## Wednesday, June 30, 2010

### I've Got Gas

I was filling up the car the other day and when resetting the odometer, accidentally switched my instrument cluster display to metric. At that point, I noticed I was about to hit 80,000 km and my average consumption was 4.1 liters per 100 km.

This is the way that countries using metric measure display fuel consumption. Rather than showing how far per unit of fuel (gallon), they show how much fuel for a given distance (100 km).

Here is a picture of the instrument cluster just before I went over 80,000 km. Notice I am going 119 km/hr, not miles per hour!

Here is the same picture, just after it changed. Notice the number to the left of 080000 is 4.1. This is the average fuel consumed for the lifetime of the car.

Let's calculate how much fuel I have used in the lifetime of this car. Just for background information, we have had the car since February of 2006, so it's four years and four months old.

Q1. How much fuel has been consumed over the 80,000 kilometers traveled?

A1. 80,000 ÷ 100 (100 km is the unit of measure) = 800 and 800 x 4.1 = 3280 liters of fuel

Q2. At an average price of \$3.00 per gallon, how much have I paid for that fuel?

A2. First we have to calculate how many gallons are in 3280 liters. Yesterday we learned that 3.8 liters equals one gallon, or 231 cubic inches. So,

3280 ÷ 3.8 = 863 gallons x \$3.00 = \$2589.50 or roughly \$2600.

Q3. Now for a more American expression of fuel economy, what is my average miles per gallon?

A3. Let's take the easiest way to solve this problem. Press the English/Metric button on the instrument cluster. The average is 57.1 miles per gallon.

This seems like extremely high fuel economy. It is. The only way you get this kind of fuel economy is with a very small, light, aerodynamic vehicle.

## Tuesday, June 29, 2010

### Larger Doses of Heavy Metal

Continuing from yesterday, today we are weighing a copper nugget. I forgot to tell you yesterday that I bought this huge hunk of so-called COPPER on eBay, from a guy in Arizona.

Here it is next to a prefab fireplace log, to show you its size.

Really, I did. That's before my wife closed my eBay account ...  :-(

The seller delivered it to my front porch, for free, in case you were wondering what the shipping cost! That was before HIS wife closed HIS eBay account ...

We put on gloves for safety, slid the scale underneath, and learned the nugget weighs 151.5 lbs, including 2 small wood planks put there to keep it from ruining our scale. Together the wood weighed 0.5 lbs, so the nugget itself is roughly 151 lbs.

Now how can we tell if it is copper? We can take its volume, multiply the volume by the relative density of COPPER (8.9) and compare the result with the weight from the scale. If this is GOLD (density 19.3) painted to imitate copper, it will weigh more. If it's STEEL (density 7.7) painted to imitate copper, it will weigh less.

OK, how do we find the volume? We can put the nugget into a tub of water, fill up the tub, and measure how much water is in the tub. Then we take the nugget out and fill the tub up the rest of the way. The extra water will give us the volume of the nugget.

One small problem. We can't lift the nugget more than an inch or two off the ground, and we don't have a hoist or handles. But we found a trash container it would fit into (mostly) so we slid the nugget into the trash can.

We turned it up on end and filled the container with water. The container held 8.25 gallons when filled to the brim. But there is a little bit of the nugget sticking up from the top - a prism shape that's a triangle 7 x 4 x 6 by 5 inches long. (Here comes some math...)

We calculated the volume of this piece (4 x 6 x 5 ÷ 2 = 60 cubic inches) and compared that volume to the number of cubic inches in a gallon. A gallon is 231 cubic inches. So we have about a quarter gallon of copper sticking up in the air. If it was below the water line, we would have needed only 8 gallons to fill the trash container. (Did you follow that reasoning?)

We had to dump out the water (since we couldn't lift out the copper). What a mess. But it's only water.

How do we know how much water fits in the trash container? My wife refills it while I start on the math. She says the container holds 10 gallons. So 10 gallons of water - 8 gallons of water = 2 gallons of copper. We had two gallons of copper in the trash container (adjusting for the part sticking up).

How can we confirm that this is correct?

First we do an estimate. The weight of two gallons of water is (8.35 x 2 = 16.70 lbs or roughly 17 lbs). We know the density of copper is 8.9 times that of water. Therefore 8.9 x 16.7 = 149 lbs.

Eureka, we've found COPPER! Gold would weigh 300 lbs and steel would weigh 129 lbs.

Now let's do it the hard way to confirm our answer. Yesterday we learned copper weighs 8.9 grams per cubic centimeter. A minute ago we learned a gallon is 231 cubic inches, or 3.8 liters.

(The older automotive types in the crowd will know
that's also the displacement of the Buick V6 Turbo engine,
later known as the 3.8L engine. See the photo below.)

3.8 liters is 3800 cubic centimeters, because a liter is 1000 cubic centimeters.

And 3800 x 8.9 grams = 33820 grams (the weight of our nugget) ÷ 454 (grams in a pound) = 74.5 lbs. What?! That's wrong. It's way way off! What happened?

Yes. The answer is off, because we had TWO GALLONS of copper, not one!

That's 149 lbs. We got it right.

Isn't this math stuff fun?

(well Doc, I was lifting this huge copper thing when I felt a twinge ...)

## Monday, June 28, 2010

### Large Doses of Heavy Metal

Sorry. I don't mean music. I mean REAL HEAVY METAL.

My wife and I saw that a gigantic gold coin sold this past week for \$4,000,000. Queen Elizabeth II is on the face side of the coin, which was minted by a Canadian Mint a few years ago, in a limited issue of 5 specimens. Each weighs 100 kg.

This put me in a research mood, and I discovered some facts about the largest gold nugget ever found. It was discovered in Australia 140 years ago. It weighed 2520 troy ounces, but some of that was dross (non-gold stuff). The net gold in that nugget was 2284 troy ounces.

Here's a chance to employ our Excel Math.

Let's start with a conversion. There are 32 troy ounces in a kilogram.

Q1. Is the coin heavier or the nugget heavier?

A1. The coin is 100 kg. There are 32 troy ounces in a kilogram, so 3200 troy ounces = 100 kg. The nugget was only 2284 ounces of gold, or 71 kg of gold. The coin is heavier.

Here's a sketch of the nugget. It was more than 18 inches across according to this scale. And here's an early photo of the nugget, with some of the happy guys who found it.

Why am I doing this post on giant gold nuggets? Why not? Who doesn't like the thought of finding something fabulously valuable? My wife's great grandfather was a gold and silver mining engineer who worked for years in Mexico. There are plenty of nuggets floating around in her family. You can read his book if you like this sort of thing.

I have a copper nugget. Or maybe it's just copper slag (surplus) from a copper mine in Arizona. I'm not sure. But I can tell you it's heavy. We keep it on the front porch, and one night some kids tried to steal it. They got only about 3 feet before dropping it on the driveway, leaving some skin behind!

The tiles are a foot square, so I estimate this nugget is as wide as that largest gold nugget. I think it weighs about 150 lbs. Shall I try to weigh it?

Q2. Which is heavier for the same volume? Gold or copper?

A2. Gold is 19.3 grams per cubic centimeter, copper is 8.9 grams per cubic centimeter. Gold is slightly more than TWICE AS HEAVY as copper. And copper is heavy!

Q3. How much heavier than water is copper?

A3. Water weighs 1 gram per cubic centimeter, so copper is 8.9 times as heavy as water.

## Friday, June 25, 2010

### Quasi-Mathematics

Today I'm going to cover a few things that are part of my daily routine of publishing math curriculum.

=======================

RELATED SUBJECTS
Certain subjects that aren't strictly math have been added to the math curriculum in American schools. We teach those things because they are related to basic math. Here are a few:

MONEY
TIME
MEASURING
SORTING
GRAPHING
REASONING
POSITION
DIRECTIONS

Why are these things part of the math curriculum? Numbers are involved. Mathematical calculations occur. Conversions are essential. Comparing happens. Explanations are needed. Even if it's not strictly "math."

=======================

SOCIAL CONTENT
We also have other concerns in our math curriculum that are of a completely different nature. In California we call this "Social Content." In our curriculum we:
• Avoid mention of any anti-social activity (littering, truancy, crime)
• Show ethnic, racial and gender diversity in choice of names and events
• We demonstrate respect for the elderly and infirm
• We try to show kids the benefits of productivity, hard work, thrift, careful shopping, etc.
• Problems should involve healthy choices in diet (no more jelly beans, M&Ms, cigarettes)
Sometimes you might find the curriculum changes slightly in ways that doesn't affect the math calculation. A name is changed, or subject matter of a problem changes, or a picture is different. When this happens, it's often due to a social concern.

=======================

TIMELY & RELEVANT
Excel Math products are used in all states and many educational environments -- public schools, private schools, homeschooling, military and overseas schools, etc. As a result, you might see things that aren't familiar to your kids.

We are based in Southern California so our examples often include the beach, the mountains and the desert. We don't talk much about snow (many local kids have never seen it).

We try to be culturally-up-to-date, so sometimes we rewrite the curriculum to take out skates and put in scooters or skateboards. We struggle to know what kids will buy with their limited funds - taking surveys of parents and kids. We need this so our money problems can be relevant. We change images because mobile phones are no longer the size of a brick.

We also want the books to be imaginative. I must admit that I like the occasional sci-fi problem, such as Dimension Woman and Dimension Man stepping in from an alternative universe to sort out the measurement wrongs in our world!  We tend not to have imaginary scenarios like talking animals "Mr Red Squirrel stored 32 nuts in the tree warehouse.

## Thursday, June 24, 2010

### 60 years, 720 months, 3120 weeks, 21,915 days

That's a long time. It's how long my mother-in-law and father-in-law have been married, as of today. It's their anniversary. Here's a picture of them about 40 years ago.

Anniversaries are fun times to remember "the old days"which for some of us were a long time ago. And they are an occasion to use our elementary school math. Here's a recent picture of Phil and Joan.

If you can imagine it, the oldest persons alive have lived nearly twice as long as my in-laws have been married! This is Eugenie Blanchard, who has been alive for 114 years, 128 days!

Let's try some math questions:

Q1. How many days has Eugenie lived?

A1. days per year (114 x 365) + leap days (114/4) + 128 days =  41,610 + 28 + 128 = 41,766

Q2. What is the percentage of days that Eugenie has lived that Phil and Joan have been married?

A2. 21915 ÷ 41,766 or simplified, they have been married for 52% of her life.

Q3. My wife and I have been married for 12,710 days. How many years had Phil and Joan been married when we got married?

A3. You can do the math yourself. The answer is 25.17 years!

## Wednesday, June 23, 2010

### How do WE use math?

School is out for the summer, and we are thinking about vacations, going to the beach, doing home improvement jobs, etc. So let's forget about exotic problems and complex calculations.

I thought I would do a little survey, and list some of the ways some of us use math around Excel Math. Here we go:

JIM
1. My job is math. I count the money. (Jim's our accountant)
2. When I go to the store and shop I need to compare prices
3. When I watch TV I have to know which buttons and channels to select on which remote
4. When I make a phone call I have to know the numbers and press them in the right order
5. When I cook I need to measure the ingredients and set the temperature on the stove

ARIEL
1. When budgeting how I can spend my paycheck
2. In my college classes
3. Shoe shopping!
4. Planning how much time I have in my daily schedule
5. Ordering food for lunch

DAVE
1. To figure out my gas mileage
2. On my five-mile run, to look at my 1-mile split times and figure out my pace
3. To determine the pallets weights for shipping products to customers
4. Comparing prices of different shipping companies
5. Determine how many hours people need to work to ship out the orders

1. To calculate travel times (distance, speed, etc) so I can arrive on time for appointments
2. To determine if there will be enough money in all the right accounts on the right days to pay the bills
3. When drumming I have to count enough beats per measure to make good music
4. Measuring wood when making things so the pieces all fit together
5. Using the weather forecast to adjust windows, doors, fans and heaters so the office is comfortable

BOB
1. Checking that customer credit card charges are valid or fraudulent
2. Deciding how many steaks I need to buy to feed my family and friends tonight
3. Keeping track of all the songs that our band has played in the past 12 years
4. Managing the calendar for all employee holidays, sick days, vacations and family leaves
5. Counting all my musical instruments

BECKY
2. Figuring change at the store
3. Telling how much time it takes to get somewhere
4. Measuring boards to make the back deck on the house
5. Counting sit-ups and push-ups when doing exercises

MIKE
1. Doing this math blog every day
2. Trying to determine the cost of something I am buying from Europe in euros
3. Auditing my mother's prescription bills from the pharmacy
4. Trying to figure out how they put 1500 new features into my iPhone with the latest software
5. Deciding what to do with the 404 messages in my email in-box

CHRIS
1. Determine how much to cut down those cabinets from IKEA to EXACTLY fit my room!
2. Whether it's cheaper to buy pre-wrapped packages of tomatoes or buy them loose by the pound.
3. To figure out if bulk food is cheaper per item than smaller packages (they rarely are!)
4. To swap between metric and imperial measurement in a country where both are used
5. To figure out which gear ratios I need on my multi-speed bicycles

## Tuesday, June 22, 2010

### Do the numbers lie, or just fib?

I have written and posted 222 blogs on math (before this one), since August 7th of 2009  last year.

In that time we have had lots of different folks visiting here. How many? Well, it's difficult to say at this time. Let's say about 6700 or so.

I can hear some of you saying "Hmm. 6700 or so? Don't you know precisely?"

No we don't. Even though I did lots of research on monitoring software and set up 3 different counting systems, the numbers continue to vary. Here's what we can measure:

FLAG Counter says 5,666 unique visitors from 124 different countries. About 58% are from the USA and 8.9% from the UK. On average 25 new people a day look at this site, while there are 41 page views.

SITE Meter says 6,634 unique visitors. About 55% are from the USA and 5% from the UK. On average 25 new people visit per day.

STAT Counter says 7,828 unique visitors. About 58% are from the USA, and 9% from the UK. On average 24 new people a day look at the site.

The highest day ever was April 28th, when I deliberately tried to get more visitors. I used popular search terms, put up pictures of flashy cars and attractive men and women, and made some promises I had no intention of keeping. And I embedded a video.

Here's the link if you care to see it.

The effort worked, because the number of visitors increased four-fold.

We don't sell advertising on this site but we do hope you will go look at the Excel Math website and buy some math curriculum for your school or for home-schooling your kids.

If not, we hope the blog will help you think about math, and why you need to know some math, and how you can use math. It certainly has made me think very deeply on the subject, at least 222 times.

Here are some reasons we are not more precise;
1. some people use more than one computer to come to our site, or more than one browser
2. counters use "cookies" saved by the browser to see if you've been here before. Some people block them
3. some users are behind "screens" the block the counters, etc. etc.

Maybe it's time to "wind the clock back" and start counting from zero again? Or not?

## Monday, June 21, 2010

I think everyone likes gold. Here are the people who like it the most, based on the amount they have stashed away. The numbers come from the World Gold Council:

Tonnes   Holder
8134       US Government
3407       Germany
2967       International Monetary Fund
2452       Italy
2435       France
1054       China
1040       Switzerland
765         Japan
669         Russia
613        Netherlands

The amount of gold here is worth a lot of money! Each metric tonne of gold represents 32,151 troy ounces. The price of gold today is \$1241 or €1007 or £840 per troy ounce.

Here's where we can use our elementary math skills, while dreaming of the value of this gold!

Q1. How much is one metric tonne of gold worth today, in US dollars?

A1. 32151 x 1241 = \$39,899,391 or rounded slightly to \$40 million bucks!

Q2. Using the euro as currency, how much more gold value does Italy hold than France?
Round your answer to a reasonable number of digits and do the work without a calculator.

A2.  We could calculate this way (32151 x 1007 x 2452) - (32151 x 1007 x 2435) = answer
But it's easier to take Italy's holdings 2452 minus France's holdings 2435 = 17.
Then we simply multiply 17 x 1007 x 32151 to get the answer.
Rounding to make it simpler in our heads means
17000 x 32000 = (17 x 32) + 000,000 or
(10 x 32) + (7 x 32) = 320 + 224 + 000,000 = roughly 550 million Euro.

Gold on pallets!

Q3. A gold bar is most often 400 ounces. How much is one gold bar worth in UK pounds?
No calculator please! Round to make it easier.

A3. 400 x \$1241 or 4 x 125 + ,000 = \$500,000 x .67 exchange rate = £335,000
or 400 x £840 per ounce = 4 x 84 + ,000 =  £336,000

PS - the price of gold has dropped to 1238.47 since I started this post! The USA holdings have dropped by \$660 million in an hour. Ouch!

## Friday, June 18, 2010

### Printer's Pallets and Profits

This week's posts on pallets forced me to learn a lot more about pallets than I had originally expected.

Here's a company whose Viking 505 machine constructs custom pallets automatically.

It turns out that most of the pallets we get from our printer are called skids. These have thicker supporting beams but no cross pieces underneath. Check the photo below. Pallets on the left with cross pieces, skids on the right without the cross pieces.

Printers use skids because they are easier to move around with a forklift. Printers' loads don't need so much lateral strength (from the cross pieces) as other loads do but they are very heavy so they need lots of vertical stability.

Here's another picture - pallet on the left, skid on the right. Notice the heavier wood blocks at the edge of the skid.

We return the skids to our printer. We buy pallets to send to our customers. We never get them back. Many companies do the same, while others keep control of their pallets. Here's the math:

A company called CHEP rents pallets and skids to people who move lots of goods. CHEP has 90% of the market for rental pallets, and owns an estimated 80 million pallets in the USA and 300 million worldwide! It's an interesting business.

• The lifespan of a pallet is 13.3 years.
• New pallet cost is \$20.
•  It costs \$5 to rent a pallet.
• Pallets rent 3.5 times a year.
This looks like a formula for getting rich!

3.5 x \$5 = \$17.5 revenue in one year for an item that cost you \$20.

The one big hitch is that CHEP has to have a sales department, provide the pallet to the user, find out where it went at the delivery end, get the pallet back, and take it to another user. There are lots of IT, inventory, transportation, repairs and other costs. They estimate payback on a pallet after 4.2 years - meaning for the next 9.1 years the pallet is profitable.

## Thursday, June 17, 2010

### Plastic, Plywood, Pine and Paper Pallets

Continuing this week's pallet theme, I took another stroll in the warehouse. Because we ship books, we must have strong and heavy pallets to carry those loads. All our pallets are made in the USA to GMA standard sizes.

One of our warehouse tenants deals with much lighter products than we do. Theirs are imported from Asia in international packaging. Their wild assortment of pallets include examples made of plastic, plywood, pine and paper.

Here is a plywood pallet. Unlike the solid beams of wood used in our pallets, this uses squares of plywood, stacked in 9 places, with strips of plywood connecting them.

There are some advantages to plastic pallets. They don't soak up water, nails don't fall out, and they use recycled material. But they can cost 5-10 times as much as wood. If they get damaged, they can't be easily repaired. Here's a pallet showing an injury where the forklift missed the slot - one more hit and the pallet corner might collapse.

There's another sort of wood pallet on their side of the warehouse. It's a much lighter construction than we buy. Notice how thin the boards are? These are soft woods, like pine, instead of the hard woods used in heavier pallets.

Pallets can always be built lighter and cheaper - for example, this paper (cardboard) one!

Both weight and price are important, especially weight. It's true that a pallet spends much of its time sitting still, but the very reason for a pallet's existence is to make movement easier. You could think of it as "an envelope" for large goods. A lighter load will be less expensive to ship.

Q1. A plastic pallet weighs 16 lbs. Our wood pallets weigh 36 lbs. What would be the difference in total weight if we ship 1200 pallet loads a year?

A1. 36 - 16 = 20 x 1200 = 24,000 lbs difference in total weight.

Q2. We calculated that we spend about \$.20 per pound to ship pallets (and books) around the West Coast. How much could we save in a year if we changed to plastic pallets?

A2. 1200 x 20 = 24,000 lbs x .20 = \$800

Q3. How much would 1200 used plastic pallets cost?

A3. 1200 x \$20 approx = \$24,000

Q4. Since we only use a pallet once (they don't come back), we would pay \$20 instead of \$3.25 for a pallet, while saving \$4 in shipping cost. Would this be a good management decision?

A4. NO!

## Wednesday, June 16, 2010

### Pallet Pieces & Pirouette

We have a third blog today on wooden pallets. Don't worry, eventually I will run out of math questions about pallets. But not yet. Today we'll investigate the standard Grocery Manufacturer's Association wood pallet we use here at Excel Math.

Here's a new pallet.  Its top side is facing us. You can see it is rectangular (48 inches x 40 inches). It consists of an array of deck boards and stringers.

Notice in the photo below that the stringers (middle pieces) have notches in them. This means you can approach and lift the pallets from all 4 directions.

Manuel brings us used pallets similar to this one. He often has to repair them, because pieces of wood get broken, nails come out, etc. This situation causes me to ask a few questions that we can easily answer with a bit of elementary Excel Math.

Q1. How many pieces of wood are there in a pallet?
A1. 7 deck boards on top, 3 stringers in the middle, and 3 deck boards on the bottom.

Q2. How many different kinds of pieces does Manuel need to have to repair our pallets?
A2. It looks like the top 7 deck boards and one bottom deck board are the same. That's one piece. The three stringers are the same. That's a second piece. The outer two bottom deck boards are the same. That's a third piece.  With 3 different pieces of wood Manuel could repair any of our standard pallets.

Here's a bonus for you - the Excel Math Pallet Pirouette!

## Tuesday, June 15, 2010

### Putting pounds on pallets

This blog is about using elementary math to solve everyday problems. This week I'm fascinated with pallets in our warehouse. Today we look at weight issues, because books are HEAVY!

There are specs for wood pallets. Have a look at Pallet Central if you are intrigued.

Now here's a bit of math:
• A single wood pallet can hold about 5000 lbs. if set by itself on a concrete floor.
• If wood pallets are stacked 2 to 4 pallets high, the limit is 1938 lbs per pallet.
• When loaded length-wise onto a pallet rack (big shelf) the limit is 2085 lbs
• When loaded width-wise on a pallet rack, the limit is 1728 lbs.
Q1. Assume we have pallets that weigh 50 lbs. We will stack them 3 high. We will load them to the nearest 100 lbs below the rated limit. What will be the ratio of load to pallet?

A1. Maximum load for stacked pallets is 1938 lbs, so if we load to the nearest 100 that's 1900 lbs.
Let's include the weight of the pallet in that overall total, so the pallet is 50 lbs and load 1850 lbs.
Fifty pounds goes into eighteen hundred fifty pounds exactly thirty-seven times.
The load to pallet ratio is 37:1

I assumed the springs on a truck were the limiting factor how much weight it can carry. Mike, our truck driver, tells me it's also critical to check the rating for the floor of the truck box or trailer. His truck has a reinforced floor so he can drive the forklift in there. A typical trailer can handle the weight of the load and a pallet jack, but NOT a forklift. The heavy forklift can crash through the floor!

I checked two of our forklifts. Each weighs 6180 lbs and has a lifting capacity of about 3000 lbs. That's not counting the propane fuel tank (70 lbs), the driver (200 lbs) and optional equipment.

Q2. What is the total weight on the truck when Mike loading 2500 lbs of books with the forklift?

A2. 6180 lbs (forklift) + 50 (pallet) + 2500 (books) + 70 (fuel) + 200 (Mike) = 9000 lbs!

## Monday, June 14, 2010

### Piles of Pallets

Pallets are the unseen workers in our modern economy. They are everywhere, like tiny shipping containers! Take a look in our warehouse and tell me how many you see:

We are a net exporter of pallets. We get loads of our math material on pallets, stacked high and wrapped in plastic. Then we break those down into smaller orders for schools. Because the orders contain a number of different size boxes, and because they have to be delivered into a school environment, we can't stack things as high and they can't be as heavy. So a few high-stacked pallets come in and lots of low-stacked pallets go out. Eventually we run out.

Manuel comes to our aid. He brings us more pallets. Here's a corner of our reserve pallet inventory. We keep them piled high near the loading dock. The machine in the front is called a pallet jack. It has batteries and electric motors, allowing one person to lift and move pallets around the warehouse and onto a truck. We have some big forklifts too.

I'm writing about pallets today because of an incident while driving my old truck to work. It's about 50 years old, and slow. But even slower was an elderly Datsun pickup with a modified flat-bed load area, piled high with pallets and sagging a bit in the rear. He only caught up and passed me when I turned off for our office, but I was able to scan his load in my rear-view mirror.

He had a lot of pallets! (Here comes the math).

Q. How many pallets did the Datsun truck carry?

A. I saw 3 rows across, 3 rows front-to-back, each stacked 10 high. 3 x 3 x 10 = 90 pallets

Q. How much did all the pallets on the Datsun truck weigh?

A. The pallets on the Datsun truck were smaller than the ones we use. The truck's 3 rows x 3 rows pile was square. Knowing the average width of a vehicle is around 6 feet I estimate the size of his pallets at 2 feet x 2 feet, or 4 sq ft each.

They were made of wood - the same kind of construction as the pallets we use for Excel Math.

Our pallets are 3 feet x 4 feet, or 12 sq ft each. I put one on our scale and learned it weighs 36 lbs.
I divide to find the weight per square foot:  36 lbs  ÷ 12 sq ft = 3 lbs/ sq ft.

With this fact I can estimate the weight of the stacks on the truck.

2 ft x 2 ft = 4 sq ft x 3 lbs/sq ft = 12 lbs per pallet.  12 lbs x 90 pallets = 1080 lbs on the truck.

## Friday, June 11, 2010

### Bee Gone

This will be my last post on bees this week. The subject is Swarming - when bees decide to fly away.

Perhaps half or more of the bees leave their hive, led by a new queen. They look for a good location in a new neighborhood. In preparation, they fill their stomachs with honey til they can barely fly. In fact they are so full they can't bend over and sting anything. That's what the books say, anyway.

Back when I was a hobbyist beekeeper, the company I worked for was "visited" by a swarm of bees. In fact, they calmly took up residence in a tree and were resting there in a clump the size of a basketball. Our problem was that the tree was between our office's back door and the front door of the lunch room.

The office manager knew I sold honey, so he assumed I kept bees. He asked me to resolve the problem. Although I knew the theory of handling swarms, that's not the same as the practice! With no time to drive home for my bee suit, I just walked out there calmly (sweating) with an empty cardboard box. I placed it under the bunch of bees, shook the tree branch, and they fell into the box.

The remaining bees buzzed around for awhile and within 10 minutes 95% of them had gone into in the box through a tiny door I had cut in one side. I put on the lid, taped over the door and took them to my car. I was given the rest of the day off to "Get those bees outta here!"

I think bees should always be saved if possible, but most bee removals end with the death of the hive. Killing the hive is less trouble for exterminators. If they are deep in the walls of your house there's really no way to get them out. If they are on a porch or in the eves - then you have a chance!

Now we will get right to a couple examples of how the math you learned in school can be helpful:

1. The fire department in Redondo Beach, California reports that they received and responded to an average of 18 bee calls per month last year. (Why did so many people call the firemen?)

Q. How many bee swarm calls did the fire department respond to in a whole year?

A. 12 x 18 = 216

2. A blogger shared his experience with a bee swarm. He wanted to catch the bees in a box but his swarm was 30 feet up in a huge tree. It was a fiasco but he persevered and got the bees. He said the swarm contained about 10,000 bees, and he was happy that he only got stung 3 times.

Q. What percentage of the bees stung this beekeeper?

One percent means one sting per hundred bees. How many stings per hundred? (Answer = None).
One tenth of a percent means one per thousand.  How many stings per thousand? (None).
One hundredth of one percent means one sting per ten thousand. How many per ten thousand? (Three).
The answer is 3 hundredths of one percent, or .03% of the bees stung this poor beekeeper.

Go here if you would like to see an illustrated version of a bees-in-the-box procedure!

## Thursday, June 10, 2010

### Bee Pollen

This week we have looked at Bee Stings, Bee Honey, and Bee Wax. Today we'll have another math session intersect with bees, as we investigate Bee Pollen. Here's one of our Excel Math bees, up to her neck in pollen.
[You can click the photos for a larger view]

And another look.

Pollination happens by chance as the bees are really looking for nectar. Pollination is their main "job" nowadays, as beekeepers can earn more by renting their hives to farmers (moving from field to field) than they can from the honey that bees produce.

About half of the total income earned by beekeepers in the USA comes from hives rented for about one month in the spring, to pollinate the almond crops in California!

But another useful product comes from this pollen. Not only do the bees eat pollen, but clever traps scrape the little balls of pollen off their legs, so it can be collected and sold to health-conscious humans.

The pollen trap device forces the bees to squeeze through small holes or a wire screen, which causes the pollen to drop off into a tray. The tighter the holes, the more efficient the trap, but it also slows down the bees and they may suffer from losing the pollen. More production is not better in this case.

People that collect pollen with traps do so for only limited periods of time and then give the bees some time without the pollen trap. This trapping business is only useful when pollen-laden flowers are present.

My stepfather used to eat bee pollen regularly, and was convinced of its healthfulness. The FDA allows it to be sold as food, but cautions that outrageous claims must not be made regarding any contributions to health. Bee pollen is not medicine.

Where's the Excel Math?, you say? Here it is. I want to know the price of pollen. The price in raw form, with no capsules, no tablets, no processing or supplements. So I scanned some websites ...

Source 1: 8 ounces \$12.50
Source 2: 10 pounds \$69.00
Source 3: 1 pound  \$17.00
Source 4: 20 ounces \$39.95
Source 5: 454 grams \$13.20
Source 6: 21 ounces \$18.95
Source 7: 7.5 ounces \$12.00
Source 8: 5 pounds \$49.50

Q. Graph these prices to show the range of the prices (per ounce) of bee pollen.

A. The bee pollen price ranges from \$.43 per ounce to \$2.00 per ounce.