Sum of N (N=1, 2, 3,...)

 
We have N consecutive natural numbers.
 
1, 2, 3, 4, 5, 6,  . . . , 100, ...., N
 
 

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When N is 6,
 

1,  2,  3,  4,  5,  6

 

are the number that we have. 
 

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Q1.  Can you try representing these numbers using cube blocks?

blocks

 

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Yes, simply, We can make number block for each number. like this.

 

1

2

3

4

5

6

number blocks

 
 

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Q2.  Now, Let's try sum of those numbers using cube blocks. How would you visualize it?
 

1 + 2 + 3 + 4 + 5 + 6

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We can combine all the blocks together.

 

1  +  2  +  3  +  4  +  5  +  6

Sum of N

 
 

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Q3. What is the sum of those numbers? Use a generalized arithmetic expression.
 

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to find generalized expression, we can also use the block image. 
 
3-1) bring the twins of 'sum of N'.
 

 
 
3-2) Put the twins together to form a rectangle. 

two sum of N

 
 
3-3) How many blocks are in the rectangle? find an arithmetic expression. 
 

 
 
3-4) How many blocks are in the 'sum of N'?
 

Sum of N

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Q4. for the number N, can you find a generalized expression? 
 

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sure. 
 
expanding our imagination from 6 to N, 
We can generalize the sum of N (N= 1, 2, 3, 4, ...). 
 

 
 
 

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Q5. Let's play the sum of N, using printed blocks. 
 
 
 

two sum of N

 
 
 

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