ACTIVITY 2 - Tremendous in Ten! CLASS 8 - Mathematics Subject Enrichment Activity-2 Topic:Exponents and Powers – Comparing Large Numbers

 ACTIVITY 2 - Tremendous in Ten!

CLASS 8 - Mathematics Subject Enrichment Activity-2
Topic:Exponents and Powers – Comparing Large Numbers

Aim:

• To develop logical reasoning and number sense by comparing extremely large numbers.

• To apply the laws of exponents and arithmetic operations in problem-solving.

• To encourage quick thinking and creativity in constructing large numbers.

Learning Objectives:

• Understand and apply the concept of exponents to represent large numbers.

• Compare numbers expressed in exponential and arithmetic forms.

• Work collaboratively to solve mathematical puzzles under time constraints.

Materials Required:

• Notebook / Worksheet (Page 47 activity)

• Pen/Pencil

• Stopwatch or timer (for 10-second challenge)

• Whiteboard/Chart paper (for group play – optional)

Procedure:

1. Divide the class into pairs (or small groups).

2. Read the rules of the game:

• Each player has 10 seconds to write down the largest number or expression using digits 0–9 and arithmetic operations.

• The winner is the one who creates the larger number.

3. Begin with Round 1 (no exponents allowed – only addition).

• Example: Roxie wrote 1013, Estu wrote 999999×999999. Compare which is bigger.

4. Play Round 2 with a new condition (exponents allowed, only addition).

• Example: Roxie wrote 101000 +  101000  + 101000  +  101000

• Estu wrote ( 101000000)×9000.

• Students compare logically which is larger.

5. Continue further rounds, changing conditions (e.g., only multiplication, exponents + any operation, etc.).

6. Record all attempts and discuss strategies after each round.

Observation:

• Students notice that exponents grow much faster than multiplication or repeated addition.

• Numbers with even slightly higher exponents far exceed large multiplications.

• Time pressure (10 seconds) makes students think creatively and strategically.

Result:

• Students are able to represent and compare large numbers using exponents.
  
  

• They understand that exponential growth is much faster than arithmetic growth.

Reflections:

1. What strategies helped you solve the problem?

• Using exponents instead of multiplication.
  
  

• Recognizing that  101000000is far greater than sums like 4× 101000

2. Was there any part of the puzzle that seemed impossible? Why?

• At first, comparing numbers like 999999² with  1013 seemed tricky, but using exponent rules made it clear.
  
  

3. How did you check whether your solution worked?

• By rewriting numbers in exponential form and applying laws of exponents.
  
  

4. What did you learn about large numbers?

• Exponents grow extremely fast compared to multiplication or addition.
  
  

• Even small increases in the exponent can drastically increase the size of the number.

Extension / Higher Order Thinking:

• Try the game using different bases (like 2, 5, 100) instead of 10.
  
  

• Explore what happens if negative exponents or fractions are allowed.
  
  

• Discuss real-life applications of exponents (population growth, computing speed, compound interest, etc.).

✨ Subject Enrichment Activity – “Tremendous in Ten” (Extended Rounds)

Procedure

1. Divide the class into pairs or small groups.

2. Read the rules of the game:

   • Each player has 10 seconds to write the largest possible number/expression using digits 0–9 and arithmetic operations.

   • Both players reveal their answers.

   • The bigger number wins the round.

3. Continue for multiple rounds with changing conditions.

4. Record answers, compare, and discuss strategies.

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Examples of Rounds & Winners

🔹 Round 1 – Only Addition (no exponents)

• Roxie wrote:
  $10 + 13$ = 23

• Estu wrote:
  $999999 + 999999$ = 1999998
  ✅ Winner: Estu (larger number)

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🔹 Round 2 – Exponents Allowed (only addition)

• Roxie wrote:
  $10^{1000} + 10^{1000} + 10^{1000} + 10^{1000}$ = $4 \times 10^{1000}$

• Estu wrote:
  $(10^{1000000}) \times 9000$ = $9000 \times 10^{1000000}$
  ✅ Winner: Estu (Exponent is far bigger, multiplication by 9000 makes it enormous)

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🔹 Round 3 – Multiplication Only

• Roxie wrote:
  $999 \times 999 \times 999$ = $997002999$

• Estu wrote:
  $999999 \times 999999$ ≈ $10^{12}$
  ✅ Winner: Estu

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🔹 Round 4 – Any Operation + Exponents

• Roxie wrote:
  $(10^{100})^{100} = 10^{10000}$

• Estu wrote:
  $9^{9999}$

  • $9^{9999}$ is slightly smaller than $10^{10000}$, but still comparable.
    ✅ Winner: Roxie (because base 10 is stronger than base 9 raised to the same magnitude)

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🔹 Round 5 – Creative Expressions (factorials allowed)

• Roxie wrote:
  $100!$ (factorial of 100)

• Estu wrote:
  $(50!)^{50}$

• Comparing: $(50!)^{50}$ is much smaller than $100!$.
  ✅ Winner: Roxie

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Class Discussion (Post-Game)

• Which operations gave the biggest growth? (Exponents > Factorials > Multiplication > Addition)

• What shortcuts helped you compare numbers quickly?

• Did anyone try “tricks” like $(9^{9999})$ vs. $(10^{1000})$?

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👉 This way, students get both fun competition and logical reasoning practice while exploring orders of magnitude.

:

Round	Allowed Operations	Your Expression	Partner’s Expression	Winner
1	Only Addition (No exponents)	999 + 999 + 999 = 2997	999999 + 999999 = 1999998	Partner
2	Addition + Multiplication (No exponents)	999 × 999 = 998001	999999 + 999999 = 1999998	Partner
3	Exponents Allowed (Only Addition)	10^100 + 10^100 = 2 × 10^100	10^1000 = 10^1000	Partner
4	Exponents Allowed (Any Operation)	(10^100)^100 = 10^10000	9^9999 ≈ 10^9544	You

✅ Winners Summary:

• Round 1 → Partner

• Round 2 → Partner

• Round 3 → Partner

• Round 4 → You

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