seen on the board that are square/cube numbers. 

👉 Question: Can you name a square or cube number that wasn’t written on the board during the game?

ANSWER:
Square numbers (Example: $4, 9, 16, 25, 36, 49, 64, 81, 100, \dots$)

Cube numbers (Example: $1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, \dots$)

2. Cube Building Challenge:

 Students may be given some number of unit cubes say, 8, 10, 25, 27, 30, 50, 64. 

They may be asked to make a bigger cube out of these given number of cubes. 

They may be asked, for which number of cubes they could make a bigger cube and which they could not. Ask them to explain.

You are given unit cubes: 8, 10, 25, 27, 30, 50, 64.

A perfect cube means the total number of cubes can be arranged into a shape where length = width = height (all sides equal). The total must be $n^3$ — a cube number.

Let’s check each one:

Number of Cubes	Can Form a Perfect Cube?	Reason
8	✅ Yes	$2\times 2\times 2=\mathrm{8<span\; class="katex"><br></span> }$$2^3$.
10	❌ No	10 is not a cube number. $2^3 = 8$ and$3^3 = 27$. 10 falls between.
25	❌ No	25 is not a cube number. $2^3 = 8$, $3^3 = 27$. 25 is not in the list.
27	✅ Yes	$3 \times 3 \times 3 = 27$. It is $3^3$.
30	❌ No	30 is not a cube number. $3^3 = 27$ and $4^3=\mathrm{64.\; 30\; falls\; between.}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$
50	❌ No	50 is not a cube number. $3^3 = 27$ and $4^3 = 64$. 50 falls between.
64	✅ Yes	$4\times 4\times 4=\mathrm{64.\; It\; is }$$4^3$.

ANSWER: 

You can make a perfect cube with: 8, 27, and 64. these numbers can form a larger cube.

ANSWER:

 You cannot make a perfect cube with: 10, 25, 30, 50 — these numbers cannot form a larger cube because these numbers are not cube numbers.

 3. Rubik’s Cube Mystery:

Look at a Rubik’s Cube. Guess:
👉 How many small unit cubes make up a complete Rubik’s Cube?

💡 Hint: A Rubik's Cube is usually a cube with equal sides — try imagining how many little cubes fit along each edge and then multiply!

A rubik cube may be shown to students to guess how many small unit cubes have been used to make it.

ANSWER: 

A standard Rubik’s Cube is a 3×3×3 cube.

$$3\times 3\times 3=27$$So, 27 small unit cubes are used to make one complete Rubik's Cube! 

??? Extra Challenge:
If you could design your own cube puzzle, how many small cubes would you choose, and why?

Inclusion of Special Children:

• Pair special children with supportive peer buddies for guidance.

• Encourage them to take active roles: throwing the dice, multiplying the numbers, or writing the scores on the board.

• This teamwork helps build confidence and fosters participation.

class 8 NCERT bridge course Answers Activity 1W1.1: Recreational Puzzle

 Bridge Programme Content: Detailed Activity 

Activities for Week1

Activity W1.1: Recreational Puzzle 

Material Required: 

A calendar of any month, coloured sketch pens and sheet of paper

May 2025

A calendar may be given to students in pairs. 

They have to observe the calendar keenly and write their observations in the notebook.

Let the students do on their own. 

Teacher can suggest question but should not reveal the conclusions before taking responses of students’ observations. 

Teacher may ask students to do the following: 

Draw boxes around square numbers (number obtained when a number is multiplied to itself two times. 9 = 3 × 3 is a square number) and colour them with a single colour. 

Draw circles around cube numbers (number obtained when a number is multiplied to itself three times. 8 = 2 × 2 × 2 is a cube number.) and colour them with a new colour. 

Draw triangle around prime numbers. O Students may be asked to choose any 2 by 2 number square grid from the calendar they have. 

Instructions for Students

1. Observing the Calendar:

Students are given a calendar (in pairs). For example, May 2025 starts on Thursday and has 31 days.

They are asked to observe patterns in the calendar and note down their own observations.
Examples of what students might observe:

• The month starts on a Thursday.

• All weeks have 7 days.

• The 1st, 8th, 15th, 22nd, and 29th are all Thursdays.

• The numbers in the same column increase by 7.

2. Marking Specific Numbers:

Using coloured pens, students mark special types of numbers:

Square Numbers (draw boxes around and colour with one colour):
→ 1, 4, 9, 16, 25

Cube Numbers (draw circles around and colour with a second colour):
→ 1, 8, 27

Prime Numbers (draw triangles around):
→ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

3. Choose any 2x2 number square from the calendar
(For example: Choose the block with 8, 9, 15, 16)

They should try to answer the following questions: 

What is the sum of the numbers in the diagonals of the grid? 

What is the sum of numbers in the diagonals?

• Diagonal 1 (8 + 16) = 24

• Diagonal 2 (9 + 15) = 24

 What magic do you observe? 

 Observation / Magic:

• The sum of both diagonals is the same in a 2x2 grid.

Based on the above activity, some reflective questions may be discussed, such as: 

Reflective Questions & Sample Student Responses

Q1: How do you differentiate between square and cube numbers?

• A square number is a number multiplied by itself once (e.g., 4 = 2 × 2).

• A cube number is a number multiplied by itself twice more (e.g., 8 = 2 × 2 × 2).

Q2: How do you identify prime numbers?

• Prime numbers have exactly two factors: 1 and itself.

• They are not divisible by any other number.

Q3: Why is the sum of diagonals always same in a 2x2 grid?

• Because the opposite corners in a 2x2 square are symmetrical and balance each other.

• The sums (top-left + bottom-right) and (top-right + bottom-left) are always equal due to arithmetic symmetry.

Extension of the Activity 

 Teacher can extend this activity by suggesting students to take a 3 by 3 grid. 

Extension Activity (3x3 Grid)

Take a 3x3 grid (e.g., from 8 to 16):

Why is the sum of diagonals always same for any 2 by 2 grid? 

They may find— 

1. The sum of diagonal numbers. 

Sum of diagonals:

• Diagonal 1 (8 + 16 + 24) = 48

• Diagonal 2 (10 + 16 + 22) = 48

2. The mean of all numbers. 

Mean of all numbers in the grid:
Sum of all numbers: 8+9+10+15+16+17+22+23+24 = 144
Mean = 144 ÷ 9 = 16

Special Observations:

• The center number (16) is the mean.

• Diagonals again have equal sums.

• There is a symmetry in the calendar numbers.

They may be asked to see what special thing they observed. 

Teacher may encourage students to explore more such patterns in the calendar

Encouragement for Exploration

Students can be encouraged to:

• Try different-sized grids (like 4x4).

• Observe symmetry across weeks.

• Explore patterns in odd/even numbers.

• Make their own puzzles from the calendar.

Circumference of the circle

Today we all use the formulas 2πr or πd to calculate the circumference of a circle. Can you believe it if I tell you that this is a Tamil invention??? Look below and you will definitely be surprised.

The formula for calculating the circumference of a circle is set in the Kanakathikaram, Kakkai Padinium etc.

 Crow Patinium

******************************

Song :-

"Vitamore seven, add four to the circle

Sattena Irati Chain

Thikaipana Churtthane"

Setting :-

(Perimeter - P, Diameter - V, Radius - Aa)

= (Vitamore seven) = V/7 

= (Add four to the circle) = V+4V/7

= (Double chain) = 2[V + 4V/7]

(Thikaipana Churtthane)

= 2[V + 4V/7

= 2[11V/7]

= 2x11V/7

= 22/7 x V

According to the present, if 22/7 = π and V=d (diameter)...

Circumference of the circle = 22/7 x V

= πd

(d = 2r) Circumference = 2πr

So today  It is a matter of pride for Tamils ​​that a Tamil has calculated the formulas used to find the circumference of a circle without using π.....

✍ Tamil Forum

Circumference of the circle 

இன்று நாம் அனைவரும் வட்டத்தின் சுற்றளவை கணிப்பதற்கு 2πr அல்லது πd எனும் சூத்திரங்களை பாவிக்கின்றோம். இது தமிழரின் கண்டுபிடிப்பு என்று சொன்னால் உங்களால் நம்ப முடியுமா??? கீழே பாருங்கள் நிச்சயம் ஆச்சரியப்படுவீர்கள்.

வட்டத்தின் சுற்றளவை கணிப்பதற்கு கணக்கதிகாரம், காக்கை பாடினியம் போன்றவற்றில் சூத்திரம் அமைக்கப்பட்டுள்ளது.

காக்கை பாடினியம்

****************************

பாடல் :-

"விட்டமோர் ஏழு செய்து

திகைவர நான்கு சேர்த்து

சட்டென இரட்டி செயின்

திகைப்பன சுற்றுத்தானே"

நிறுவல் :-

(பரிதி - ப, விட்டம் - வி, ஆரை - ஆ என வைத்தால்)

= (விட்டமோர் ஏழு செய்து) = வி/7 

= (திகைவர நான்கு சேர்த்து) = வி+4வி/7

= (சட்டென இரட்டி செயின்) = 2[வி + 4வி/7]

(திகைப்பன சுற்றுத்தானே)

= 2[வி + 4வி/7

= 2[11வி/7]

= 2x11வி/7

= 22/7 x வி

தற்காலத்தின் படி 22/7 = π எனவும் வி=d (விட்டம்) எனவும் கொண்டால்...

வட்டத்தின் சுற்றளவு = 22/7 x வி

= πd

(d = 2r ஆக) சுற்றளவு = 2πr

ஆக இன்று வட்டத்தின் சுற்றளவு காண பயன்படுத்தப்படும் சூத்திரங்களை தமிழன் π பயன்படுத்தாமலே கணித்துள்ளான் என்பது தமிழருக்கு பெருமையே.....

✍ தமிழ் கருத்துக்களம்