Chatting about Sums of Consecutive Numbers

It has been so much fun to connect with classes about the Sums of Consecutive Numbers problem!  I have been so impressed with the thinking and problem solving skills of students!  A 1st grade class had the fantastic idea to use a measurement tool as a number line!

A 4th grade class at my school used video chat to connect with a 4th grade class in Dublin, Ohio.  Before our chat, students explored the problem and discussed questions with their homeroom classes.  Some of the questions they explored included:

• Were there any numbers that couldn't be made by the sum of consecutive numbers?
• What happened if you added 3 numbers?  Or 4 numbers? 
• Could you predict whether the sum would be even or odd based on the number of addends?
• Is there a pattern?  If so, how might you describe it?
• Is there anything special about the prime numbers in comparison to the composite numbers?  What do you notice?

Last week, the classes were able to connect and share their observations:

Some of the observations students made included:

1. When you have 2 consecutive addends, the sum is an odd number.  For example, 3 + 4 = 7.
2. When you have 3 consecutive addends, the sum is a multiple of 3.  For example, 1 + 2 + 3 = 6 and 6 is a multiple of 3.
3. When you have 4 consecutive addends, the sum is NOT a multiple of 4.  They are curious why the pattern that seems to work for 3 addends does not work with 4 addends.  For example, 1 + 2 + 3 + 4 = 10 and 10 is not a multiple of 4.
4. When you have 5 consecutive addends, the sum is a multiple of 5.  For example, 1 + 2 + 3 + 4 + 5 = 15 and 15 is a multiple of 5.

The conversation generated further questions.  We're hoping that students can explore these questions in groups and then we can have small groups video chat rather than a whole group video chat.

Using technology to connect with others and share our mathematical thinking is a great way to take our learning beyond the physical walls of our school building!