Class 8 NCERT bridge course Answers Activity W 4.4 Exploring Data Through Graphs and Charts

 Activity W 4.4 - Exploring Data Through Graphs and Charts

 Procedure

 A project may be given to students to collect the data from reliable sources. 

Students should be divided into groups of 4–5. 

1. Every group has to collect data on the following topics: 

 Temperature of your city in the month of July for the last 5 years. 

 Literacy rate of any 5 states of India in the last five years. 

How many students of your class like ice-cream among the following: 

vanilla, chocolate cone, butter scotch, strawberry and kesar-pista. 

What is the favourite game among the following: cricket, football, basketball, tennis, badminton and volleyball. 

 Collect data from the students of your class.

2. Each group has to make a table with tally marks. 

3. Each group has to draw a bar graph, line graph and pictograph for the collected data. 

Teacher will provide opportunity to every group to present their work in front of the whole class. 

Here is an example: 

Take population of a country in different decades. 

Represent the data as a pictograph, bar graph and line graph. 

 Pictograph 

😊 = 20 crore people.

Bar Graph

Line Graph

Discuss:

1. What is the difference between these three graphs?

Graph Type	Use	Visual Advantage
Pictograph	Uses icons or symbols to show data.	Makes data fun and easy to understand.
Bar Graph	Uses bars to represent quantities.	Great for comparing groups or categories.
Line Graph	Connects data points to show changes over time.	Best for showing trends and progressions.

• Pictograph:
  A pictograph uses pictures or symbols to represent data. Each symbol stands for a specific number of items. It makes the data easy to read and more visually interesting, especially for younger audiences.

• Bar Graph:
  A bar graph uses rectangular bars (either vertical or horizontal) to show the quantity of different categories. The length of the bar shows how large or small the value is. It is useful for comparing data from different groups.

• Line Graph:
  A line graph uses points connected by lines to show trends over time. It helps to easily spot increases or decreases in the data and is best used for data that changes continuously (like temperature or literacy rates).

2. In which situation could a line graph not be drawn from the data collected by the students and why?

A line graph cannot be drawn for:

• Ice-cream preferences

• Favourite games

Reason:
A line graph is used for continuous data or to show change over time.
Ice-cream flavours and favourite games are examples of categorical data (choices, not numbers that change over time). Since these are simply preferences without any timeline or continuous flow, a line graph would not be appropriate.

• Line Graphs are for time-based or continuous data (like temperature or literacy rate).

• Bar Graphs & Pictographs are great for category-based data (like games or ice-cream).

SOME FUNNY ANSWERS

 WRITE 10 VEGETABLE NAMES.

I AM NON-VEGETARIAN.

SOLVE 

11x = π

x =  π / 11

Solve  

X² = 25

x = 5

PROVE TH MID POINT THEOREM

Class 8 NCERT bridge course Answers Activity W 4.3 pictorial patterns

 Activity W 4.3  Pictorial patterns

Students may be asked to extend the following pictorial patterns further for two steps. 

Express each of these as a numerical pattern as directed. 

1. Stacked Squares

Count the number of small squares in each case and write it. 1, 4, ... 

Extend the sequence till 10 terms. 

ANSWER: 

Number Pattern:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Do you find any pattern? 

ANSWER: 

Pattern Observed:

These are square numbers — the number of squares increases by the next odd number each time.

Formula: Number of squares=n² where  n is the position in the sequence.

2. Stacked Triangles

Count the number of small triangles in each case and write it. 

ANSWER: 

1,4,9

 

Extend the sequence till 10 terms.

ANSWER: 

Number Pattern:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

 Do you find any pattern? 

Pattern Observed:

• This is a square number pattern.

• Formula: Tn​=n²

Where $T_n$ is the number of small triangles in the nth figure.

3. Koch Snowflake

 To get from one shape to the next shape in the Koch Snowflake sequence, one replaces each line segment ‘—’ by a ‘speedbump’ +. 

As one does this multiple times, the changes become tinier with very extremely small line segments.

 Extend it by three more steps. 

 How many total line segments are there in each shape of the koch snowflake? 

 Starting with an equilateral triangle (Step 0).

At each step, each line segment is replaced by 4 smaller segments.

Step	Formula	Total Line Segments
0	$3 \times 4^0 = 3$	3
1	$3 \times 4^1 = 12$	12
2	$3 \times 4^2 = 48$	48
3	$3 \times 4^3 = 192$	192
4	$3 \times 4^4 = 768$	768
5	$3 \times 4^5 = 3072$	3072

What is the corresponding number sequence?

ANSWER:

Corresponding Number Sequence:   3,12,48,192,768,3072,12288,…

• Each new step multiplies the number of line segments by 4.

• Formula:

$$\text{Total segments at step } n = 3 \times 4^n.$$

Class 8 NCERT bridge course Answers Activity W 4.2 square numbers through a pattern!

 Activity W 4.2  - Square numbers through a pattern! 

Teacher can give either printed sheets of the following number pattern to students or draw the number pattern on the blackboard. 

Procedure 

Observe the following number pattern: 

The Pattern

• 1

• 1 + 3 = 4

• 1 + 3 + 5 = 9

• 1 + 3 + 5 + 7 = 16

• 1 + 3 + 5 + 7 + 9 = 25

These sums are:
1,     4,     9,     16,     25 — which are perfect square numbers!

1. Write next 5 rows in the same pattern:

1+3+5+7+9+11=36

1+3+5+7+9+11+13=49

1+3+5+7+9+11+13+15=64

1+3+5+7+9+11+13+15+17=81

1+3+5+7+9+11+13+15+17+19=100

These numbers are square numbers: $6^2, 7^2, 8^2, 9^2, 10^2$.

2. Add the numbers of each row and write the result. 

Row	Numbers	Sum
1	1	1
2	1 + 3	4
3	1 + 3 + 5	9
4	1 + 3 + 5 + 7	16
5	1 + 3 + 5 + 7 + 9	25
6	1 + 3 + 5 + 7 + 9 + 11	36
7	1 + 3 + 5 + 7 + 9 + 11 + 13	49
8	1 + 3 + 5 + 7 + 9 + 11 + 13 + 15	64
9	1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17	81
10	1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19	100

3. Observe these numbers and name the type of these numbers.

They are square numbers!
$1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, 8^2, 9^2, 10^2$.

4. Write these numbers in other possible ways:

• As squares: $1^2, 2^2, 3^2, 4^2, 5^2, \dots$
  

• As repeated additions of odd numbers.

• As dot patterns in square shapes.

5. Draw the result of each row on the grid sheet: keeping in mind that 1 box on grid is equal to 1 unit square. 

• Each sum forms a square on the grid — for example:

  • Sum = 1 → $1\times 1$

  • Sum = 4 → $2\times 2$

  • Sum = 9 → $3\times 3$

  • Sum = 16 → $4\times 4$

  • Sum = 25 → $5\times 5$

  • and so on.

Reflection and Discussion 

What difference are you observing in these various square boxes on the grid sheet?

The squares grow larger as the row number increases — each time the area grows by the next odd number.

What pattern have you observed?

The pattern is:
Sum of the first $n$ odd numbers  = n².

Q: Can you tell the sum of consecutive first 10 odd numbers?
A: Sum = 10² = 100

 How do you calculate the sum without writing and adding the numbers actually? 

Q: How do you calculate the sum without writing and adding the numbers actually?
A: Use the formula : Sum = n²

Write the rule or formula to find the sum of n consecutive odd numbers?

Q: Write the rule or formula to find the sum of $n$ consecutive odd numbers?
A: Sum of first n odd numbers=n².

Extended Learning and Exploration 

Teacher can give various number patterns like square number pattern, triangular number pattern, Virahanka/fibonacci number. 

 Students have to discover the rule of assigned number patterns.

similar patterns like:

• Triangular numbers: $1, 3, 6, 10, 15...$

• Fibonacci numbers: $1, 1, 2, 3, 5, 8...$