I hope you've been doing well during this first full week of Fall. As the matter of fact, have you noticed how the days are becoming much shorter and the nights seem to be getting longer? And what about the changes to the leaves on the trees...those same leaves that only a few months ago were a bright vibrant green, have since faded to the colors of brown, yellow, orange, and red...these occurrences tell me one thing...the season is changing and the earth needs those changes in order to complete the cycle that connects us to nature...in fact that has to happen so that one season can balance the other (i.e. Fall Harvest=crops; Winter= transformed soil that helps bring new life to spring flowers, etc.) I say that while thinking back to a math conversation that I had with a couple of 4th graders earlier this week. I was curious to see what they knew about balance as it relates to the equal sign, so I showed them the problem 4+8=____+5. One of the children was quick to say that 12 went on the line because 4 +8=12, but the other child kept looking across the problem before telling me that 7 should go on the line. When I asked each of them to explain their thinking, the first child said she knew that 4+8=12 so that meant 12 belonged on the line then you just add the 5 to get 17. The other child disagreed and said he knew that 4+8=12 and he knew that the line was for the number that he could add to 5 that would equal 12. He said he knew that number had to be 7. While the first child was right when adding the first two numbers, she didn't see how the equal sign was there to balance the problem out; this means that whatever you have on one side of an equation has to be balanced by the number on other side.. this was something the second child realized right away.
I had the students look at some more problems similar to that and when they came to the last one, I purposely made sure it was a true or false problem which was 8=8. This time around the first child smiled and said "oh now I get it"! She emphatically responded "that's true, 8 is definitely equal to 8". When I asked her to explain her thinking she said "if you have 8 things on one side and 8 on the other, you're not trying to find the total, you just want to see if one means the same as the other...like 11+11 is the same as 22, that's why 8 is equal to 8"... she was so proud of herself, and of course that made my heart happy because both children gained an understanding of the equal sign and it's purpose when writing equations. See, beyond mathematics, we all need a sense of balance. It's what gives us the stability we need to keep moving in a world that has so many uncertainties. As in the case of mathematics, the equal sign is that balance that gives a problem stability when children are trying to make sense of the relationship between numbers.
Under this week's Intentional Toolkit I shared a few resources that highlight the important role that the equal sign plays in math, I hope you find them useful. And speaking of balance, did you know that we are now in the season of the zodiac sign that represents balance? Yep, that zodiac sign goes to those super amazing, super talented, super intuitive LIBRAS...which I happen to be!!!! Shout out to all my fellow Libras who love justice, balance, and harmony; it's our season to celebrate the blessing of life! And if this isn't your birthday month, I still hope that you'll take time to enjoy the beauty of this upcoming month as well...until next time...go out there and be GREAT!