Yesterday for school, we calculated how much trash our family of three generates per day. We collected our trash for three days. Since some days have little trash, and other days have more, I wanted to get a better idea of where we stood. (We did discuss "high trash" weeks like birthdays and Christmas when we have boxes and wrapping paper, etc.) But on average, we generate about one pound each day.
My children are 5 (and 5 months) and 6 (and 11 months). I am exact with their ages, because if they were in school, there is NO WAY this problem would be put in front of them. First, I asked how to figure out how much trash we generated in one day if we know how much trash we generated in 3 days. They kind of threw around some close ideas, so I drew an illustration that worked out their thoughts more concretely. "What if I took each piece in the trash and cut it into three equal pieces. I would put each piece into a pile, and have three piles when I'm done. Would you say that I split the trash into three even stacks, representing the three days? And would one stack represent the trash we would generate in one day?" Their eyes began to light up. Since we had already talked about fractions, they quickly recognized that we had split the trash into thirds.
I then drew a circle on a paper and said, "this circle represents the three days worth of trash that we collected. How can I divide the "trash" to help me figure out the amount generated in one day?"
"Divide it into three equal parts."
I tried my best at making "thirds" and it was at least sufficient. I then showed how I can not only divide a circle into thirds, or the trash into thirds, but a number into thirds (division- a new concept). They now know that we generate one pound per day.
"How many do we generate in a week?" To which my FIVE year-old responded, "Seven." Sign her up for MIT, folks!
She new the answer was 7, but did not know how to explain why. So I let her brother think and verbalize. I then explained how you could add 1+1+1+1+1+1+1 to get 7, or you could say "1 TIMES 7." I knew they got it once we needed to know how many pounds we generate in a month, and used "30" as the number of days per month.
When we started working on the number of pounds per year, I first was going to use the result from our monthly figure, but my 6 year old helped me realize something when he said, "figure out how many days there are in a year and times that..." It occurred to me that he was dead on. Since there are not 30 days in every month, you cannot simply multiply that result by 12. You need to go back to the daily amount and multiply it by 365 for the most accurate result.
There was never any reason for them to know how many days there are in a year, but they know now!
This is a great example of the many concepts taught in one activity. And this was part of "science," not math! It also shows that children understand much more than we give them credit for. I've mentioned this often in my blog, but in case you are a new reader, my daughter isn't even supposed to be in kindergarten yet, according to her birthday. And here she is at home, dividing, multiplying, and problem solving!
My children are 5 (and 5 months) and 6 (and 11 months). I am exact with their ages, because if they were in school, there is NO WAY this problem would be put in front of them. First, I asked how to figure out how much trash we generated in one day if we know how much trash we generated in 3 days. They kind of threw around some close ideas, so I drew an illustration that worked out their thoughts more concretely. "What if I took each piece in the trash and cut it into three equal pieces. I would put each piece into a pile, and have three piles when I'm done. Would you say that I split the trash into three even stacks, representing the three days? And would one stack represent the trash we would generate in one day?" Their eyes began to light up. Since we had already talked about fractions, they quickly recognized that we had split the trash into thirds.
I then drew a circle on a paper and said, "this circle represents the three days worth of trash that we collected. How can I divide the "trash" to help me figure out the amount generated in one day?"
"Divide it into three equal parts."
I tried my best at making "thirds" and it was at least sufficient. I then showed how I can not only divide a circle into thirds, or the trash into thirds, but a number into thirds (division- a new concept). They now know that we generate one pound per day.
"How many do we generate in a week?" To which my FIVE year-old responded, "Seven." Sign her up for MIT, folks!
She new the answer was 7, but did not know how to explain why. So I let her brother think and verbalize. I then explained how you could add 1+1+1+1+1+1+1 to get 7, or you could say "1 TIMES 7." I knew they got it once we needed to know how many pounds we generate in a month, and used "30" as the number of days per month.
When we started working on the number of pounds per year, I first was going to use the result from our monthly figure, but my 6 year old helped me realize something when he said, "figure out how many days there are in a year and times that..." It occurred to me that he was dead on. Since there are not 30 days in every month, you cannot simply multiply that result by 12. You need to go back to the daily amount and multiply it by 365 for the most accurate result.
There was never any reason for them to know how many days there are in a year, but they know now!
This is a great example of the many concepts taught in one activity. And this was part of "science," not math! It also shows that children understand much more than we give them credit for. I've mentioned this often in my blog, but in case you are a new reader, my daughter isn't even supposed to be in kindergarten yet, according to her birthday. And here she is at home, dividing, multiplying, and problem solving!
