Equivalent Fractions

Equivalent fractions is all about self-discovery. After the kids have seen enough models of fractions, they really notice the equivalence of some of them on their own. This leads us to a discussion about why the fractions are equivalent - because they represent the same amount, they're just broken into differently-sized pieces. After drawing enough examples on their own, the kids realize there is a multiplication/division relationship as well. This saves them the time of drawing the pictures!

Our journal entry

Our class poster

Fraction Kits

This week we made fraction kits. This kit is a great tool for students to use to explore the relationship between fractional pieces. As we made it, we discussed how we were making it. "I'm taking one whole and folding it into two equal pieces. What have I made?" "Now I am taking one whole and folding it into two equal pieces, then folding it again to half all those pieces. What have I made?" etc.

After we made the kits and discussed them, we played a game where we have to roll a fraction die and try to cover our entire whole before our partner covered theirs. This lead to some great discussion about how much they had left after each roll.

Next we played a game where we started with our whole covered by two halves and rolled the die to try to uncover the entire whole before our partner. They were responsible for exchanging their halves for the pieces they need. For example, if they rolled 1/16, they had to exchange a half for a combination that still equaled a half but included at lease one 1/16 piece so they could remove it.

  

Our Earth's Natural Resources

This week we discussed Earth's natural resources. A resource is anything used by man. Natural resources are resources that are not man-made. We cannot make more.

The students read an article and made a flip book detailing the difference between a renewable resource and a non-renewable resource. Renewable resources replace themselves in our lifetime. Non-renewable resources, such as fossil fuels, cannot be replaced in our lifetime.

We also discussed why it is important to conserve both renewable and non-renewable resources.

Outside of a foldable

Inside of a foldable

Plant Growth in Different Soils

We planted radish seeds (because they sprout quickly) in gravel, topsoil, sand, and clay and then we observed them every day for five days. Gravel, sand, and topsoil all sprouted, while clay had no growth at all. We noticed the topsoil sprouted faster than gravel and sand. We also observed the topsoil had the healthier-looking sprouts. Gravel's sprouts were a bit brown in color, and sand's sprouts were more withered. The kids were surprised the seeds grew in gravel and sand! We discussed that gravel and sand were not providing as much nutrients as the topsoil, hence the pitiful sprouts. Also, clay didn't produce plant growth because it is too packed together to allow roots to grow. We concluded topsoil was the best soil with regards to plant growth.

Division without Dividing?!?!

Today we began division. I always get my kids' attention 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 348 divided by 2. We start by taking out easy groups of 2, perhaps 100 groups of two. 100 groups of 2 would be 200, so we subtract 200. Then we can take another 50 groups of 2, which is 100, away from our number. Next we take out 20 groups of 2, which is 40. Finally, we can take out 4 groups of 2, or 8, to get to zero. 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 50 groups of 2 and then 20 groups of 2 out, we could have just taken out 70 groups of 2. We continue to take out groups until we can no longer take any more. Once what is left is smaller than our divisor, we have taken out all the groups we can. I have two examples here, One with a remainder and one without. I've tried to color-code them so they make sense.

Water Retention

Gravel Water Retention

Water retention in different types of soils is one of those concepts where figuring out the process for the experiment is every bit as important as the actual results. I want the kids to come up with a way to test this on their own and be able to measure their results. They generally come up with lots of great ways to allow soil to absorb water, but they can struggle a bit when trying to make the amount of water absorbed measurable. The discussion of our plan oftentimes takes longer than our actual experiment. It's worth it, though, because it really makes them use their noggins! Eventually they come up with this...

To test water retention of different types of soils, we use a graduated cylinder, panty hose (which the kids think is hilarious!) and different types of soil. We put each individual type of soil (200ml) into the panty hose, SLOWLY add 200 ml of water, and figure our how much water was retained by the soil by looking at the amount of water than fell into the beaker. The kids are always surprised by how much water the sand retains!

Sand Water Retention

Top Soil Water Retention

Soil Texture

The students are responsible for knowing the properties of soil in 4th grade - color, texture, water retention, and plant growth. We began by looking at color and texture. The students observed top soil, clay, sand, silt and gravel. They added a bit of water to each soil type to help them really feel the texture. They had to determine if the soils make a ball, and if they are grainy, silky, or sticky. Then they predicted what the texture would be like when different soils were mixed together, such as clay and sand, before actually mixing them together. We had a bit of a water spill on one of the plates, so we used that opportunity to revisit erosion. They were able to see the soil being carried away by the water, while the rocks stayed in their place. We discussed the fact that rocks take much longer to erode than soil.

Adding water to our soil

Water eroding the soil

Divisibility Rules

This week we listed out multiples of many numbers, and used these lists to help us come up with some divisibility rules. We thought knowing these rules might help us when determining factors of larger numbers. 

Breaking Apart Numbers in Multiplication

What we did this week was go through our basic facts and determine which ones we know quickly, and the ones with which we still need some practice. We made a list of those we're still working on, and came up with ways to "get" to that answer. For example, if 9 x 12 is still a struggle, we could think of it as (9 x 10) + (9 x 2). We made the arrays to go with the problem, which made visualizing the strategy a little easier.

If a student can visualize breaking apart a number for basic multiplication, it's going to make his life much easier when we get to 2-digit by 2-digit multiplication. It's so important for the kids to understand the place value involved in larger multiplication, and also to learn to make their numbers work for them. Flexibility with numbers is a HUGE concept to grasp, and it has arguably the greatest impact on the success of a mathematician!!!!!!

How Water Can Change the Shape of Rocks

To test how water can change the shape of rocks, we had to get a little creative. Obviously we don't have the kind of time to watch weathering, erosion, and deposition in real-time. :) In order to speed process up a bit, we used limestone rocks that had been soaking in water overnight. This made them very soft.

We weighed the mass of our rocks, which was 54g. We also observed the rocks' edges were very jagged and sharp. We put our rocks into a glass jar with about 1/2 cup of water. We shook our jar for 3 minutes, removed our rocks, and checked their mass again. This time, the mass was 46g, and the edges of the rocks were smoother and more rounded. We put our rocks back into the water and shook again for 6 minutes. This time, when we measured the mass, it was35g. By now, the rocks were completely smooth, and much smaller. The water was completely full of sediment by this point as well.

We discussed how this is related to a river rushing over pebbles. They become more and more smooth, and will eventually become smaller in size.

After 3 minutes of shaking

After 6 minutes of shaking

Changes to our Land

This week we began to discuss changes to land. First, we talked about what kinds of changes can happen to our land. We discussed the meaning of weathering, erosion, and deposition. In 4th grade we focus on changes caused by wind, water, and ice, and do investigations that show how each can affect the land. 


We started with our investigation of wind. The kids made a sand dune in their box lids, trying to make the dune come to a point as much as possible. They then predicted what would happen when the wind (the kids blowing through straws) hit the sand. Most thought the sand would move to the other end of the box, forming a new dune. When they blew the wind, however, they notices the sand really just spread all over the box. We discussed why this happened, focusing on the size of the sand particles in relation to where they landed. We also talked about why the particles didn't form another dune. The kids came to the conclusion is was because the box was too slippery, so the particles just blew around all over the box lid. We did notice a stronger stream of air was needed to move the larger particles. We finished up by looking at some really cool pictures of wind erosion. We discussed how wind can cause erosion:  by picking up the particles (just like our experiment) and slamming them into objects such as rocks. Eventually, the rock is going to wear down from repeatedly being hit by sediment.

Arrays

When we begin talking about arrays, we start by defining what they are. Arrays are not new to our 4th graders, so they are quick to tell us an array is a group of objects with equal rows and columns. We discuss counting arrays, and how we don't need to count each individual item. We can simply find the number of rows and the number of columns, then multiply them together. This works because we're talking about combining equal groups, which is multiplication.

After this discussion, the kids spend some time finding different arrays around our room. We talk about the dimensions of the arrays found, as well as how many items are in the arrays. This is added to our journal.

Matter Rotations

This week we reviewed mass, volume, and density, and also began discussing the idea of conductors of heat. (We'll talk more about conductors when we get to circuits.) The students went through rotations covering each topic.
Rotation #1 was a can of Coke and a can of Diet Coke, and the students placed them in a tub of water to measure distance each sank. The regular coke sank to the bottom, while the Diet Coke did not. This lead to a discussion about the mass of sugar versus the mass of artificial sweetener, and their relative densities. I brought in a sample of each so that the students could feel the difference in mass. It a BIG difference!
Rotation #2 included a wooden spoon, a plastic spoon, a rubber spoon, and a metal spoon. The students predicted which spoon(s) would be good conductors of heat, then we put the spoons in hot water for 1 minute. We took the spoons out and timed how long it took for a small piece of butter to begin melting when placed on the spoon. We quickly noticed the metal was by far the best conductor.
Rotation #3 was about predicting and measuring the volumes of different liquids.
Rotation #4 included measuring the mass of many different objects using a triple beam balance.

Density Tubes

Beginning the density tube

We're discussing density in science, so to explore it a bit, we used three different solutions and determined their relative density. Before class I prepared three solutions. Solution #1 was 400mL of water and 10 drops of blue food coloring. Solution #2 was 400 mL of water, 10 drops of red food coloring, and 3 tablespoons of salt. Solution #3 was 400 mL of water, 10 drops of green food coloring, and 6 tablespoons of salt. The kids did not know the properties of the liquids. Their only instructions were to build the density tube, and add the liquids in a way that the layers stayed separate. All the kids began in different orders, and they all had a mix of liquids! After lots of trial-and-error, all the groups were able to get their liquids into the correct order. I discussed with each group individually why the liquids had to be ordered in this way. We discussed density, which liquid must be our most dense, and which liquid must be our least dense. We also related the density of the red liquid to the other liquids.

A completed density tube

Multiplying by Multiples of 10

When we begin discussing multiplying by multiples of 10, we start by finding the factors of 100, 200, and 300. This is a great discussion, especially when we get to the factors of 200 and 300. The kids self-discover the relationship between the factors of 100 and the factors of 200 and 300. As we have this discussion, I casually comment that 4 x 50 and 50 x 4 both equal 200. I make this comment again when we get to 5 x 60 and 6 x 50 for 300. This leads the kids to notice the rule for multiplying by multiples of 10. We can just multiply the numbers that are NOT zero first, then we can add the appropriate amount of zeros. The kids absolutely think this is magic! :) Surely it isn't supposed to be this easy?!?!