How much trash do we generate per day?

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!

Counting by Fives

This is an activity that my son enjoyed a lot, so I thought I would share. We started using this when he was five years old, doing kindergarten work. He could count by fives perfectly, but I wanted to make sure that he could recognize the numbers as well. I printed out the numbers 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 fairly large on cardstock paper. I then cut them into little squares. I gave them to him all mixed up, and had him put them in the correct order. For beginning learners, you can start with half of the numbers, and then add the second half once your child gets those down. I cannot stress how helpful this is when learning about money, and counting nickels! We coincidentally did this shortly before the "nickels" section in his time and money book came up.

We also used the same concept with recognizing the months and days of the week. Simple enough, and it's fun, too!

Algebra for Four Year Olds

A few days ago, I was sitting in McDonald's with my children, waiting for them to finish eating. Out of boredom, I developed a great little game that they have enjoyed playing. I put my hand behind my back and said, "I have 3 fingers up behind my back, and two up here (holding two up). How many do I have up all together?" My four year old looked at both of her hands under the table and set them up and counted. "Five!"

The game continued and I actually saw right there in McDonald's, my four year old "get" counting on. She finally stopped counting ALL of the fingers and started with one number and then counted on the rest. After a while, I asked questions like, "If I have 5 fingers up behind my back, and I need to have 8 fingers up, how many do I need to put up on this hand?" And of course, they both got these every time.

Now, my daughter will be five in three months. Because she has a November birthday, she does not meet the cut off for starting kindergarten this year. She is learning to read, she is figuring out missing addend problems, and her skills test all showed that she is on a 5-6 year old level (that was at age 3). Imagine if I were depending on public schools to educate my child! Not only would I have to make her wait an entire year, I know that kids coming out of our local kindergarten are not even reading. After having taught my son to read last year, I just can't imagine why children are not reading out of kindergarten! Even an average child should be able to read to a degree.

Anyway, we still play the game everyday, and my daughter loves asking ME "finger problems!" She has figured out that she has to check to make sure I'm right! And yes, we will be doing kindergarten this year, because unlike the school system, I have common sense!

P.S. I almost forgot. One of the problems I gave was to see how my son would handle it. I said, "I have 100 fingers up behind my back, and 5 up here. How many do I have up?" He answered 105, but then I asked him, "HOW can I have 100 fingers up behind my back?!" We all got a laugh out of that!

It's JUST a Geoboard!

Last week we were at the school supply store and I remembered reading about a geoboard in the next week's lessons when I saw one in the midst of the math supplies. I thought, "It's jut a board with some nails in it!" and put it down. Then I noticed it was ONLY $3.95 or so and figured we might use it at some point, so I added it to my pile. I didn't get the colored rubber bands because we had perfectly good rubber bands at home!

I put it with the school stuff and the next time we did school, brought it out with the lesson materials. Before I even had to say anything, my 6 year old was adding rubberbands and creating a design. Before we finished school he was fighting over it with my 4 year old. They LOVED this thing! He played with it all day, and then, get THIS: he put it under his pillow at bed time! Here is one of the designs that he created. He also took the picture! He made countless designs that day, and I bet if I look, it is still under his pillow. Here is a great resource for geoboard lessons.