2013
Oct 02

The Average Bears: Mr. Mean, Mr. Median & Mr. Mode

by Hannah Holt »

16 comments


Last week, my son asked me, “What does average mean?” I thought it was an interesting question, socially and mathematically.

Averages look at groups of things (or individuals) and point out what’s common, normal, or ordinary.

As you can probably tell from this loosey-goosey definition there is more than one way to find an average. So how do you find an average? To help us out, I want to introduce you to a few bears. First there is Yogi. He is…

smarter than

{Image: http://en.wikipedia.org/wiki/Yogi_Bear, text added}

Then there are Mr. Mean, Mr. Median, and Mr. Mode. They are your average bears:

Mean Median Mode

One day, Yogi Bear wanted to know how the squirrels in Jellystone Park were doing. He called for Mr. Mean, Mr. Median, and Mr. Mode and said:

Yogi: Go find out how the average squirrel is doing.

Mr. Mean went to Squirrel Tree first. The squirrels had differing amounts of acorns.

squirrels and acorns

Mr. Mean is mean. He took all their acorns and counted them. There were seventy acorns and seven squirrels. He divided all the acorns into seven piles. Each squirrel got 10 acorns:

squirrels and acorns mean

This made some of the squirrels happy and some mad! Mr. Mean went back to Yogi and said:

Mr. Mean: The squirrels are great. The average squirrel has 10 acorns.

But after Mr. Mean left, the squirrels who lost acorns took them back. So all the squirrels had the same number of acorns as before.

Mr. Median went to Squirrel Tree second. Mr. Median loves the middle. He found the squirrel with the middle amount of acorns and reported this number to Yogi.

squirrels and acorns median

Mr. Median: The squirrels are okay. The average squirrel has 7 acorns.

Finally Mr. Mode went to see the squirrels. Mr. Mode loves whatever happens most often.

squirrels and acorns mode

He came back and said…

Mr. Mode: The squirrels are terrible!!! The average squirrel only has one acorn.

Whom should Yogi Bear believe? He sent the Three Average Bears to Squirrel Tree and they all came back with different answers. What do you think is the best average?

Three Ways to Find an Average:

1. Mean: Add up all the parts and divide by the number of pieces. (40+12+8+7+1+1+1)/7 This is the most commonly used average.

2. Median: Arrange all the numbers from most to least. Pick the middle number. If you have an even number of data, take the mean of the two middle numbers.

3. Mode: Look through all the numbers and count how often each number happens. Pick the number that happens most often.

Note: As an engineer, I often faced situations with more than one “right” answer. A good engineer can usually make the numbers say almost anything. However, a great engineer uses her judgement to find the best and most accurate way to present the data. Some clients pressure you to give them the answers they want. However, this never pays off in the long run. Someone could get hurt. And even if no one gets hurt, someone else is bound to look at the data later. If they find data splicing, your client could get sued and lose more money than if you had told them the truth. Also, you could lose your licence for bad engineering practice. Engineering is more than number crunching; it’s about being honest and using good judgement.


2013
Sep 26

Carrot Canoes and Archimedes’ Principle

by Hannah Holt »

9 comments


I’m working on a new picture book about buoyancy, so I’ve had boats on the brain lately. Like, could you turn a carrot into a boat?

carrot boat 1

Carrots don’t float. Well, I supposed if you found a dried out carrot it might float, but for the most part carrots sink.

carrot boat 2

{See, I cut off the end of a carrot and put it in water… Thunk! It sunk.}

But what if we took a carrot peeler and hollowed out the inside of a carrot?

carrot boat 3

Ta da! It floats…

carrot boat 4

Now why does the first carrot sink while the second carrot floats? They are both carrots, right?

Let’s talk about buoyancy. Buoyancy is the lift water gives you. You might have noticed you feel lighter jumping in water than on land. That’s because the water pushes you up.

Weee2

How much does water push you up?

water weight

It pushes you up… the weight of the water you just replaced? Or as Archimedes Principle states:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Wow, that was a lot of words! Let’s go back to our carrot. Before we hollowed out our carrot, water still pushed up on the carrot. But the carrot was heavier than the amount of water it moved. In other words, it was too dense. So it sank.

carrot before and after2

In the second case, the carrot was lighter. The water could hold it up and it floated. You can make a carrot into a boat!

A few activities by grade-level:

Kindergarten-1st Grade: Take a potato, an apple, a carrot, and a pea. What ones float? What ones sink? Make a hypothesis: What else do you think will float? Now test it.

2nd -3rd Grade: I started with 2 cups of water (about 500 mL). The carrot and the water together have a volume of 2 ¼cups (about 525 mL). How big (in volume) is the carrot? Answer: ¼ cups big (or about 25 mL in volume)

4th – 5th Grade: One milliliter of water (volume) has a mass of one gram. The carrot took up 25 milliliters of water. How many grams of water did the carrot replace? Answer: 25 grams {You might have to walk them through this.}

6th Grade: Archimedes’ Principle says that the buoyant force on our carrot can be found like this:

The Volume of the Water (displaced by the carrot) x The Density of the Water x Gravity

If the Volume of the Water = 25 (cm³)

and the Density of the Water = 1 (g/cm³)

and Gravity = 10 (m/s²… I rounded for calculating ease.)

What is the buoyant force on the carrot?

{Answer: 25 x 1 x 10 = 250 g• m/s²} Advanced students might be interested in the units, but the main goal here is to try and plug the values into the equation.


2013
Jul 03

How Do Plants Make Food

by Hannah Holt »

8 comments


Last summer we regrew green onions and celery from stubs.It worked so well that the celery is now as tall as my two-year-old:

celery

We wanted to see if we could do the same thing with lettuce. We put a Romain lettuce stub in a small bowl of water and waited…

Lettuce growth

It’s day 14 and we have some respectable looking lettuce leaves. Cool. Huh?

Along with this project we read The Magic School Bus Gets Planted. After reading the book, my five-year-old asked, “How do plants make food out of water and air?” Or…

How Question

I could have given him a one word answer (photosynthesis!). But he asked a thoughtful question and I thought it deserved an equally thoughtful answer.

First we talked about what is water made of?

Atoms: atoms are tiny, tiny building blocks. They are like the mini-legos of life. Atoms are so small you cannot see them with your eyes or even a magnifying glass. You need a special looking machine (an electron microscope) to see the biggest atoms. Some atoms like to hangout with other atoms:

hydrogen

And others prefer to keep to themselves:

argon

When a group of atoms hang out together, it is called a molecule.

Water is made of molecules. Water molecules look like this:

water molecule

Air is also made of molecules. It is made of lots of different molecules, but the molecule that plants use is called carbon dioxide. It is a carbon atom with two oxygen atoms:

carbon dioxide molecule

Now let’s talk about food, like sugar. Yup, that’s right… some plants use sugar for energy. But they don’t eat it. They make it. Here is what one type of sugar looks like:

sucrose molecule

Let’s check if we have all the right building blocks. To make sugar we need carbon, hydrogen, and oxygen. Can we get all of those atoms from water and air?

YES! From water we get hydrogen and oxygen, and from air we get more oxygen and carbon. Here is how plants use air and water to make food:

photosynthesis2

The “big dance” that rearranges the atoms is called PHOTOSYNTHESIS. Photosynthesis means light (photo) and making-stuff (synthesis). Plants take water and air and use light to turn atoms into food. If you have the right building blocks and the right conditions, you can make almost anything.

Note: My seven-year-old liked this discussion, but it was a bit too much for my five-year-old. If this is too much detail for your tykes, here is the two sentence explanation:

Q: How do plants make food out of air and water?

A: Under the right conditions air and water can be turned into sugar (and other foods). The process of turning air and water into food for plants is called photosynthesis.

Extension activity: Playdoh Molecules

playdoh molecules

What you’ll need

  • Different colors of playdoh
  • Cut up straws

Form the playdoh into balls and connect them using bending straws bits. See if you can make all the different molecules in this posts.