Class 8 NCERT bridge course Answers Activity W 3.2 Let’s Brainstorm

 Activity W 3.2 Let’s Brainstorm 

 Students may be asked to solve the following puzzles either in groups or individually.

 They may explain their strategy of obtaining the result. 

Let’s Brainstorm 

Puzzle 1: Symbol Grid

1. The grid below has symbols that contain a whole number value less than 10. 

Each symbol has its own value. 

The numbers you see at the end of each row and column are the sums of the figures’ values for that row or column.

Can you find out the value of each symbol ? 

ANSWER:

Let’s name the shapes:

• 🟦 Pentagon = P

• 🔺 Triangle = T

• ⭐ Star = S

• ➕ Plus = C

And solve!

Row equations:1️⃣ 

1. P+T+P+S=15

2. C+S+P+S=23

3.T+C+T+?=16

4. S+T+?+P=14

Column equations:

1. P+C+T+S=20

2. T+S+C+T=24

3. P+P+T+?=7

4. S+S+?+P=17

SOLVE

From Row 3 and Column 3, the missing symbol must be the same in both — let’s call it X for now.

Let’s focus on easy rows:

Row 3:  T+C+T+X=16

Row 4:   S+T+X+P=14

Col 3:  P+P+T+X=7

Let’s assume X = 0 to test:

From Col 3:   𝑃+P+T=7

From Row 3:  T+C+T=16

So  2T+C=16.

From Col 1: P+C+T+S=20.

And from Row 1: 2P+T+S=15.

From Row 3:  2T+C=16

From Col 3:  2P+T=7

From Row 4: S+T+P=14 (since X=0)

Now solving this small system:

From (2)  2P+T=7 → T=7−2P

Substitute into (1):

2(7−2P)+C=16

14−4P+C=16

C=4P+2.

Now substitute into Col 1:

P+C+T+S=20.

Substitute 

C=4P+2 and 

T=7−2P:

P+(4P+2)+(7−2P)+S=20

Simplify:

P+4P+2+7−2P+S=20

3P+9+S=20

S=11−3P.

If  P=1: 

S=11−3(1)=8

T=7−2(1)=5

C=4(1)+2=6

Now check Row 2:

C+S+P+S=23

6+8+1+8=23 

SOLUTION:

• 🟦 Pentagon P=1
• 🔺 Triangle T= 5
• ⭐ Star  S = 8
• ➕ Plus C = 6

Puzzle 2: Symbol Equation

2. Here, you are given two representations, where symbols have been used. 

Each symbol represents a numeric value. Find the value of each symbol.

SOLUTION:

Given the equations:

• • 🟦 Blue Square = S

  • 🔺 Orange Triangle = T

  • 🟡 Yellow Circle = C

  • ⭐ Star = R

EQUATION 1:  S+S+S=15 --> 3S = 15 --> S = 5

EQUATION 2:  T+T+S=13 -->  2T + 5 = 13 --> 2T = 8 --> T = 4

EQUATION 3 : T+C+S=15 --> 4 + C + 5 = 15 --> C = 15 - 9=6

EQUATION 4: C+C+S=?

EQUATION 5: C + T + T = ?

EQUATION 6 : C + T = 8

EQUATION 7: C + T = 4

EQUATION 8 : R + S =12 --> R + 5 = 12 --> R = 12 -5 =7

EQUATION 9 : R + S = S

EQUATION 10 : S + S = R --> 2S = R

SOLUTION:

🟦 Blue Square (S)

= 5

🔺 Orange Triangle (T)

= 4

🟡 Yellow Circle (C) =

6

⭐ Star (R)

= 12 - 5 = 7

🟡 + 🟡 + 🟦 = 6 + 6 + 5 = 17

🟡 + 🔺+ 🔺 = 6 + 4 + 4 = 14

Puzzle 3: Make 5+5+5 = 550 True

3. Make the following equation true by drawing/putting/writing a single line.

SOLUTION : 

 Just draw a slanted line on the first "+" to turn it into 4:

545 + 5 = 550! 

Puzzle 4:Roman Numeral Trick 

What should be added to IX to make six?

Add S in front of IX to form SIX.
So the answer is: Add ‘S’! 

Teachers may try to find some more such puzzles that will engage students in the process of exploration

Puzzle 1: Symbol Sums

Symbol	Meaning
🍎 Apple = ?
🍌 Banana = ?
🍇 Grapes = ?

Equations:

1. 🍎 + 🍎 + 🍎 = 18

2. 🍌 + 🍎 + 🍌 = 16

3. 🍇 + 🍇 + 🍎 = 20

Find the value of each fruit!

Solution:

1. 🍎 + 🍎 + 🍎 = 18 → 🍎 = 6

2. 🍌 + 6 + 🍌 = 16 → 2🍌 = 10 → 🍌 = 5

3. 🍇 + 🍇 + 6 = 20 → 2🍇 = 14 → 🍇 = 7

Final Answer:
🍎 = 6, 🍌 = 5, 🍇 = 7.

Puzzle 2: Number Logic

Symbol	Meaning
🐾 Paw = ?
🐟 Fish = ?
🦴 Bone = ?

Equations:

1. 🐾 + 🐾 + 🐟 = 22

2. 🐟 + 🦴 + 🦴 = 14

3. 🐾 + 🦴 = 13

Find the value of 🐾, 🐟, 🦴.

Solution:

From (3):
🐾 + 🦴 = 13 → 🦴 = 13 - 🐾.

Substitute into (2):
🐟 + 2(13 - 🐾) = 14
Simplify and solve using substitution or trial.
For example:
If 🐾 = 8, 🦴 = 5.

Now check in (1):
8 + 8 + 🐟 = 22 → 🐟 = 6.

 So final values:
🐾 = 8, 🐟 = 6, 🦴 = 5.

Puzzle 3: Matchstick Equation

Make the equation correct by moving 1 matchstick:

6 + 4 = 9  

Solution:
Move one stick from "6" to make it "5":

5 + 4 = 9 

Class 8 NCERT bridge course Answers Activity W 3.1 Understanding Denseness of Fractions

 Activities for Week 3 

Activity W 3.1 Understanding Denseness of Fractions 

Objective:

To understand that there are endless fractions between any two given fractions.

Through this activity, students will get an idea about the denseness of fractions. 

That is, they will be able to know that they can find as many fractions as possible between any two fractions. 

This activity will also help to improve number sense and reasoning skills with fractions. 

Material Required 

Long rolls of paper strips 

 Scissors 

 NCERT Mathematical kits (if present in school) 

 Blank cards

Procedure

 Step 1 

Write two fractions, say, 1/4 and 1/2 on the board and the students may be asked to check, if there are fractions between them. 

Discuss that denseness of fractions means that there can be as many fractions as we want between the two fractions. 

Step 2: 

Hands-on Exploration 

 Take two copies of a paper strip

Ask the students to fold those strips in 2 equal halves. 

Take one of the strips and cut it into two equal parts with the help of scissors.  

Take one part and keep it on the other strip. 

 Take the remaining half and put it on the first half. 

 Continue this process until the students are unable to cut remaining part in to 2 equal parts

Discussion to Explore

1. What does this activity explain?

ANSWER:

This activity explains that fractions are dense — meaning, between any two fractions, no matter how close they are, there are always more fractions that can fit in between.

2. Can we divide these strips further more? If yes, then to what extent?

ANSWER:

 Yes, we can keep dividing the strip into smaller and smaller pieces endlessly — in theory, we can keep cutting the parts infinitely, because between any two fractions, there is always another fraction.

3. If half of a unit is 1/2, then what will be the half of 1/2?

ANSWER:

 Half of 1/2 is:

$\frac{1}{2} \div 2 = \frac{1}{4}$

​
 So, the half of 1/2 is 1/4.

4. Does 1/4 lie in between 0 and 1/2?

ANSWER:

 Yes!
1/4 is greater than 0 but less than 1/2, so it lies between 0 and 1/2 on the number line.

5. How many fractions can lie between 2 fractions?

ANSWER:

Infinite fractions can lie between any two fractions.
No matter how close two fractions are, there will always be more fractions between them.

6. Ask students, if they see gaps between their fractions.

ANSWER:

 Yes, students will observe gaps between fractions on the strip or number line, which shows there is always room for another fraction in between.

7. Challenge: “Is there another fraction that can go between these parts of strips?”

ANSWER:

 Yes! Always.

For example, between 1/4 and 1/2, you can find:

$\frac{1}{4} + \frac{1}{2} \div 2 = \frac{3}{8}$

​
And between 1/4 and 3/8, you can again find:

$\frac{1}{4} + \frac{3}{8} \div 2 = \frac{5}{16}$

​
And so on... endlessly!

Fractions are dense — there is always another fraction between any two fractions, no matter how small the gap looks.

 Extension 

Students may be motivated to observe and generalise the above processs to find a fraction between two fractions 

A simple formula to find a fraction between two given fractions:

$$\text{New Fraction} = \frac{\text{Fraction 1} + \text{Fraction 2}}{2}$$

This gives a new fraction that lies exactly between the two.

You can also practice this on a number line or using the Math Kit for better understanding!

Conclusion:

Through this activity, I learned that fractions are dense. This means that between any two fractions, there are infinite fractions. No matter how close two fractions are, we can always find another fraction between them by using the formula:

$$\text{New Fraction} = \frac{\text{Fraction 1} + \text{Fraction 2}}{2}$$

This activity helped me understand that fractions can be divided into smaller and smaller parts, and there is no end to the number of fractions that can exist between any two numbers. Using strips, number lines, or the Math Kit makes this concept easier and fun to learn!

 

Class 8 NCERT bridge course Answers Activity W2.6 Fraction Pizza Party

  Class 8 NCERT bridge course Answers Activity W2.6

Activity W2.6 Fraction Pizza Party

LO: Identify fractional parts of quantities. 

Fraction Pizza Party This activity will help students understand fractional quantities by creating and comparing pizza slices.

Material Required 

 Large paper circles (representing pizzas) 

 Coloured markers or crayons 

Scissors 

Multiple flashcards with fraction amounts 

(for example, 2 pieces of 1/2, 4 pieces of 1/4 and 6 pieces of 1/6)

 Procedure 

1. Divide students into small groups and give each group a paper pizza. 

2. Call 1 student from each group and ask them to choose 1 set of fractions. 

3. Ask them to cover pizza paper with the help of fractions one-by - one. 

4. No gap and no overlapping are allowed. 

5. Find out and note down “How many total slices are left’’ after putting each slice? 

6. Take ½ parts and combine them to form a whole. How many such parts do you see, are required?

1. Take the 1/8 parts and combine them to form a whole. How many 1/8 parts would be required to make a whole?

ANSWER:
To make one whole pizza using 1/8 parts:
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 8/8 = 1 whole.
So, 8 pieces of 1/8 are required to make a whole pizza.

One way to find this is:

 1/8 + 1/8 = 2/8 

2/8 + 1/8 = 3/8 

3/8 + 1/8 = 4/8

4/8 + 1/8 = 5/8, etc.

 Students may be encouraged to explore other ways, if possible. 

If you combine all the slices given to you, can you make a whole pizza again?

2. After placing the first 1/2 piece, how many pieces do you need to complete the whole pizza?
ANSWER:
After placing 1 piece of 1/2, one more 1/2 piece is needed.
So, 1 more piece of 1/2 is required.

Will 1/2 + 1/2 pieces give a whole pizza?
ANSWER:
Yes!
1/2 + 1/2 = 1 whole pizza. 

3. After placing the first 1/3 piece, how many pieces do you need to complete the whole pizza?
ANSWER:
You need 2 more pieces of 1/3 to complete the pizza.

Was the remaining area covered by 2 pieces of 1/3?
ANSWER:
Yes! 1/3 + 1/3 = 2/3. Adding the first piece (1/3), all three together make:
1/3 + 1/3 + 1/3 = 3/3 = 1 whole pizza. 

Could 1/3 + 1/3 + 1/3 pieces complete the whole pizza? 

ANSWER:
Yes!

4. After placing the first 1/4 piece, how many pieces do you need to complete the whole pizza?
ANSWER:
You need 3 more pieces of 1/4 to complete the pizza.

Does the remaining area get covered by 3 pieces of 1/4?
ANSWER:

Yes! 3 pieces of 1/4 will cover the remaining area.

Does 1/4 + 1/4 pieces complete the whole pizza?
ANSWER:
No! 1/4 + 1/4 = 2/4 = 1/2, so it covers only half.

If not, then how many pieces are required?
ANSWER:
You need 4 pieces of 1/4 to make one whole pizza.

Does it mean that 1/4 + 1/4 is equal to half or 1/2?
ANSWER:
Yes!
1/4 + 1/4 = 2/4 = 1/2.

Can we say 1/4 + 1/4 + 1/4 = 3/4?

ANSWER:
Yes!
1/4 + 1/4 + 1/4 = 3/4.

Does 1/4 + 1/4 + 1/4 + 1/4 pieces complete the whole pizza?
ANSWER:
Yes!
1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1 whole pizza. 

Class 8 NCERT bridge course Answers Activity W2.5

Students may be encouraged to fill in the blank spaces. The NEP 2020 encourages use of such games, which make children explore and connect different mathematical concepts.

Solution of this fun math puzzle step by step

Starting from the top-left and moving along the paths

x + 2 = 19

x = 19 - 2 =17

19 + x = 21

x = 21-19 =2

21+x = 24

x = 24 - 21 = 3

x - 4 = 8

x = 8 + 4 = 12

21 - 1 = 20

20 - 17 = 3

17 - 11 = 6

15 - 1 = 14

x + 3 = 15

x = 15 -3 = 12

x + 1 = 25

x = 25 -1 = 24

x - 5 = 18

x = 18 + 5 =23

6 + 7 = 13

8 + 6 =14

13 - 8 = 5

6 x 4 = 24