Class 8 NCERT bridge course Answers Activity W 4.5 Building Towers with Blocks

 Activity W 4.5: Building Towers with Blocks 

Material Required 

 Different coloured blocks. 

 Paper and pencil for recording results. 

Explain to the students that each block will represent a number, and stacking blocks will help illustrate exponents.

For example, stacking 2 blocks means 2¹ and stacking 4 blocks means 2² and so on

Procedure & Observation

Ask students to create towers representing different powers of 2: 

 For 2¹  , they stack 2 blocks. 

 For 2² , they stack 4 blocks. 

 For 2³ , they stack 8 blocks. 

Students stack blocks to represent powers of 2:

Exponent	Mathematical Form	Number of Blocks	3-D Shape Formed
2¹	2	2 blocks	Cuboid
2²	4	4 blocks	Cube (if arranged as 2x2x1)
2³	8	8 blocks	Cuboid or Cube (if arranged as 2x2x2)

1. After stacking blocks for different exponents, students may be made to explore what 3-D shape they get. 

For example, 2¹ gives a cuboid, whereas 2² gives a cube and so on. 

Discussion:

What 3-D shape do they get?

• For 2¹ = 2 blocks, students usually get a Cuboid (because two blocks form a rectangular shape).

• For 2² = 4 blocks, if arranged symmetrically (2x2), they can get a Cube.

• For 2³ = 8 blocks, if arranged as 2x2x2, it forms a Perfect Cube.

Conclusion:

• When the blocks can be arranged equally in all three dimensions (length, width, and height), the shape is a cube.

• Otherwise, it remains a cuboid.

They may see for which exponent of 2 they get a cube and for which other a cuboid. 

Can they get any other 3-D shape other than a cube or cuboid?

No, using only simple stacking of square or rectangular blocks, the shapes are usually limited to cuboids or cubes.

Other 3-D shapes like pyramids or spheres cannot be formed unless the block shape or stacking style is changed. 

2. They may observe as to how the number of blocks increases as the exponent increases. 

Is there any pattern?

Is there any pattern in the number of blocks as the exponent increases?

Yes! The number of blocks doubles every time the exponent increases by 1.

Exponent	Number of Blocks
2¹	2
2²	4
2³	8
2⁴	16

Pattern:
As the exponent increases by 1, the number of blocks is multiplied by 2.

Conclusion:
This activity helps visualize how exponents grow and how they relate to 3-D shapes like cubes and cuboids. The number of blocks follows a clear doubling pattern as the exponent increases.

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:

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