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	$2^3$.
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
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.