Humans vs Narwhals

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SWBAT compare nutritional requirements of omnivores such as humans with that of carnivores such as big cats and narwhals.

Big Idea

Who's the REAL meat eater here? Let's do some math and find out!


7 minutes

Note to the Teacher:

In this lesson students will be comparing the quantity of protein consumed by different animals.

The lesson is designed at two levels.

Level 1: Students compare the amount of meat eaten by different animals and write and solve simple word problems.

Level 2:  In order  to make the comparisons more meaningful, students (with support) calculate the amount of protein consumed by different animals in proportion to their overall size


Ask students to make an estimate about how many kilograms of meat the average person consumes in a year.  They may also estimate in pounds, as this is still the more familiar unit of measure.  I then have several students share with the class and I have the other students respond because this is a supported structure in which to have them practice MP3: Construct viable arguments and critique the reasoning of others.  I teach this lesson in the 4th quarter so while they are still developing an understanding of weights and measures, they do have an idea about how to make a reasonable versus a preposterous guess.

A typical hamburger is approximately 1/4 of a pound.  A reasonable guess would be anywhere from 10 pounds (equivalent of 40 hamburgers in a year, with NO other meat) to hundreds.  A thousand or a million is, of course, unreasonable.  

As we talk through their guesses, I help students multiply their guess for a day times the approximate number of days in a year (350).  

I would remind them that kilograms are more than pounds, very approximately double, so whatever they put down for their guess in kilograms, the amount in pounds should be larger!  A good benchmark for pounds/kilograms is an "average" adult who might weigh 150 lbs or 68 kilograms.

Guided Activity

45 minutes

This is how I teach this lesson:

"There will be several steps to find the average amount of meat eaten by a narwhal per day.  All of the math is based on rough estimates

The first question we need to answer is, what number should we use?  25?  50?  Think…  (A child will suggest that the number in the middle, or an average, should be chosen.  If this is not suggested by a student, ask questions that lead them to that realization). 

Go to step one on your Humans vs Narwhals - part 1 study guide.  Finding the midpoint between two numbers is the same as finding the average of the two numbers.  So, an alternative strategy here would be to add 25 + 50 and divide by 2.  Either way, you obtain an answer of 37.5, which can be rounded up to 38 lbs of food per day for a typical narwhal.

Since the narwhal doesn't eat this amount every day, because it does most of its hunting and feeding during 9 months of the year, we have an extra step that I'll take you through. We will need to multiply the 38 lbs x the days in 9 months, then divide that by the approximate number of days in a year to get the daily average.  An average looks at the whole year, and the narwhal doesn't eat much during the summer, so we have to bring that information into the equation. 

Under step two a write the following equation:  (I've provided kg and lb so you have a choice)

pounds   38 x (9 x 30) = n     That will be the total amount the narwhal eats in a year in lbs. 

kilograms  17 x (9 x 30) = n  That will be the total amount the narwhal eats in a year in kg.

Help the students solve for that.  Some of my students can decompose and solve it but it is okay to have them calculate the 9 x 30 and then use a calculator for:

38 (pounds ) x 270 days = 10,260 lbs. or 17 (kilograms) x 270 days = 4,590 kg

Now I want you to think of what equation we could solve to find the number of kilograms of meat eaten per day by a narwhal.  If you have an idea, write the equation on the line under step two b.  Don't worry about making a mistake.  I just want you to think about this.  There is an extra line where we will write the final equation together.  (Hint, if needed, you will be  using division).  

Total weight of meat eaten in a year divided by 365 = amount eaten in a day!

4590 kg divided by 365 = 12.5 kg/ day  (approx 28 lbs or 112 child sized hamburgers)

Now, what we need to keep in mind as we look at these numbers is that a narwhal is much bigger than a human.  It most certainly eats more meat than we do, but does it eat more in relation to its size?

To figure this out, we will go through step 3.  We will take the weight of the average narwhal, 1200 kg/ 2646 lbs. and figure out how much meat it eats for each 100 lbs. on this body.  This is not third grade math, so don’t worry about it if you don’t understand it yet.  We just need to be able to compare the amount the narwhal eats to the amount a typical person eats.  Our typical person is 150 lbs. to keep everything in metric from here on, and to give us an easy number to work with, we'll say our human is 100 kg.  That's a bit heavier than average but nothing out of the ordinary.  A lot of the people you see walking around, especially tall people, are about 220 lbs.   

So, for step 3, first we will take the narwhal's weight and find out what divisor we need to use to end up with a quotient of 100.  (This is all in metric since that's the standard). Write this on your paper:  

1200 kg divided by ? = 100 kg.


Yes, 12.  1200 kg divided by 12 = 100 kg.  

Now, since we divided the weight of the narwhal by 12 to get our 100 kg that is our equivalent of our human contestant, we'll divide the amount of meat they eat in a day by 12 also.  Otherwise the comparison would be out of balance.

So, write this on your paper:  12.5 divided by 12 = ?  We know what 12 divided by 1 is. What do you think this will be?  Think...

We can go ahead and write 1 kg of food for 100 kg of narwhal.  (Actually 1.04 - close enough)!  

There you go!  We've solved our first problem!  A narwhal consumes about 1 kg (2.2 lbs) of food for 100 kg of weight.  That would be like a tall man eating about 8 small hamburgers, and nothing else, all day.  (The idea I'm hoping to lead them to is that even though some of these animals consume an enormous quantity of meat, per their body size it's actually less than what we eat). 

Note to teacher:  Here are a few Polar Bear Notes  to help you work through the second example."

Here is an additional page with two more examples that can be worked through with the class. The value in doing all of this together is that when they are give the numbers to complete the calculation on their own, they will have an about where the numbers originated.  It's important that they don't just compare the quantity of meat eaten per day because without knowing the size of the animal that data is distorted and misleading.  Humans vs Narwhals Part 2.

Wrap up

5 minutes

This was a very complex task and it is okay if students did not fully understand all the steps.  They should be able to explain something they understood.

Write the amount of meat consumed by each of the example animals, narwhal, polar bear, mountain lion, and black bear up on the board.  Ask them to make an observation about how much meat the omnivore (black bear) compared to the other 3 animals which are carnivores.  Have them write their idea on the back of their study guide.

Then have students compare how much the average American eats (from the lesson More Meat!) with how much the carnivores eat and how much the omnivore eats.  Remind students that our bodies are designed to be omnivorous.