Division without Dividing???

Today we began division. I always suck my kids in by telling them I'm going to teach them how to divide without division. They never believe me, but it doesn't take long for them to figure out where I'm going. We use multiplication to divide! After all, multiplication is way more fun than division, right? ;)

We begin with numbers that have no remainder, such as  256 divided by 2. We start by taking out small groups of 2, perhaps 10 groups of two. 10 groups of 2 would be 20, so we subtract 20. Then we can take another 10 groups out. After we do this a few times, the kids make the connection they can take bigger groups out and save themselves a few steps. Instead of taking 10 groups of 2 out 5 times, they can just take 100 groups of 2 out from the get-go. Then we continue to take out groups until we can no longer take any more. I have two examples here, and I've tried to color-code them so they make sense.

Multiplication Matrix Box

Our class anchor chart

Close-up of the box itself

An example

We finally began 2-digit by 2-digit multiplication this week! The kids are absolutely loving the matrix box we use to introduce 2x2 multiplication!! They love it because it's super easy. I love is because it shows them the place value involved in 2x2 multiplication. They can actually see the process of multiplying the ones and tens of one number by the ones and tens of the second number. When they finally move to vertical multiplication, they'll actually understand why they put zeros here and there.Yea! There's nothing better than actually understanding WHY you do something!!!

The matrix box can actually be formatted to fit more than 2x2 multiplication. We'll be working on making our matrix boxes the size we need next week. More to come!!

Mixtures and Solutions

We began to investigate the difference between a mixture and a solution by making hot cocoa. First we examined the properties of the cocoa power - solid, brown, small granules, powdery - and the properties of the water - clear, liquid, tasteless. Then we combined them and talked about what happened. The two ingredients combined chemically to form a new substance. This is called a solution. Solutions cannot be separated physically, but require something more complex, such as evaporation. We'll get into separating solutions next week!

Then we listed out the properties of the popcorn and water. The kids filled a graduated cylinder almost to the top with water, then added as much popcorn as they could to raise the water level to the top. They were amazed by how much popcorn they could add to the water before the water level started to rise! That just added a little bit of fun to the investigation. When they finally achieved this, we discussed what they made was a mixture. The water's properties had remained the same, and they hadn't formed a new substance. Mixtures can be separated by physical means, such as filtration. We'll be looking at lots of physical ways to separate mixtures next week as well.

Popcorn Lab

Frozen "solid" of shortening and kernels

 The purpose of the popcorn lab was for the kids to have a visual example of what atoms look/behave like in all three states of matter. We began with a frozen "solid" of shortening with kernels (our atoms) packed in it.  The atoms are tightly packed in, and aren't moving. Then I challenged the kids to, without opening the bag, make their solid a liquid by adding thermal energy. They quickly figured out rubbing the solid was the fastest way to do this. After the solid became a liquid, we observed the atoms and noticed they were looser, not all touching, and moved around in our bag. Finally, I took a solid out of its bag and placed it in a beaker on a hot plate. We quickly got to see the solid changing states. As more and more thermal energy (heat) was added, the atoms finally became so energized they couldn't be contained in the beaker any longer and tried to escape. We kept this from happening with the foil.

After we finished our investigation, we discussed why these things happened to our atoms. The thermal energy gives the atoms so much energy, the result is the atoms becoming more and more active. This causes the change in states. We also discussed what this would look like if we removed thermal energy and went in reverse.

The solid beginning to melt

Liquid form

Student journal sheet page 1

Our "gas"

Student journal sheet page 2

Student journal sheet page 3

Balloon in a Bottle

Balloon without a hole

Balloon with a hole

Today we worked on properties of matter. After making predictions about what we thought would happen, we attempted to blow up a balloon in a 2-liter bottle. The balloon wouldn't blow up. So we removed the balloon to try to blow it up, and it worked just fine. Clearly, it wasn't a balloon issue!

We tried again, as unsuccessfully as before. Finally, we punched a hole in the bottle and tried again. This time it worked! We discussed why it worked this time, coming up with the idea that all matter, even gas, takes up space. When we blew up the balloon, we could feel the air coming out of the hole. The balloon was pushing the air out because matter cannot occupy the same space.

You should have seen all the red faces trying to blow up the balloons! It was priceless!