Enhancing Mathematical Understanding

👀 What you see ?

• Same number of dots each time 
• No change in dots 

🎯 Key Understanding

• Each term has the same number of dots 
• Pattern does not grow 

🧠 Rule

• Add 0 each time

📌 Sequence

• 1, 1, 1, 1, 1, 1 ...

👀 What you see ?

• One dot is added each time 

🎯 Key Understanding

• Each term has one more dot than before 
• Numbers increase step by step 

🧠 Rule

• Add 1 each time

📌 Sequence

• 1, 2, 3, 4, 5, 6 ...

👀 What you see ?

• Dots increase by 2 each time 
• One dot remains unpaired 

🎯 Key Understanding

• Cannot be divided into equal pairs 
• One dot is always left 

🧠 Rule

• Start from 1 and Add 2 each time

📌 Sequence

• 1, 1 + 2,  1 + 2 + 2, 1+ 2 + 2 + 2 ...
• 1, 1 + 2, 3 + 2, 5 + 2, 7 + 2, 9 + 2 ...
• 1, 3, 5, 7, 9, 11 ...

👀 What you see ?

• Dots are added in pairs 
• Each step adds 2 dots 

🎯 Key Understanding

• Dots can be grouped into equal pairs 
• No dot is left 

🧠 Rule

• Start from 2 and Add 2 each time

📌 Sequence

• 2, 2 + 2, 2 + 2 + 2, 2 + 2 + 2 + 2 ...
• 2, 2 + 2, 4 + 2, 6 + 2, 8 + 2 ...
• 2, 4, 6, 8, 10, 12 ...

👀 What you see ?

• Dots form a triangle 
• A new row is added each time 
• Each new row has one more dot 

🎯 Key Understanding

• Each term shows total dots in the triangle 
• Numbers grow by adding next counting number

🧠 Rule

• Start from 1 and Add: +2, +3, +4, +5…each time

📌 Sequence

• 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4 ...
• 1, 1 + 2, 3 + 3, 6 + 4, 10 + 5 ...
• 1, 3, 6, 10, 15, 21, . . .

👀 What you see ?

• Dots form a square 
• Equal number of rows and columns
• Length, width of square are increasing by 1 unit each time

🎯 Key Understanding

• Each term shows area of corresponding square
• Total dots = rows × columns 

🧠 Rule

• Write areas of squares with dimensions as counting numbers one by on

📌 Sequence

• 1 x 1, 2 x 2, 3 x 3, 4 x 4, 5 x 5, 6 x 6 ...
• 1, 4, 9, 16, 25, 36 ...

👀 What you see ?

• Blocks form a cube (3D) 
• equal length, width and height in each shape

🎯 Key Understanding

• Each term shows volume of corresponding cube
• Total dots = length x width x height

🧠 Rule

• Write volume of cubes with dimensions as counting numbers one by one

📌 Sequence

• 1 x 1 x 1, 2 x 2 x 2, 3 x 3 x 3, 4 x 4 x 4 ...
• 1, 8, 27, 64, 125, 216 ...

👀 What you see ?

• Dots form a hexagon 
• Layers grow around the center 

🎯 Key Understanding

• Each term adds a new outer layer 
• Shape remains hexagonal 

🧠 Rule

• Start from 1 and Add: +6, +12, +18, +24…each time

📌 Sequence

• 1, 1 + 6, 1 + 6 + 12, 1 + 6 + 12 + 18 ...
• 1, 7, 19, 37, 61, 91 ...

👀 What you see ?

• Dots double each time 

🎯 Key Understanding

• Each term is double the previous 
• Growth becomes faster 

🧠 Rule

• Start from 1 and then keep Multiplying 2 each time

📌 Sequence

• 1, 1 x 2, 1 x 2 x 2, 1 x 2 x 2 x 2 ...
• 1, 1 x 2 , 2 x 2, 4 x 2, 8 x 2, 16 x 2 ...
• 1, 2, 4, 8, 16, 32 ...

👀 What you see ?

• Number of triangles increases very quickly 
• Triangles are getting tripled each time

🎯 Key Understanding

• Each term is three times the previous 
• Growth is faster than powers of 2 

🧠 Rule

• Start from 1 and then keep multiplying 3 each time

📌 Sequence

• 1, 1 x 3, 1 x 3 x 3, 1 x 3 x 3 x 3 ...
• 1, 1 x 3 , 3 x 3, 9 x 3, 27 x 3, 81 x 3 ...
• 1, 3, 9, 27, 81, 243 ...