Скачать или смотреть LATEST NCERT CLASS 8 MATHS CHAPTER 5A NUMBER PLAY PAGES 112, 113

LATEST NCERT CLASS 8 MATHS CHAPTER 5A NUMBER PLAY PAGES 112, 113

IS THIS A MULTIPLE OF ?
SUM OF CONSECUTIVE NUMBERS

Anshu is exploring sums of consecutive numbers. He has written the
following —
7 = 3 + 4
10 = 1 + 2 + 3 + 4
12 = 3 + 4 + 5
15 = 7 + 8
= 4 + 5 + 6
= 1 + 2 + 3 + 4 + 5

Now, he is wondering —
• “Can I write every natural number as a sum of consecutive numbers?”

• “Which numbers can I write as the sum of consecutive numbers in more than one way?”

• “Ohh, I know all odd numbers can be written as a sum of two consecutive numbers. Can we write all even numbers as a sum of consecutive numbers?”

• “Can I write 0 as a sum of consecutive numbers? Maybe I should use negative numbers.”

Explore these questions and any others that may occur to you. Discuss them with the class.

Take any 4 consecutive numbers. For example, 3, 4, 5, and 6. Place ‘+’ and
‘–’ signs in between the numbers. How many different possibilities exist?
Write all of them.

Eight such expressions are possible. You can use the diagram below to
systematically list all the possibilities.

Evaluate each expression and write the result next to it. Do you notice
anything interesting?

Now, take four other consecutive numbers. Place the ‘+’ and ‘–’ signs as you have done before. Find out the results of each expression. What do you observe?

Repeat this for one more set of 4 consecutive numbers. Share your fiindings.